PhysicsPhysics QuestionsElectrostatic Potential And Capacitance Questions for CBSE Class 12th

Electrostatic Potential And Capacitance Questions for CBSE Class 12th

Two identical thin rings each of radius R are placed co-axially at a distance R apart. If Q 1 and Q 2 are respectively the charges uniformly spread on the two rings, the work done in moving a charge q from the centre of one ring to that of the other is :

A fixed uniformly charged ring of radius 3 m has a positive linear charge density -50 μC/m. A point charge 5 μC is moving towards the ring along its axis such that its kinetic energy at A is 5 J. Its kinetic energy at the centre of ring will be nearly :

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    A charge q is placed in an uniform electric field E. If it is released from rest, then kinetic energy of the charge after travelling a distance y will be :

    A charge of 5 C experiences a force of 5000 N, when it is moved in a uniform electric field. The potential difference between two points separated by a distance of 1 cm is

    A charged particle of mass 4 gm and having a charge +1 μ C is fired from a point with speed 10 m/s where electric potential is 4×10 5 V in the direction where electric potential is decreasing, find the potential at a point (in x 10 5 volts) where its speed becomes 10 2 m / s m/s. Express your answer in multiple of 10 5 .

    The variation of electrostatic potential with radial distance r from the centre of a positively charged metallic thin shell of radius R is given by the graph

    1728 drops of mercury of equal radii possessing equal charges combine to from a big drop. Then the capacitance of bigger drop compared to each individual small drop is times.

    From the supply of identical capacitors rated 8 mF, 250volt, The minimum number of capacitors required to form a composite 16 mF, 1000 v capacitor is

    Two identical rings P and Q of radius 0.1 m are mounted coaxially at a distance 0.5 m apart. The charges on the two rings are 2 μ C and 4 μ C, respectively. The work done in transferring a charge of 5 μ C from the center of P to that of Q is

    A and B are two points at a separation of 50 cm in a uniform electric field of 24 V/m. If V A and V B are potentials at A and B respectively, the select the wrong option.

    A capacitor is made of two square plates each of side ‘a’ making a very small angle α between them, as shown in figure. The capacitance will be close to :

    In the circuit shown in the figure, terminal B is grounded and potential of terminal A is 10 volt. Then charge stored in 3 μ F Capacitor is

    Two charges q 1 and q 2 are placed 30 cm apart, as shown in Fig. 2.135. A third charge q 3 is moved along the arc of a circle of radius 40 cm from C to D. The change in the potential energy I of the system is q 3 4 πε 0 k , where k is :

    As per this diagram a point charge y + q is placed at the origin O. Work A done in taking another point charge – Q from the point A (0, a) to another point B (a, 0) along the straight path AB is :

    There are 27 drops of a conducting fluid. Each has a radius r and they are charged to a potential V 0 . These are combined to form a bigger drop. Its potential will be :

    Consider a dipole with dipole moment 4.8 x 10 -30 cm. Let a point P lies 4.1 x 10 -9 m away from centre of dipole. Match the values of potentials given in column-II with column-I and mark the correct choice from the given codes. Column-I Column-II i. Point is along axis of dipole nearer to positive-charge: p. -1.8 X 10 -3 V ii. Point is 45° above the axis but nearer to positive charge. q. 1.8 X 10 -3 V iii. Point is 45° above the axis but nearer to negative charge. r. 2.6x 10 -3 V Codes:

    A charge of 10 e.s.u. is placed at a distance of 2 cm from a charge of 40 e.s.u. and 4 cm from another charge of 20 e.s.u. The potential energy of the charge 10 e.s.u. is (in ergs)

    A charge of 5 C experiences a force of 5000 N when it is kept in a uniform electric field. What is the potential difference between two points separated by a distance of 1 cm?

    Charges 5 μ C, –2 μ C, 3 μ C and –9 μ C are placed at the corners A, B, C and D of a square ABCD of side 1 m. The net electric potential at the centre of the square is

    A solid conducting sphere having a charge ‘Q’ is surrounded by an uncharged concentric conducting hollow spherical shell. Let the P.D between the surface of the solid sphere and that of the outer surface of the hollow shell be V. If the shell is now given a charge of –3Q. The new PD between the same two surfaces is

    A point charge Q is placed inside a conducting spherical shell of inner radius 3R and outer radius 5R at a distance R from the centre of the shell. The electric potential at the centre of the shell will be.

    A field of 100 Vm –1 is directed at 30 o to positive x-axis. Find (V A –V B ) if OA = 2 m and OB = 4 m

    The electric potential in a region along the X-axis varies with x according to the relation V (x) = 4 + 5 x 2 Then

    A parallel plate condenser of capacity C is connected to a battery and is charged to a potential V. Another condenser of capacity 2 C is connected to another battery and is charged to a potential 2 V. The charging batteries are removed and now the condensers are connected in parallel in such a way that the positive plate of one is connected to negative plate of other. The final energy of this system is

    Two parallel plate capacitors of capacitances C and 2C are connected in parallel and charged to a potential difference V by a battery. The battery is then disconnected and the space between the plate of capacitor OF CAPACITY C is completely filled with a material of dielectric constant K. The potential difference across the capacitor now becomes

    A 4 μ F capacitor is charged by a 200 V supply. It is then disconnected from the supply and is connected to another uncharged 2 μ F capacitor. The energy lost in the process is

    A spherical conductor of radius 2m is charged to a potential of 120 V. It is now placed inside another hollow spherical conductor of radius 6m. Calculate the potential to which the bigger sphere would be raised

    A parallel plate capacitor is maintained at a certain potential difference. When a dielectric slab of thickness 3 mm is introduced between the plates, the plate separation had to be increased by 2 mm in order to maintain the same potential difference between the plates. The dielectric constant of the slab is

    Three charges Q , + q and + q are placed at the vertices of a right angled isosceles triangle as shown The electrostatic energy of the configuration is zero if Q is equal to

    Between the plates of a parallel plate condenser a plate of thickness t 1 and dielectric constant k 1 is placed. In the rest of space there is another plate of thickness t 2 and dielectric constant k 2 . The potential difference across the condenser will be

    A parallel plate capacitor of plate area A and plate separation d is charged to potential V and then the battery is disconnected . A slab of dielectric constant K is then inserted between the plates of the capacitors so as to fill the space between the plates . If Q, E and W denote respectively the magnitude of charge on Each plate, the electric field between the plates (after the slab inserted) and work done on the system in question in the process of inserting the slab , then state incorrect from the following:

    A parallel plate capacitor of area A, plate separation d and capacitance C is filled with three different dielectric materials having dielectric constants k 1 ,  k 2 and k 3 as shown. If a single dielectric material is to be used to have the same capacitance C in this capacitor, then its dielectric constant k is given by [Take k 1 =2 , k 2 =4 , k 3 =6 ]

    A sphere of 4cm radius is suspended in a hollow sphere of 6cm radius. The inner sphere is charged to potential 3 e.s.u. and the outer sphere is earthed. The charge on the inner sphere is

    Seven capacitors each of capacity 2 μ F are to be so connected to have a total capacity 10 11 μ F . Which will be the necessary figure as shown

    In the network shown, if the potential difference between the plates of 3 μF capacitor is 5 volt, the charge stored in 2 μF capacitor is

    Plates of a parallel plate capacitor are connected to the terminals of a battery. If the separation between the plates is doubled, then the electric field at a point in the space between the plates

    The capacitance of a parallel plate capacitor is formed due to the

    In the network shown, the charge on the capacitor in steady state is

    A capacitor C is fully charged with voltage V 0 . After disconnecting the voltage source, it is connected in parallel with another uncharged capacitor of capacitance C 2 . The energy loss in the process after the charge is distributed between the two capacitors is:

    Two capacitors of capacitance C and 2C are charged to potential differences V and 2V , respectively . These are then connected in parallel in such a manner that the positive terminal of one is connected to the negative terminal of the other . The final energy of this configuration is :

    A parallel plate capacitor has plate of length ‘ l ’ , width ‘w’ and separation of plates is ‘d’. It is connected to a battery of emf V. A dielectric slab of the same thickness ‘d’ and of dielectric constant k = 4 is being inserted between the plates of the capacitor. At what length of the slab inside plates, will the energy stored in the capacitor be two times the initial energy stored?

    In the circuit shown, charge on the 5 μ F capacitor is :

    A charge 10 esu is placed at a distance of 2 cm from a charge 40 esu and 4 cm from another charge -20 esu. The potential energy of the charge 10 esu is ( in erg) :

    A charge Q is placed at the centre of a circle of radius R. The work done in moving a charge q from A to B so as to complete a semi-circle is :

    The diagrams below show regions of equipotentials : A positive charge is moved from A to B in each diagram :

    Two point charges are kept at a separation r , magnitude of electric force experienced by each charge is F. If the separation between the charges is halved, electro static potential energy stored in the system is

    Two insulated charged· conducting spheres of radii 20 cm and 15 cm, respectively, and having an equal charge of 10 C are connected by a copper wire and then they are separated. Then

    As shown in the figure, charges +q and -q are placed at the vertices B and C of an isosceles triangle. The potential at the vertex A is

    Three charges are placed at the vertices of equilateral triangle of charge q each. What is the net potential energy, if the side of equilateral triangle is l ?

    In Millikan’s oil drop experiment, an oil drop carrying a charge Q is held stationary by a potential difference 2400 V between the plates. To keep a drop of half the radius stationary the potential difference had to be made 600 V. What is the charge on the second drop?

    Two equal charges q are placed at a distance of 2a and a third charge -2q is placed at the midpoint. The potential energy of the system is

    When a charge of 3 coulombs is placed in a uniform electric field, it experiences a force of 3000 N. Within this field, potential difference between two points separated by a distance of 1 cm is

    Two parallel plates separated by a distance of 5 mm are kept at a potential difference of 50 V. A particle of mass 10 -15 kg and charge 10 -11 C enters in it with a velocity 10 7 m/s. The acceleration of the particle will be

    Two plates are 2 cm apart. A potential difference of 10 volt is applied between them. The electric field between the plates is

    If identical charges (-q) are placed at each corner of a cube of side b, then electric potential energy of charge ( +q) which is placed at centre of the cube will be

    When a proton is accelerated through 1 V, then its kinetic energy will be

    Three charges Q, (+q) and (+q) are placed at the vertices of an equilateral triangle of side I as shown in the figure. If the net electrostatic energy of the system is zero, then Q is equal to

    Equipotentials at a great distance from a collection of charges whose total sum is not zero are approximately

    Work done in moving a positive charge on an equipotential surface is

    The capacity of a condenser is 4 x 10 -6 farad and its potential is 100 volts. The energy released on discharging it fully will be

    A condenser of capacity 50 μF is charged to 10 volts. Its energy is equal to

    In an isolated charged parallel plate capacitor the electrostatic potential energy stored in it is 12µJ. Find the work done in increasing the separation between the plates to 2 times its original value.

    If an uncharged parallel plate capacitor is connected to a battery in a circuit without any resistance, then it will be

    Figure shows equipotential surfaces concentric at ‘O’, the magnitude of electric field at distance r (in meter) measured from O

    An electric field is given by E = ( y i ^ + x j ^ ) N C . Find the work done (in J) in moving a 1 C charge from r A = ( 2 i ^ + 2 j ^ ) m to r B = ( 4 i ^ + j ^ ) m .

    The lines of force of the electric field of a positive charge (+q) and a negative charge (-q) are shown in figs. (A) and (B) below. Then the wrong option is

    The energy stored in the capacitor as shown in the figure (a) is 4.5 x 10 -4 J. If the battery is replaced by another capacitor of 900 pF as shown in figure (b), then the total energy of system is

    The effective capacitance of two capacitors of capacitances C 1 ‘ and C 2 ‘ (with C 2 ′ > C 1 ′ ) connected in parallel is 25/6 times the effective capacitance when they are connected in series. The ratio C 2 ′ C 1 ′ is :

    You are given thirty two capacitors each having capacity 4 μ F. How do you connect all of them to prepare a composite capacity having capacitance 8 μ F?

    Two spherical conductors A and B of radii o and b (b > a) are placed con-centrically in air. The two are connected by a copper wire as shown in fig. Then the equivalent capacitance of the system is

    A 10 μ F capacitor is charged to a potential difference of 50 V and is connected to another uncharged capacitor in parallel. Now the common potential difference becomes 20 volts. The capacitance of second capacitor is

    Two capacitors 2 μ F and 4 μ F are connected in parallel. A third capacitor of 6 μ F capacity is connected in series. The combination is then connected across a 12 V battery. The voltage across 2 μ F capacity is

    Three identical, parallel conducting plates A, .B and C are placed as shown in fig. Switches S 1 and S 2 open, and can connect A and C to earth when closed. +Q charge is given to B.

    The radius of a soap bubble whose potential is 16V is doubled. The new potential of the bubble will be

    The dimension of (1/2) ε 0 E 2 ε 0 : permittivity of free space; E : electric field) is

    An electron of mass m and charge e is accelerated from rest through a potential difference V in vacuum. The final speed of the electron will be

    The dimension of (1/2) ε 0 E 2 ( ε 0 : permittivity of free space; E : electric field) is

    A capacitor of 2 μ F is charged as shown in the diagram. When the switch S is turned to position 2 , the percentage of its stored energy dissipated is

    A parallel-plate capacitor of area A, plate separation d and capacitance C is filled with four dielectric materials having dielectric constants K 1 , K 2 , K 3 a n d K 4 as shown in the figure. If a single dielectric material is to be used to have the same capacitance C in this capacitor, then its dielectric constant k is given by

    A parallel plate air capacitor of capacitance C is connected to a cell of emf V and then disconnected from it. A dielectric slab of dielectric constant K, which can just fill the air gap of the capacitor, is now inserted in it. Which of the following is incorrect?

    Four equal charges Q are placed at the four corners of a square of each side ‘a’ . Work done in removing a charge –Q from its center to infinity is

    The displacement of a charge Q in the electric filed E = e 1 i ∧ + e 2 j ∧ + e 3 k ∧ is   r = a i ∧ + b j ∧ . The work done is

    Separation between the plates of a parallel plate capacitor is d and the area of each plate is A . When a slab of material of dielectric constant ‘k’ and thickness t ( t < d ) is introduced between the plates its capacitance becomes

    In the following circuit the resultant capacitance between A and B is 1 μ F . Then value of C is

    The capacities of two conductors are C 1 and C 2 and their respective potentials are V 1 and V 2 . If they are connected by a thin wire, then the loss of energy will be given by

    In the figure a capacitor is filled with dielectrics. The resultant capacitance is

    Two square plates of side ‘a’ are arranged as shown in the figure. The minimum separation between plates is ‘d’ and one of the plate is inclined at small angle α with plane parallel to another plate. The capacitance of capacitor is (given α is very small)

    A parallel plate capacitor is of area 6 c m 2 and a separation 3 m m . The gap is filled with three dielectric materials of equal thickness (see figure) with dielectric constants K 1 = 10 , K 2 = 12 and K 3 = 14 . The dielectric constant of a material which when fully inserted in above capacitor, gives equivalent capacitance would be :

    A parallel plate capacitor having cross-sectional area A and separation d has air in between the plates. Now an insulating slab of same area but thickness d/2 is inserted between the plates as shown in figure having dielectric constant K(= 4). The ratio of new capacitance to its original capacitance will be,

    An electron (charge = 1.6 × 10 − 19 coulomb) is accelerated through a potential of 1,00,000 V. The energy required by the electron is × 10 − 14 J .

    The electric potential at the surface of an atomic nucleus Z = 50 of radius 9.0 × 10 − 13 c m is × 10 4 V .

    A particle has a mass 400 times greater than that of the electron and charge is double than that of a electron. It is accelerated by 5 V of potential difference. Initially the particle was at rest, then its final kinetic energy will be eV.

    The potential at a point due to a positive charge of 100 C at a distance of 9m is 10 x V. What is x value.

    A proton is about 1840 times heavier than an electron. When it is accelerated by a potential difference of 1kV , its kinetic energy will be eV.

    Four plates each of area A are connected to the terminals of a battery of emf ‘V’. Then charge on plate 2 is

    A 2 μ F capacitor is charged to 100 V, and then its plates are connected by a conducting wire. The heat produced is

    Electric field and potential at a point due to a point charge are 100 v/m and 0.5 volt respectively. Then distance of the point from the point charge is

    Two identical parallel plate capacitors are connected in series and a 12 volt battery is connected across this combination. Now a dielectric slab having dielectric constant 2 is inserted into the space between the plates of one of the capacitors and the slab completely fills the space between the plates. Then potential difference between the plates of this capacitors is

    In a region of space, O a uniform electric field E = ( 3 i ^ + 4 j ^ ) V m exists. If the potential at the origin is 10 V, what is the potential at the point A ( 2 m , 1 m ) ?

    Two particles each having charge of 5 μC are placed at a separation of 1m. what would be the work done by external force in pulling them apart slowly by 2m, so that new separation becomes 3m?

    A 5 μ F capacitor is charged fully by a 220V supply. It is then disconnected from the supply and is connected in series to another uncharged 2.5 μ F capacitor. If the energy change during the charge redistribution is X 100 J then value of X to the nearest integer is .

    A 10 μ F capacitor is fully charged to a potential difference of 50V. After removing the source voltage it is connected to an uncharged capacitor in parallel. Now the potential difference across them becomes 20V. The capacitance of the second capacitor is:

    A solid non conducting sphere of radius R contains some positive charge uniformly distributed throughout its volume. Then electric potential at a radial distance γ

    In the electric field of a point charge q a certain charge is carried from point A to B, C, D and E the work done :

    Charges +q and -q are placed at points A and B respectively. Which are at a distance 2 L apart,C is the midpoint between A and B. The work done in moving a charge +Q along the semicircle CRD is :

    For an infinite line of charge having charge density A lying along x-axis, the work done in moving charge from C to A along arc CA is :

    An electric charge 10 – 3 μC is placed at the origin (0, 0) of X -Y co-ordinate system. Two points A and B are situated at ( 2 , 2 ) and (2, 0) respectively. The potential difference between the points A and B will be :

    Two points P and Q are maintained at the potential of 10 V and – 4 V respectively. The work done in moving 100 electrons from P to Q is :

    The variation of potential with distance r from a fixed point is shown in figure. The electric field at r = 3 cm is :

    A hollow conducting sphere has inner radius 5cm and outer radius 8cm then find maximum possible potential of conductor if breakdown electric field of air is 3 x 10 6 V / m :

    Uniform electric field of magnitude 100 V /m in space is directed along the line y = 3+ x. Find the potential difference between points A (3, 1) and B (I, 3) :

    When an uncharged metallic sphere A is brought near a positively charged metallic sphere B, then

    The electric potential V is given as a function of distance x (metre) by V = 9 + 10 x − 2 x 2 volt. Then electric field at x = 1 m is

    In the circuit shown, potential difference across the 4   μ F capacitor is

    A thin metal plate P is inserted between the plates of a parallel plate capacitor of capacity C in such a way that its edges touch the two plates. The capacity now becomes :

    Two metal plates form a parallel plate condenser. The distance between the plates is d. A metal plate of thickness d/2 and of the same area is inserted completely between the plates. The ratio of capacitances in the two cases (later to initial) is :

    The work done in increasing the voltage across the plates of a capacitor from 5 V to 10 V is W. The work done in increasing the voltage from 10 V to 15 V will be :

    A parallel plate capacitor with air between the plates has a capacitance of 9 pF. The separation between its plates is d. The space between the plates is now filled with two dielectrics. One of the dielectrics has dielectric constant k 1 = 3 and thickness d/3 while the other one has dielectric constant k 2 = 6 and thickness 2d/3. Capacitance of the capacitor is now :

    Equivalent capacitance of the given combination of five capacitances between A and C is :

    Two identical capacitors A and B shown in the given circuit are joined in series with a battery. If a dielectric slab of dielectric constant K is slipped between the plates of capacitor B and battery remains connected, then the energy to capacitor A will :

    A 2μF capacitor is charged to a potential difference 30V and the charging battery is disconnected. It is then connected to a series combination of capacitors C 1 = 2μF and C 2 = 4μF, as shown. Both C 1 and C 2 are initially uncharged. When the switch S is closed, charge redistributes. Final potential difference across C 1 will be :

    Fig. shows four plates each of area A and separated from another by a distance d. What is the capacitance between P and Q?

    A capacitor of capacitance 2 μF cannot withstand a voltage more than 5000 V and another capacitor of capacitance 4 μF cannot withstand more than 4000 V. If these capacitors are connected in series, maximum voltage which the combination can withstand is :

    Equivalent capacitance between x and y points in the given Fig. 3. 79 is :

    A 400 pF capacitor is charged with a 100 V battery. After disconnecting battery this capacitor is connected with another 400 pF capacitor. Then find out energy loss.

    Four plates are located at a distance ‘d’ apart from one another. The extreme plates are interconnected. A potential difference of V is applied to the inner plates. The electric field E between ‘1’ and ‘2’ plates is :

    When an additional charge of 2C is given to a capacitor, energy stored in it is increased by 21 %. The original charge of the capacitor, is :

    Two spheres of radius a and b are charged and joined by a wire. The ratio of electric fields due to spheres of radius a and b is

    The radii of two metallic spheres P and Q are r 1 and r 2 respectively. They are given the same charge. If r 1 > r 2 , then on connecting them with a thin wire, then

    Ten electrons are equally spaced and fixed around a circle of radius R. Relative to V = 0 at infinity, the electrostatic potential V and the electric field E at the centre C are

    If electric potential at any point is V = -5x + 3 y + 15 z, where V, x, y and z are in SI units, then the magnitude of the electric field (in SI unit) is

    What is the potential energy of the two equal positive point charges of 1 μC each held 1 m apart in air?

    If a unit positive charge is taken from one point to another over an equipotential surface, then

    A metallic sphere bas a charge of 10 μC. A unit negative charge is brought from A to B both 100 cm away from the sphere but A being east of it while B being on west. The net work done is

    There is 10 units of charge at the centre of a circle of radius 10 m. The work done in moving 1 unit of charge around the circle once is

    An electron of mass m and charge e is accelerated from rest through a potential difference Vin vacuum. The final speed of the electron will be

    In the rectangle shown below, the two comers have charges q 1 = -5 μC and q 2 = +2.0 μC. The work done in moving a charge +3.0 μC from B to A is ( take 1 / 4 πε 0 = 10 10 N – m 2 / C 2 )

    There are two equipotential surface as shown in figure.The distance between them is r. The charge of -q coulomb is taken from the surface A to B, the resultant work done will be

    A capacitor is charged by using a battery which is then disconnected. A dielectric slab is then slipped between the plates, which results in

    A variable condenser is permanently connected to a 100 V battery. If the capacity is changed from 2 μF to 10 μF, then change in energy is equal to

    Four point charges Q 1, Q 2 , Q 3 and Q 4 are placed at the four corners A, B, C and D of a rectangle having sides 40 cm and 30 cm as shown in figure. Potential at the centre O is found to be 20 volt. If the charge Q 4 at corner D is removed, potential at O is found to be 2 volt. Then the value of Q 4 is

    Two equipotential surface can never (a) intersect each other (b) touch each other

    The figure shows on air corad capacitor connected to a battery. Electric field at a point between the plates is found to be E 0. Now a dielectric slab is introduced in the space between the plates and electric field at a point in side the dielectric slab is found to be E. Then

    A spherical space of radius R is carrying some electric charge uniformly distributed over its entire volume. P is a point inside the sphere at a radial distance r from the centre. If the potential at P is 11/8 times the potential at the surface of the spherical space, then

    In the arrangement shown, the equivalent capacitance between points A and B is

    In a region of space a uniform electric field E = ( 2 i ^ + 3 j ^ ) V / m exists. A(3, 0)m and B(0, 2)m are two points. Then potential difference between A and B is

    If the electric potential at a distance of 10 cm from a point charge is -2 volt, intensity of electric field at that point is

    A point charge Q is placed at the centre of a thick metallic uncharged shell of inner radius r 1 , and outer radius r 2 . Which of the following groups correctly show the variation of potential with distance from centre?

    A thin metallic shell of radius ‘a’ carrying a charge ‘-Q’ is concentrically placed inside another thin metallic shell of radius ‘2a’ carrying a charge ‘+Q’ now the two shells are connected by a then wire. Then select the correct option.

    In the arrangement shown in figure, the capacitors are indentical. When S 1 is closed and S 2 is open, equivalent capacitance between A and B is 4µF. What will be the equivalent capacitor between A and B when S 1 is open and S 2 is closed?

    In a region of space the value of electrostatic potential at each of the points (1,0,0), (0,1,0), (0,0,1) is 8 volt. The value of the electrostatic potential at the origin of coordinate (0,0,0) is 10 Volt. Find the value of electrostatic potential at point (1,1,1)

    What is the induced dipole moment developed per unit volume of a dielectric when placed in an external electric field called?

    Two identical condensers M and N are connected in series with a battery. The space between the plates of ‘M’ is completely filled with dielectric medium of dielectric constant 8 and a copper plate of thickness d/2 is introduced between the plates of N. (d = distance of separation of the plates). Then the potentials of M and N are respectively.

    A parallel plate capacitor (condenser) has a certain capacitance (capacity). When 2/3 rd of the distance between the plates is filled with a dielectric, the (capacity) capacitance is found to be 2.25 times the initial capacitance. The dielectric constant of the dielectric

    Two identical thin rings, each of radius R metre are co-axially placed at distance R metre apart. If Q 1 and Q 2 coulomb are respectively the charges uniformly spread on the two rings, the work done in moving a charge q from the centre of one ring to that of the other is :

    A parallel plate capacitor with air as medium between the plates has a capacitance 10 mF. The area of the capacitor is divided into two equal halves and filled with two media having dielectric constants K 1 = 2 and K 2 = 4. The capacitance of the system will be

    Two circuits (a) and (b) have charged capacitors of capacitance C, 2C and 3C with open switches. Charges on each of the capacitor are as shown in the figures. On closing the switches.

    The capacitance of the system is C. If the key is closed, the total energy loss is equal to

    Before connecting to the circuit shown in figure, all capacitors were uncharged. The circuit now is in steady state. Now the switch S is closed. During the time the steady state is reached again Column – I Column – II (i) Charge on C 1 p. increases (ii) Charge on C 2 q. decreases (iii) Charge on C 3 r. remains same (iv) Charge on C 4 s. becomes zero Now, match the given columns and select the correct option from the codes given below.

    A parallel plate capacitor of capacitance C is connected to a battery and is charged to a potential V 0 . Another capacitor of capacitance 2C is charged to a potential of 2V 0 . Now both capacitors are connected to each other in such a way that positive plate of one is connected to negative plate of the other. The final potential difference across the combination is

    An insulating rod with linear charge density of 40 μ C/m and linear mass density of 0.1 kg/m is released from rest in a uniform electric field E = 100 V/m directed perpendicular to the rod. If rod is released and after travelling 2m down the field, speed of rod is found to be (v/10) m/s, then value of v is

    In the circuit shown, the cells are ideal and of equal emfs. The capacitance of the capacitor is C and the resistance of the resistor is R. Xis first joined to Y and then to Z. After a long time, the total heat produced in the resistor will be

    A conducting sphere A of radius ‘a’ with charge Q, is placed concentrically inside a conducting shell B of radius ‘b’. The sphere B is earthed. ‘C’ is the common center of A and B. Study the following statements. i. The potential at a distance r from C, where r<a is zero. ii. The Potential difference between A and B is 1 4 π ε 0 Q 1 a − 1 b iii. The potential at a distance r from C, where a ≤ r ≤ b   is  1 4 π ε 0 Q 1 r − 1 b Which of the above statements are correct?

    If the distance between the two charges is decreased then electrostatics potential energy of the system

    Statement-1: The capacitance of a parallel plate capacitor increased, when a metallic slab is introduced between plates of a capacitor. Statement-2: The electric field inside metallic slab does not reduce to zero.

    A mass m = 20 g has a charge q = 3.0mC. It moves with a velocity of 20 m/s and enters a region of electric field of 80 N/C in the same direction as the velocity of the mass. The velocity of the mass after 3 seconds in this region is

    The electric potential V is given as a function of distance x (metre) by V = 5 x 2 + 10 x − 9 volt . Value of electric field at x = 1 is

    An alpha particle is accelerated through a potential difference of 10 6   volt . Its kinetic energy will be

    The potential at a point, due to a positive charge of 100 μC at a distance of 9m, is

    Two unlike charges of magnitude q each are separated by a distance 2d. The potential at a point midway between them is

    How much kinetic energy will be gained by an α – particle in going from a point at 70 V to another point at 50V

    If E is the electric field intensity of an electrostatic field, then the electrostatic energy density is proportional to

    Two charges of 4 μC each are placed at the corners A and B of an equilateral triangle of side length 0.2 m in air. The electric potential at C is 1 4 πε 0 = 9 × 10 9 N – m 2 C 2

    Ten electrons are equally spaced and fixed around a circle of radius R. Relative to V = 0 at infinity, the electrostatic potential V and the electric field E at the centre C are

    Electric charges of + 10 μC , + 5 μC , − 3 μC and + 8 μC are placed at the corners of a square of side 2 m. the potential at the centre of the square is

    Fig. shows two parallel equipotential surfaces A and .B kept at a small distance r from each other. A point charge of – q coulomb is taken from the surface A to B. The amount of net work W done will be given by

    Four charges each equal to q are placed at the corners of a square of side I The electric potential at the centre of the square is

    Four equal charges Q are placed at the four corners of a square of side a each. Work done in removing a charge -Q from its centre to infinity is

    Two concentric spheres of radii R and r have similar charges with equal surface densities ( σ ). The electric potential at their common centre will be

    Two conducting spheres of radii r 1 and r 2 have same electric field near their surfaces. The ratio of their electric potential is

    A particle of mass 2 gm and a charge 1 μ C is held at rest on a frictionless horizontal surface at a distance of 1 metre from a fixed charge of 1 mC. If the particle is released it will be repelled, The speed of the particle when it is at a distance of 10 metres from the fixed charge is

    A particle A has charge +q and particle I has charge + 4 q with each of them having the same mass m. When allowed to faII from rest through the same electric potential difference, the ratio of their speeds V A /V B will become

    Two conducting spheres of radii r 1 and r 2 are equally charged. The ratio of their potentials is

    The capacitance of a spherical condenser is 1 μ F, If the spacing between the two spheres is 1 mm, the radius of the outer sphere is

    The capacity of a parallel plate condenser is C. If a dielectric of relative permittivity K and thickness equal to one-fourth of the plate separation is placed between the plates, then its capacity becomes C’. The value of C’/C will be

    A parallel plate condenser with a dielectric of dielectric constant K between plates has a capacity C and is charged to a potential V volt. The dielectric slab is slowly removed from between the plates and then reinserted. The net work done by the system in this process is

    64 small drops of water having the same charge and same radius are combined to form one big drop. The ratio of capacitance of big drop to small drop is

    The plates of a parallel plate capacitor are charged up to 100 volt. A 2 mm thick plate is inserted between the plates, then to maintain the same potential difference, the distance between the capacitor plate is increased by 1.6 mm. The dielectric constant of the plate is

    When a dielectric is introduced between two parallel plates of capacitor, the lines of forces are as shown in fig.

    Three capacitors are connected across a 45 V power supply as shown in fig. What is the charge on the 6 μ F capacitor ?

    Let us suppose the earth (radius 6400 km) had a net charge equivalent to one electron n/m 2 of its surface area. Its potential in volt will be

    A parallel plate capacitor of plate area A and plate separation d is charged to a potential V and then battery is disconnected. A slab of dielectric constant K is then inserted between the plates of the capacitor so as to fill the space between the plates. If Q E and If denote respectively, the magnitude of charge of each plate, the electric field between the plates (after the slab is inserted) and work done on the system in question in the process of inserting the slab, then

    You are given 8 metallic plates, Any two plates arc to be separated from each other so that capacitance of the capacitor formed by them is 1 μ F. What is the maximum capacitance one can obtain with them

    The equivalent capacity between the points A and B in the following figure will be

    If n drops, each of capacitance C, coalesce to form a single big drop, then the ratio of the energy stored in big drop to that in each small drop will be

    A parallel plate capacitor is made by stacking n equally spaced plates connected alternately. If the capacitance between any two adjacent plates is C, then the resultant capacitance is

    A rectangular parallel-plate capacitor has a dielectric slab that partially fills the space between the plates as shown in fig. The energy of the capacitor with charge q is

    Parallel plate capacitor is constructed using three different dielectric materials as shown in fig. The parallel plates, across which a potential difference is applied are of area A cm 2 and separated by a distance d cm. The capacitance across AB is

    Two insulated metallic spheres of 3 μ F and 5 μ F capacitances are charged to 300 V and 50 V respectively. The energy loss, when they are connected by a wire, is

    Two identical metal plates are given positive charges Q 1 and Q 2 (<Q 1 ) respectively. If they are now brought close together to form a parallel plate capacitor with capacitance C, the potential difference between them is

    On plate of a capacitor is connected to a spring as shown in fig. Area of both the plates is A. In steady state, separation between the plates is 0 8 d (spring was in its natural length and the distance between the plates was d when the capacitor was uncharged). The force constant of the spring is approximately

    If n drops of mercury, each charged to a potential V, coalesce to form a single drop, the potential of the big drop will be

    Three charges Q , + q and + q are placed at the vertices of a right-angled isosceles triangle as shown. The net electrostatic energy of the configuration is zero if Q is equal to

    As shown in the figure, charges +q and -q are placed at the vertices B and C of an isosceles triangle. The potential at the vertex A is

    Two conducing concentric hollow spheres of radii a and 2a respectively are shown in the diagram. The inner shell has net charge Q on its surface. The outer shell is neutral. If the outer shell is connected to the earth the heat generated through the connecting wire is

    Identical charges each of – q are placed at each corners of cube of side ‘b’. Then electrostatic potential energy of charge +q which is placed at the centre of the cube will be

    A circuit element is placed in a closed box. At time t=0 , a constant current generator supplying a current of 1 amp is connected across the box. Potential difference across the box varies according to graph shown in figure. The element in the box is:

    The electrostatic force between the metal plates of an isolated parallel plate capacitor C having a charge Q and area A , is

    In a region, the potential is represented by V(x, y, z) = 6x – 8x – 8y + 6yz, where V is in volts and x, y, z are in metres. The electric force experienced by a charge of 2 coulomb situated at point (1, 1, 1) is

    Two thin dielectric slabs of dielectric constants K 1 a n d K 2 ( K 2 < K 2 ) are inserted between plates of a parallel plate capacitor, as shown in the figure. The variation of electric field E between the plates with distance d as measured from plate P is correctly shown by

    A conducting sphere of radius R is charged to a potential of V volts. The electric field at a distance r(>R) from the center of the sphere would be

    Find the equivalent capacitance across A & B

    Two capacitors C 1 and C 2 having capacitance 2 mF and 4 mF respectively are connected as shown in the figure. Initially C 1 has charge 4 mC and C 2 is uncharged. After long time closing the switch S :

    A parallel plate air capacitor has capacity C, distance of separation between plates is d and potential difference V is applied between the plates. Force of attraction between the plates of the parallel plate air capacitor is

    A charged particle q is shot towards another charged particle Q which is fixed, with a speed ν . It approaches Q upto a closest distance r and then returns. If q were given a speed 2 ν , the closest distances of approach would be

    If potential (in volts) in a region is expressed as V(x, y, z) = 6 x y – y + 2yz , the electric field (in N/C) at point (1,1,0) is

    A, B and C are three points in a uniform electric field. The electric potential is

    Mark the correct statement (V is electric potential and E is electrostatic field)

    A solid sphere of radius R is charged uniformly through out the volume. At what distance from its surface is the electrostatic potential is one third of the potential at the centre.

    A parallel plate air capacitor has a capacitance of 50 μ F . The plates are at a distance d apart. If a slab of thickness t ( t ≤ d ) and dielectric constant 4 is introduced between the parallel plates, then the capacitance will be

    Two identical charge particles having charge q and mass m are placed ‘L’ distance apart. If one charge is fixed and other free to move. Find its speed when distance between them becomes 2L.( K = 1 4 π ε 0 )

    Four identical square plates of side a are arranged as shown. The equivalent capacity between points A and B is

    A capacitor is charged by a battery. The battery is removed and another identical uncharged capacitor is connected in parallel. The total electrostatic energy of resulting system

    The diagrams below show regions of equipotentials. A positive charge is moved from A to B in each diagram.

    A drop of water of mass 18 × 10 − 6 k g     falls away from the bottom of a charged conducting sphere ( 2.5 × 10 − 6 C ) of radius 20cm carrying with it charge of 10 − 9 coulomb . What is the speed of the drop when it has fallen 30cm? ε 0 = 1 4 π × 9 × 10 9               g = 9.8 m / s 2

    Charges of + 10 3 × 10 − 9 C are placed at each of the four corners of a square of side 8cm . The potential at the intersection of the diagonals is

    Two parallel plates have equal and opposite charge. When the space between them is evacuated the electric field between the plates is 2 × 10 5   V / m . When the space is filled with dielectric the electric field becomes 1 × 10 5    V / m . The dielectric constant of the dielectric material is

    On rotating a point charge Q around a charge Q in a circle of radius r. The work done will be

    Three particles each having a charge of 10 μ C are placed at the corners of an equilateral triangle of side 10cm. The electrostatic potential energy of the system is (Given 1 4 π ε 0 = 9 × 10 9 N − m 2 / C 2

    There is an electric field E in x-direction. If the work done on moving a charge 0.2C through a distance of 2m along a line making an angle 60 o with the X-axis is 4.0 J , what is the value of E

    Two plates are 2cm apart a potential difference of 10 volt is applied between them . The electric field between the plates is

    In the rectangle shown below the two corners have charges q 1 = − 5 μ C and q 2 = + 2.0 μ C The work done in moving a charge + 3.0 μ C From B to A is (take 1 / 4 π ε 0 = 10 10     N − m 2 / C 2   )

    Two opposite and equal charges 4 × 10 − 8 coulomb when placed 2 × 10 − 2 cm away from a dipole. If this dipole is placed in an external electric field 4 × 10 8 newton / coulomb the value of maximum torque and the work done in rotating it through 180 0 will be

    The capacity of a condenser is 4 × 10 − 6 farad and its potential is 100 volts . The energy released on discharging it fully will be

    Two charges q 1 and q 2 are placed 30cm apart shown in the figure. A third charge q 3 is moved along the arc of a circle of radius 40cm from C to D. The change in the potential energy of the system is q 3 4 π ε 0 k Where k is

    In the circuit diagram shown in the adjoining figure, the resultant capacitance between P and Q is

    Four plates of equal areas A are separated by equal distances d and are arranged as shown in the figure. The equivalent capacity is

    An air capacitor of capacity C = 10 μ F is connected to a constant voltage battery of 12   V . Now the space between the plates is filled with a liquid of dielectric constant 5. The charge that flows now from battery to the capacitor is

    A conducting sphere of radius R, carrying charge Q, lies inside an uncharged conducting shell of radius 2R. If they are joined by a metal wire,

    A spherical capacitor consists of two conducting concentric spherical shells of radii a and b a < b :

    If on the concentric hollow spheres of radii r and R > r the charge Q is distributed such that their surface densities are same then the potential at their common centre is

    A parallel plate capacitor with air as medium between the plates has a capacitance of 10 μ F . The area of capacitor is divided into two equal halves and filled with two media as shown in the figure having dielectric constant k 1 = 2 and k 2 = 4 . The capacitance of the system will now be

    Three charges Q ,   + q and + q are placed at the vertices of a right-angled isosceles triangle as shown. The net electrostatic energy of the configuration is zero if Q is equal to

    Two charges + 3.2 × 10 − 19 C and − 3.2 × 10 − 19 C kept 2.4 A 0 apart forms a dipole. If it is kept in uniform electric field of intensity 4 × 10 5   v o l t / m then what will be its electrical energy in stable equilibrium

    Four equal point charges Q each are placed in the xy plane at (0, 2), (4, 2), (4, -2) and (0, -2). The work required to put a fifth charge Q at the origin of the coordinate system will be :

    In the adjoining figure, four capacitors are shown with their respective capacities and the P.D. applied. The charge and the P.D. across the 4 μ F capacitor will be.

    In a certain region of space with volume 0 . 2 m 3 , the electric potential is found to be 5V throughout. The magnitude of electric field in this region is:

    A short electric dipole has a dipole moment of 16 × 10 − 9 Cm . The electric potential due to the dipole at a point at a distance of 0.6 m from the centre of the dipole, situated on a line making an angle of 60 o with the dipole axis is : 1 4 πε 0 = 9 × 10 9 N   m 2 / C 2

    The capacitance of a parallel plate capacitor with air as medium is 6 μF With the introduction of a dielectric medium, the capacitance becomes 30 μF The permittivity of the medium is ε 0 = 8 .55 × 10 − 12 C 2 N − 1 m − 2

    Choose the wrong statement a) work done in moving a charge on equipotential surface is zero b) electric lines of force are always normal to equipotential surface c) when two opposite charges are brought nearer, then electrostatic potential energy of the system increases d) electric lines of force diverge at positive charge and converge towards negative charge

    The capacitors C 1 , C 2 a n d C 3 are uncharged initially and connected to A, B and C with potentials V 1 , V 2 a n d V 3 respectively. The potential of the junction D is :

    A large metallic plate is facing a charged sheet having charge density is placed parallel to plate at a distance l from the plate. Potential at point P at a distance x from the sheet is

    To form a composite 16 μ F ,   1000 V capacitor from a supply of identical capacitors marked 8 μ F ,   250 V , we require a minimum number of capacitors

    In the figure shown, the potential drop across each capacitor is (assume diodes to be ideal)

    The space between the plates of a parallel plate capacitor is filled completely with a dielectric substance having dielectric constant 4 and thickness 3 mm and its capacitance is C. The distance between the plates in now increased by inserting a second sheet of thickness 5 mm and dielectric constant K. If the capacitance of the capacitor so formed is C/2 then the value of K is

    If a positive charge is shifted from a low potential region to high potential region. The electrical potential energy :

    Two identical capacitors C 1 and C 2 of equal capacitance are connected as shown in the circuit. Terminals a and b of the key k are connected to charge capacitor C 1 using battery of emf V volt. Now disconnecting a and b the terminals b and c are connected. Due to this, what will be the percentage loss of energy?

    An electric field is given by E = y i ^ + x j ^ N / C . Find the work done (in J) by electric field in moving a 1C charge from r A = 2 i ^ + 2 j ^ m to r B = 4 i ^ + j ^ m

    A parallel-plate capacitor is to be designed, using a dielectric of dielectric constant 5, so as to have a dielectric strength of 10 9 Vm – 1 . If the voltage rating of the capacitor is 12 kV, the minimum area of each plate required to have a capacitance of 80 pF is :

    The capacitor of capacitance 4 μ F and 6 μ F are connected in series. A potential difference of 500   v o l t s applied to the outer plates of the two capacitor system. Then the charge on each capacitor is numerically μ C .

    The total capacity of the system of capacitors shown in the adjoining figure between the points A and B is × 10 − 8 F .

    The capacity of a parallel plate condenser is 5 μ F . When a glass plate is placed between the plates of the conductor its potential between becomes 1 / 16   t h of the original value. The value of dielectric constant will be

    In the arrangement shown, the charge on capacitor (1) is

    A 2 μ F parallel capacitor is connected to a 20 volt battery as shown in figure. Now the plates of the capacitor are pulled apart to increase their separation to two times its present value in 0.5 second. Then average current flown through the battery during this period is

    In the network shown charge on the 2 μF capacitor is

    The equivalent capacitance between x and y is

    Find out the euivalent capacitance between A and B. Take plate area = A and C   =   ε o A d

    The ratio of capacitance of two capacitors filled with dielectrics of same dimensions but of different values K and K/4 arranged in two ways as shown in Figure-(1) and Figure-(2) is

    A capacitor of capacitance 1 μF withstands a maximum voltage of 6 kV, while another capacitor of capacitance 2 μF withstands a maximum voltage of 4kV. If they are connected in series, the combination can withstand a maximum of

    In the arrangement shown, the potential difference between points a and b is

    A spherical shell of radius ‘a’ with charge ‘Q’ is expanded to radius ‘2a’, work done by the electrical force in the process is

    Ten capacitors are joined in parallel and charged with a battery up to a potential V. They are then disconnected from the battery and joined in series. Then, the potential of this combination will be

    One plate of a capacitor is fixed, and the other is connected to a spring as shown in Fig. Area of both the plates is A. In steady state (equilibrium), separation between the plates is 0.8d (spring was unstretched, and the distance between the plates was d when the capacitor was uncharged). The force constant of the spring is approximately

    A condenser of capacity “C” is charged to a potential “V” and connected to an uncharged condenser of capacity “C”. The loss of energy during the sharing of the charges is

    An uncharged aluminum block has a cavity within it. The block is placed in a region where a uniform electric field is directed upward. Which of the following is a correct statement describing conditions in the interior of the block’s cavity?

    A parallel plate capacitor has plates of area A and separation d and is charged to a potential difference V. The charging battery is then disconnected and the plates are pulled apart until their separation is 2d. What is the work required to separate the plates?

    At distances of 5 cm and 10 cm from the surface of a sphere, the potentials are 600 V and 420 V. Find the potential at its surface

    Four capacitors with capacitances C 1 = 1 mF, C 2 = 1.5 mF, C 3 = 2.5 mF and C 4 = 0.5 mF are connected as shown and are connected to a 30 volt source. The potential difference between points a and b is

    The effective capacitance between the points P and Q of the arrangement shown in the figure is

    If three charges ‘q’ each are placed at the vertices of an equilateral triangle. What is the net potential energy, if the side of equilateral triangle is l   c m ?

    In given arrangement of the capacitors, one 3 μ F capacitor has got of energy 600 μ J . Then the potential difference across 2 μ F capacitor is

    Two concentric spherical conducting shells of radii R and 2R carry charges Q and 2Q respectively. Change in electric potential on the outer shell when both are connected by a conducting wire is k = 1 4 π ε 0

    At a point in space, the electric field points toward north. In the region surrounding this point, the rate of change of potential will be zero along

    A capacitor is charged to store an energy U. The charging battery is disconnected. An identical capacitor is now connected to the first capacitor in parallel. The energy in each capacitor is now

    A 16 μ F capacitor, initially charged to 5V, is started charging at t=0 by a source at the rate of 40 t μ C / s . How long will it take to raise its potential to 10V?

    A parallel plate capacitor has plates of area A separated by distance ‘d’ between them. It is filled with a dielectric which has a dielectric constant that varies as k x = K 0 1 + α x where ‘x’ is the distance measured from one of the plates. If α d < < 1 , the total capacitance of the system is best given by the expression

    A 60 pF capacitor is fully charged by a 20 V supply. It is then disconnected from the supply and is connected to another uncharged 60 pF capacitor in parallel. The electrostatic energy that is lost in the process by the time the charge is redistributed between them is (in nJ)

    Two identical parallel plate capacitor are connected in series combination as shown in figure. Potential difference across capacitor1 is found to be 4 volt. Now separation between the plates of capacitor 2 is halved. Then new potential difference across 1 will be

    At a point in space, the electric field points toward north. In the region surrounding this point, the rate of change of potential will be zero along

    Effective capacitance of parallel combination of two capacitors C 1 and C 2 is 10 μ F. When these capacitors are individually connected to a voltage source of 1 V, the energy stored in the capacitor C 2 is 4 times that of C 1 . If these capacitors are connected in series, their effective capacitance will be:

    Consider two charged metallic sphere S 1 and S 2 of radii R 1 and R 2 , respectively. The electric fields E 1 (on S 1 ) and E 2 (on S 2 ) on their surfaces are such that E 1 / E 2 = R 1 / R 2 . Then the ratio V 1 o n    S 1 / V 2 o n    S 2 of the electrostatic potentials on each sphere is :

    A small electric dipole p = 10 − 9 i ^   N / C is placed at the origin. A ( 1 , 0 m ) and B ( 0 , 1 m ) are two points. Then ( V A − V B ) is

    A charge Q is distributed over two concentric conducting thin spherical shells radii r and R (R=n r). If the surface charge densities on the two shells are equal, the electric potential at the common centre is:

    On closing the switch S, the amount of charge flows from A to B is

    In the circuit show in the figure, the total charge is 750 μ C and the voltage across capacitor C 2 is 20 V. Then the charge on capacitor C 2 is :

    Two isolated conducting spheres S 1 and S 2 of radius 2 3 R and 1 3 R have 12 μ C and − 3 μ C charges, respectively, and are at a large distance from each other. They are now connected by a conducting wire. A long time after this is done the charges on S 1 and S 2 are respectively :

    Concentric metallic hollow spheres of radii R and 4R hold charges Q 1 and Q 2 respectively. Given that surface charge densities of the concentric spheres are equal, the potential difference V(R) – V(4R) is :

    Hydrogen ion and singly ionized helium atom are accelerated, from rest, through the same potential difference. The ratio of final speeds of hydrogen and helium ions is close to :

    A two point charges 4q and −   q are fixed on the x-axis at x = − d 2 and x = d 2 , respectively. If a third point charge ‘q’ is taken from the origin to x = d along the semicircle as shown in the figure, the energy of the charge will :

    A Solid sphere of radius R carries a charge Q + q distributed uniformly over its volume. A very small point like piece of it of mass m gets detached from the bottom of the sphere and falls down vertically under gravity . This piece carries charge q. if it acquires a speed v when it has fallen through a vertical height y (see I figure ) then : ( assume the remaining portion to be spherical )

    Ten charges are placed on the circumference of a circle of radius R with constant angular separation between successive charges. Alternate charges 1,3, 5,7,9 have charge (+q) each, while 2,4,6,8,10 have charge (-q) each. The potential V and the electric field E at the centre of the circle are respectively. (Take V = 0 at infinity)

    An alternating voltage v = 100 cos ⁡ 100 π t volt is applied across a 100 μ F capacitor. Then average electrostatic energy stored in it is

    A spherical metallic shell of radius 10 cm is charged to a potential of 100 volt. Then its surface charge density is

    In the circuit shown, the equivalent capacitance between points A and B is

    Electric potential at a point in a region of space is given by V = 3 x 2 volt, where x is in metre. Then electric field at x = 1m is

    Plate area of a parallel plate capacitor is 1   c m 2 and plate separation is 0.1 mm. The space between the plates is completely filled by a dielectric slab of dielectric constant 3. Then capacitance of the capacitor is

    Two point charges +Q and − Q 2 are kept at a separation and potential energy at the mid point joining the charges is -0.8 U. Now +2Q charge is added to each of the point charge. Then potential energy at the same point has a magnitude of

    A proton is about 1840 times heavier than an electron. When it is accelerated by a potential difference of 1 kV, its kinetic energy will be

    In a parallel plate capacitor of capacitance C, if plate area is doubled and plate separation is halved, the capacitance becomes

    At a point in a region of space

    Electric potential at a point P on the axis of a short dipole is 4 × 10 − 3 volt. If distance of point P from the centre of the dipole is 10 cm, find the electric field at that point.

    If the intensity of electric field on the surface of a thin metallic charged spherical shell of radius 10 cm is 10 V/m, then potential at a distance 10 cm from the surface of the shell is

    Two capacitors each of capacity C are connected as shown in the circuit across a battery. W 1 is the total energy stored in two capacitors when switch is closed. Now the switch S is opened and the two capacitors are immersed in a liquid of dielectric constant K, then the total energy stored in two capacitors is W 2 . The ratio of W 1   a n d   W 2 is

    A very large sphere having charge 100e (e is equal to the charge of electron) uniformly distributed on the surface is compressed slowly and uniformly till its radius reduces to 1 m. The work done by the electric forces in this process is: (in J)

    A uniform electric field pointing in positive x-direction exists in a region. Let A be the origin, B be the point on the x-axis at x = + 1 cm and C be the point on the y-axis at y =+ 1 cm. Then the potential at the points A, Band C satisfy :

    The shows two parallel equipotential surfaces A and B at same potential kept at a distance ; apart from each other. A point charge -q is taken from surface A to B, the amount of net work done W will be :

    The energy which an electron acquires when accelerated through a PD of 1 volt is called :

    Point charges q 1 = 2 μC and q 2 = – 1 μC are kept at points x = 0 and x = 6 respectively. Electric potential will be zero at the points:

    Two thin wire rings each having a radius R are placed at a distance d apart with their axes coinciding. The charges on the two rings are + q and – q. The potential difference between the centres of the two rings is :

    The variation of potential with distance r from a fixed point is shown in Fig. 2.127. The electric field at r = 5 cm, is :

    If electric field is given by E = 100 x 2 i ^ , the potential difference between points x = l 0 and x = 20 is :

    A particle of mass 2g and charge 1 μC is held at rest on a frictionless horizontal surface at a distance of 1m from a fixed charge 1mC. If the particle is released, it will be repelled. The speed of the particle when it is at a distance of 10m from the fixed charge is :

    A uniform electric field 400 N/C acts along positive y-axis. P is a point having co-ordinates (0.6 m, -0.2 m) and R another point, with co-ordinates (-0.4 m, 0.6 m). If electric potential at P is 200 V, potential at R will be :

    Four particles, each of mass m and charge q, are held at the vertices of a square of side ‘a’, as shown in Fig. 2.132. They are released at t = 0 and move under mutual repulsive forces . Speed of any particle when its.distance from the centre of square doubles, is :

    A uniform electric field of magnitude 5 x 10 3 N / C is directed along the negative x-direction. Co-ordinates of point A in the Fig. 2.134 are (-40 cm,+ 20 cm) and those of point Bare (20 cm, -60 cm). Potential difference between A and B, i.e., V A – V B along the arc of a circle of radius 2 m is :

    Three concentric spherical shells have radii a, band c (a < b < c) and have surface charge densities σ , – σ and σ respectively. If V A , V B and V C denote the potentials of the three shells, then for c = a + b, we have :

    Eight equal charged tiny drops are combined to form a big drop. If the potential on each drop is 10V. Then potential of big drop will be :

    Identical charges (-q) are placed at each comer of a cube of side b then electrical potential energy of charge (+q) which is placed at the centre of the cube will be :

    Four point charges -Q, -q, 2q and 2Q are placed, one at each comer of the square. The relation between Q and q for which the potential at the centre of the square is zero is:

    Two metallic spheres of radii 1 cm and 3 cm are given charges of – 1 x 10 – 2 C and 5 x 10 – 2 C , respectively. If these are connected by a conducting wire, the final charge on the bigger sphere is :

    The electric potential Vat any point (x, y, z ), all in metres in space is given by V = 4 x 2 volt. The electric field at the point (1, 0, 2) in volt/meter, is :

    In a region, the potential is represented by V(x, y, z) = 6x- 8xy-8y+6yz,where V is in volts and x , y,z are in metres. The electric force experienced by a charge of2 coulomb situated at point ( 1, 1, 1) is :

    In the network shown initially S 1 is closed and S 2 is open. Now S 1 is opened and at the same time S 2 is closed. Find the loss of energy in the process. [Given C = 2 μ F , ​  V = 6 volt ]

    If potential (in volts) in a region is expressed as V(x, y, z) = 6xy – y+ 2yz, the electric field (in N/C) at point ( 1, 1, 0) is :

    A solid conducting sphere has a charge – 2Q and is surrounded by a neutral concentric hollow conducting spherical shell of double the radius. The potential difference between the solid sphere and the shell is V. The shell is, now given a charge – 3 Q; the new potential difference between them will be :

    A,B,C,D,P and Q are points in a uniform electric field. The potentials of these points are V (A) = 2 volt, V(P) = V(B) = V(D) = 5 volt and V(C) = 8 volt. The electric field at P is :

    A metal sphere A of radius r 1 charged to a potential ϕ 1 is enveloped by a thin walled conducting spherical shell B of radius r 2 Then ϕ 2 of the sphere A after it is connected by a thin conducting wire to the shell B will be :

    In the network shown, if C = 2 μ F , equivalent capacitance between A and B is

    Two thin spherical conducting shells are at a large distance apart. One of radius 10 cm carries a charge of +0.5 μC and the other of radius 20 cm carries a charge of+ 0. 7 μC. The charge on each, when they are connected by a suitable conducting wire, is respectively :

    A 10 μF capacitor is charged by.a battery of emf 100 V. The energy drawn from the battery and the energy stored in the capacitor, are respectively :

    A parallel plate capacitor having a plate separation of 2 mm is charged by connecting it to a 300 V supply. The energy density is :

    Two insulating plates are both uniformly charged in such a way that the potential difference between them is V 2 – V 1 = 20 V . (i.e. ,plate 2 is at a higher potential). The plates are separated by d = 0. 1 m and can be treated as infinitely large. An electron is released from rest on the inner surface of plate 1. What is its speed when it hits plate 2? e = 1 . 6 x 10 – 19 C , m 0 = 9 . 11 x 10 – 31 kg

    A 40 μF capacitor in a defibrillator is charged to 3000 V. The energy stored in the capacitor is sent through the patient during a pulse of duration 2 ms. The power delivered to the patient is :

    A parallel-plate capacitor of area A, plate separation d and capacitance C is filled with four dielectric materials having dielectric constants k 1 , k 2 , k 3 and k 4 as shown in the figure. lf a single dielectric material is to be used to have the same capacitance C in this capacitor, then its dielectric constant k is given by :

    Three capacitors each of value 3 μF are available. The minimum and maximum capacitance which may be obtained by use of these are :

    The dielectrics K 1 and K 2 are filled between the plates of a capacitor as shown in Fig. 3.57 (A). The capacity of the system is :

    In the arrangement of capacitors shown in Fig. 3.61, the capacitors are initially uncharged, and now are connected with switch S open. Find the potential of point b and the amount of charge flowing through the switch, when it is closed :

    A capacitor is charged until its stored energy is 3 J and the charging battery is removed. Another uncharged capacitor is then connected across it and we find that the charge distributes equally. Final value of total energy stored in the electric fields is :

    In Fig. 3.69 equivalent capacitance between x and y is 9 4 μF . Value of capacitance C is :

    Total energy stored in the condenser system shown in Fig. 3. 76 will be :

    A network of four capacitors of capacity equal to C 1 = C , C 2 = 2 C , C 3 = 3 C , C 4 = 4 C are connected to a battery as shown in the Fig. 3.81. The ratio of the charges on C 2 and C 4 is :

    Two condensers, one of capacity C and the other of capacity C 2 , are connected to a V-volt battery , as shown. The work done in charging fully both the condensers is :

    A capacitor of 2μF is charged as shown in the diagram. When the switch S is turned to position 2, the percentage of its stored energy dissipated is :

    Suppose two deuterons must get as close as 10 -14 m in order for the nuclear force to overcome the repulsive electrostatic force. The height of the electrostatic barrier is nearest to

    An air capacitor consists of two identical parallel plates A and B as shown in figure. Plate A is given change Q and plate B is given a charge 3Q . P is the median plane of the capacitor. If C 0 is the capacitance of the capacitor then

    A, B and C are three large, parallel conducting plates, placed horizontally. A and C are rigidly fixed and earthed. B is given some charge. Under electrostatic and gravitational forces, B may be

    A capacitor of capacitance C = 3  μF is first charged by connecting it across a 10V battery by closing key K 1 . It is then allowed to get discharged through 2   Ω and 4   Ω resistor by closing the key K 2 and opening key K 1 .The total energy dissipated in the 2   Ω resistor is equal to

    Equipotential surfaces are shown in figure. Then the electric field strength will be

    Inside a hollow charged spherical conductor, the potential

    A hollow metal sphere of radius 5 cm is charged so that the potential on its surface is 10 V. The potential at the centre of the sphere is

    A charge of 10 -9 C is placed on each of the 64 identical drops of radius 2 cm. They are then combined to form a bigger drop. Find its potential.

    If a charged spherical conductor of radius 10 cm has potential V at a point distant 5 cm from its centre, then the potential at a point distant 15 cm from the centre will be

    Two metal spheres of radii R 1 and R 2 are charged to the same potential. The ratio of charges on the spheres is

    1\vo charges of 4μC each are placed at the comers A and B of an equilateral triangle of side length 0.2 m in air. The electric potential at C is 1 4 πε 0 = 9 × 10 9 N – m 2 C 2

    Two electric charges 12 μC and-6 μCare placed 20 cm apart in air. There will be a point P on the line joining these charges and outside the region between them, at which the electric potential is zero. The distance of P from -6 μC charge is

    The radius of a soap bubble whose potential is 16V is doubled. The new potential of the bubble will be

    Potential at a point x-distance from the centre inside the conducting sphere of radius R and charged with charge Q is

    In an hydrogen atom, the electron revolves around the nucleus in an orbit of radius 0.53 x 10 -10 m. Then the electrical potential produced by the nucleus at the position of the electron is

    A thin spherical conducting shell of radius R has a charge q. Another charge Q is placed at the centre of the shell. The electrostatic potential at a point p a distance R 2 from the centre of the shell is

    A hollow conducting sphere is placed in an electric field produced by a point charge placed at P as shown in figure. Let V A , V B , V C be the potentials at points A, B and C respectively. Then

    The electric potential at the surface of an atomic nucleus (Z = 50) of radius 9.0 x 10 -13 cm is

    The radius of nucleus of silver (atomic number = 47) is 3.4 x 10 -14 m. The electric potential on the surface of nucleus is (e = 1.6 x 10 -19 C)

    The insulated spheres of radii R 1 and R 2 having charges Q 1 , and Q 2 , respectively, are connected to each other. There is

    Two insulated charged spheres of radii 20 cm and 25 cm, respectively, and having an equal charge Q are connected by a copper wire, and then they are separated. Then

    A conducting sphere of radius 10 cm is charged 10 μC. Another uncharged sphere of radius 20 cm is allowed to touch it for some time. After that if the sphere are separated, then surface density of charges on the spheres will be in the ratio of

    Two charge +q and -q are situated at a certain distance. At the point exactly midway between them,

    Four charges +Q, -Q, +Q, -Q are placed at the corners of a square taken in order. At the centre of the square

    Electric lines of force are as shown in the figure. Then potential at point P

    A hollow metal sphere of radius 5 cm is charged such that the potential on its surface is 10 V. The potential at a distance of 2 cm from the centre of the sphere is

    The charge given to a hollow sphere of radius 10 cm is 3.2 x l0 -19 coulomb. At a distance of 4 cm from its centre, the electric potential will be

    A uniform electric field having a magnitude E 0 and direction along the positive X-axis exists. If the potential Vis zero at x = 0, then its value at X = +x will be

    An electron enters between two horizontal plates separated by 2 mm and having a potential difference of 1000 V. The force on electron is

    An oil drop having charge 2e is kept stationary between two parallel horizontal plates 2.0 cm apart when a potential difference of 12000 volts is applied between them. If the density of oil is 900 kg/m 3 , the radius of the drop will be

    Two plates are at potentials -10 V and +30 V. If the separation between the plates is 2 cm, the electric field between them is

    A uniform electric field exists in x-y plane. The potential of points A(-2 m,2 m),B(-2 m,2 m) and C(2 m, 4 m) are 4 V, 16V and 12 V, respectively. The electric field is

    Electric potential is given by V = 6 x – 8 xy 2 – 8 y + 6 yz – 4 z 2 Then electric force acting on 2C point charge placed on origin will be

    If electric potential at any point is V = -6x + 2y+ 9z, where V, x, y and z are in SI units, then the magnitude of the electric field (in SI unit) is

    The electrostatic potential on the surface of a charged conducting sphere is 100 V. Two statements are made in this regard: S 1 : At any point inside the sphere, electric field intensity is zero. S 2 : At any point inside the sphere, the electrostatic potential is 100 V. Which of the following is a correct statement?

    The potential field of an electric field E = ( y i ^ + x j ^ ) is

    If uniform electric field E = E 0 i ^ + 2 E 0 j ^ , where E 0 is a constant, exists in a region of space and at (0, 0) the electric potential V is zero, then the potential at (x 0 , 0) will be:

    An isolated system consists of two charged. particles of equal mass. Initially the particles are far apart, have zero potential energy, and one of the particles has nonzero speed. If the dissipation is neglected, which of the following is true for the total energy of the system at any later time?

    If E is the electric field intensity of an electrostatic field, then the electrostatic energy density is proportional to

    At distance ‘r’ from a point charge, the ratio U V 2 (where ‘U’ is energy density and ‘V’ is potential) is best represented by

    A sphere of radius 1 cm has potential of 8000 V, then energy density near its surface will be

    Three particles, each having a charge of 10 μC are placed at the corners of an equilateral triangle of side 10 cm. The electrostatic potential energy of the system is (Given 1 4 πε 0 = 9 × 10 9 N – m 2 / C 2 ).

    When a positive q charge is taken from lower potential to a higher potential point, then its potential energy will

    When one electron is taken towards the other electron, then the electric potential energy of the system

    When a negative charge is taken at a height from earth’s surface, then its potential energy

    Three charges Q, + q and +q are placed at the vertices of a right-angled isosceles triangle as shown. The net electrostatic energy of the configuration is zero if Q is equal to

    Figure shows some equipotential lines distributed in space. A charged object is moved from point A to point B. Which of the following statements is true?

    In the electric field of a point charge q, a certain charge is carried from point A to B, C, D and E. Then the work done

    In the figure the charge Q is at the centre of the circle. Work done is maximum when another charge is taken from point P to

    In the following diagram the work done in moving a point charge from point P to point A, Band C is respectively as W A , W B and W C , then

    The electric field intensity at all points in space is given by E = 3 i ^ – j ^ volts/metre. The nature of equipotential lines in x-y plane is given by

    There is an electric field E in X-direction. If the work done on moving a charge 0.2C through a distance of 2 m along a line making an angle 60 ° with the X-axis is 4.0 J, what is the value of E?

    A particle A has charge +q and a particle B has charge +4q with each of them having the same mass m. When al.lowed to fall from rest through the same electric potential difference, the ratio of their speed v A v B will become

    Four identical charges +50 μC each, are placed one at each corner of a square of side 2 m. How much external energy is required to bring another charge of +50 μC from infinity to the centre of the square? Given 1 4 π ε 0 = 9 × 10 9 Nm 2 C 2

    Two point charges 100 μC and 5 μC are placed at points A and B respectively with AB = 40 cm. The work done by external force in displacing the charge 5 μC from B to C, where BC = 30 cm, angle ABC = π 2 and 1 4 πε 0 = 9 × 10 9 Nm 2 / C 2 , is

    An alpha particle is accelerated through a potential difference of 10 6 volts. Its kinetic energy will be

    A charge of 5 C is given a displacement of 0.5 m. The work done in the process is 10 J. The potential difference between the two points will be

    How much kinetic energy will be gained by an a-particle in going from a point at 70 V to another point at 50 V ?

    A proton is accelerated through 50,000 V. Its energy will increase by

    The ratio of momenta of an electron and an α -particle which are accelerated from rest by a potential difference of 100 volt is

    The displacement of a charge Q in the electric field E = e 1 i ^ + e 2 j ^ + e 3 k ^ is r ^ = a i ^ + b j ^ . The work done is

    Two positive point charges of 12 μC and 8 μCare 10 cm apart. The work done in bringing them 6 cm closer is

    If a particle of mass ‘m’ and charge ‘q’ is accelerated through a potential difference of V volt, its energy will be

    A ball of mass1 g and charge 10 – 8 C moves from a point A where potential is 600 volt to the point B where potential is zero. Velocity of the ball at the point B is 20 cm. The velocity of the ball at the point A will be

    The work done in bringing a 20 coulomb charge from point A to point B for distance 0.2 m is 2 J. The potential difference between the two points will be (in volt)

    4 x 10 20 eV energy is required to move a charge of 0.25 coulomb between two points. What will be the potential difference between them?

    Kinetic energy of an electron accelerated through a potential difference of 100 V is

    A particle has mass 400 times than that of electron and is double than that of electron. It is accelerated by 5 V of potential difference. Initially the particle was at rest. Its final kinetic energy will be

    An α-particle is accelerated through a potential difference of 200 V. The increase in its kinetic energy is

    If an electron moves from rest from a point at which potential is 50 volt to another point at which potential is 70 volt, then its kinetic energy in the final state will be

    The work done in carrying a charge of 5 μC from a point A to a point Bin an electric field is 10 mJ. The potential difference (V B – V A ) is then

    Consider two points 1 and 2 in a region outside a charged sphere. Two points are not very far away from the sphere. If E and V represent the electric field vector and the electric potential, which of the following is not possible?

    The energy of a charged capacitor is given by the expression (q = charge on the capacitor and C = capacity of capacitor

    A conducting sphere of radius 10 cm is charged with 10 μC. Another uncharged sphere of radius 20 cm is allowed to touch it for some time. After that if the spheres are separated, then surface density of charges on the spheres will be in the ratio of

    Charges of + 10 3 × 10 – 9 C are placed at each of the four comers of a square of side 8 cm. The potential at the intersection of the diagonals is

    Electric charges of +10μC,+5μC,-3μC and +8μC are placed at the comers of a square of side 2 m . The potential at the centre of the square is

    The potential at a point due to a positive charge of 100 μC at a distance of 9 m, is

    A hollow conducting sphere of radius R has a charge ( +Q) . on its surface. What is the electric potential within the sphere at a distance r = R 3 from its centre?

    A spherical conductor of radius 2 m is charged to a potential of 120 V. It is now placed inside another hollow spherical conductor of radius 6 m. Calculate the potential to which the bigger sphere would be raised.

    Eight drops of mercury of equal radii possessing equal charges combine to form a big drop. Then the capacitance of bigger drop compared to each individual small drop is

    The electric potential V is given as a function of distance x (metre) by V=(5x 2 + 10x – 9) volt . Value of electric field at x = 1 is

    An electron enters in high potential region V 2 from lower potential region V 1 , then its velocity

    The figure gives the electric potential V as a function of distance through five regions on x-axis. Which of the following is true for the electric field E in these regions?

    Sixty-four drops are joined together to form a bigger drop. If each small drop has a capacitance C, a potential V, and a charge q, then the capacitance of the bigger drop will be

    Two spherical shells are as shown in figure. Let r be the distance of a point from their common centre. Then, match the following columns and mark the correct choice from the given codes. Column-I Column-II i. Electric field for r < R 1 p. is constant for q 2 and vary for q 1 ii. Electric potential for r < R 1 q. is zero for q 2 and vary for q 1 iii. Electric potential for R 1 < r <R 2 r. is constant iv. Electric field for R 1 < r <R 2 s. is zero Codes:

    Equipotential surfaces are shown in figure. Then the electric field strength will be

    In moving from A to B along an electric field line, the electric field does 6.4 x 10 -19 J of work on an electron. If ϕ 1 , ϕ 2 are equipotential surfaces, then the potential difference (V C – V A ) is

    Four equal charges Q are placed at the four comers of a square of each side is ‘a’. Work done in removing a charge -Q from its centre to infinity is

    A charge (-q) and another charge (Q) are kept at two points A and B respectively. Keeping the charge ( +Q) fixed at B, the charge (-q) at A is moved to another point C such that ABC forms an equilateral triangle of side l. The net work done in moving the charge (-q) is

    An electron (charge= 1.6 x 10 -19 coulomb) is accelerated through a potential of 1,00,000 volts. The energy requiredby the electron is

    An uncharged metallic sphere A of radius R is concentrically placed inside another sphere. Then metallic spherical shell of radius 2R carrying a charge Q. Now the sphere A is earthed. If P be a point at a radial distance 1.5 R from the centre of the spheres, then potential at P is

    P is a point at a distance r 1 from a point charge Q and potential at P is found to be 5 volt.. Now another point charge 4Q is placed at a distance r 2 from P such that intensity of electric field at P becomes zero. Then final potential at P will be

    The plate area and plate seperation of a parallel plate capacitor are 10 mm 2 and 0.2 mm. The capacitor is connected to a battery of emf 10 volt. Now a dielectric slab of dielectric constant k = 4 is inserted into the capacitor. Then intensity of electric field inside the dielectric slab will be

    In the arrangement will be the potential difference between the terminals A and B after the battery is removed and the switch S is closed ?

    A metallic sphere of radius R is charged to a potential V. If is brought in contact with an uncharged metallic sphere of radius R/2 and then separated. Then potential of the smaller sphere will be

    In a region of space as we are moving along positive x-axis, electric potential is gradually decreasing. Then electric field at any point on the x-axis is directed along

    8 identical capacitors each of capacitance 2µF are to be combined to obtain an equivalent capacitor of capacitance 1µF . Then which of the following combinations is possible?

    A spherical drop of mercury of diameter 8 cm is charged to a potential of 12 volt. The drop is broken into 8 equal drops, then potential of each drop is

    An isolated copper sphere is charged and the electrostatic energy stored in it is 16µJ. An internal agent supplies some charge in the sphere so that its charge becomes doubled, then work done by the external agent is

    In the arrangement shown, when a dielectric slab having dielectric constant K is inserted in the capaciter of capacitance C, the reading of the volt meter becomes 1/5th of previous value.Then value of K is

    In the arrangement shown, if intensity of electric field at point A is ‘E’, then intensity of electric field at B will be (The capacitors have the same plate area)

    Two equal point charges are kept at a separation of r = 8 cm from each other and potential energy of the system is found to be U. Now 50 % of charge is transferred from one charge to another. What will be the new separation between the charges for which the electrostatic potential energy of the system will be U?

    The potential at the origin is zero due to electric field E = 20i + 30j NC –1 . The potential at point P(2m, 2m)

    Two charges q 1 and q 2 are placed 30 cm apart, as shown in the figure. A third charge q 3 is moved along the arc of a circle of radius 40 cm from C to D. The change in the potential energy of the system is q 3 4 πε 0 k , where k is

    Equal and opposite charges q are placed at points A and B as shown in Fig and P 1 and P 2 are equidistant points from O. The ratio of potential at P 1 and P 2 is

    The radius of the circular plates of a parallel plate condenser is ‘r’. Air is there as the dielectric. The distance between the plates if its capacitance is equal to that of an isolated sphere of radius r’ is

    The effective capacitance in μ F in between A and B will be

    Given a number of capacitors labelled as C, V. Find the minimum number of capacitors needed to get an arrangement equivalent to C net , V net

    Two metal spheres, one of radius R and the other of radius 2R respectively have the same surface charge density σ . They are brought in contact and separated. What will be the new surface charge densities on them?

    The work done in increasing the P.D. across the plates of a capacitor from 4 V to 6 V is W. The further work done in increasing the P.D. from 6 V to 8 V is

    Two condensers, one of capacity C and the other of capacity C/2, are connected to a V volt battery, as shown. The work done in charging fully both the condensers is

    Initially the spheres A & B are at potential V A and V B . The potential of A when sphere B is earthed

    A parallel-plate capacitor of area A, plate separation d and capacitance C is filled with four dielectric materials having dielectric constants k 1 , k 2 ,k 3 and k 4 as shown in the figure below. If a single dielectric material is to be used to have the same capacitance C in this capacitor, then its dielectric constant k is given by

    A fully charged capacitor has a capacitance C. It is discharged through a small coil of resistance wire embedded in a thermally insulated block of specific heat capacity s and mass m. If the temperature of the block is raised by ∆ T , the potential difference V across the capacitance is

    A parallel plate capacitor has an electric field of 10 5 V/m between the plates, If the charge on the capacitor plate is 1 μ C , the force on each capacitor plate is

    Three uncharged capacitors of capacities C 1 , C 2 and C 3 are connected as shown in the figure to one another and the points A, B and C are at potentials V 1 , V 2 and V 3 respectively. Then the potential at O will be

    A capacitor of capacitance C 1 = 1 μ F charged up to a voltage V = 110 V is connected in parallel to the terminals of a circuit consisting of two uncharged capacitors connected in series and possessing capacitances C 2 = 2 μ F and C 3 = 3 μ F. Then, the amount of charge that will flow through the connecting wires is

    A capacitor of capacity C 1 is charged to the potential of V 0 . On disconnecting from the battery, it is connected with a capacitor of capacity C 2 as shown in the adjoining figure. The ratio of energies of system of capacitors before and after the connection of switch ‘ S ’ will be

    A capacitor of capacity C 1 is charged to the potential of V 0 . On disconnecting from the battery, it is connected with a capacitor of capacity C 2 as shown in the adjoining figure. The ratio of energies of system of capacitors before and after the connection of switch ‘ S ’ will be

    Three charged concentric non conducting shells are given charges as shown in the figure. Find the potential at point A:- Take k = 1 4 π ε 0

    Find the equivalent capacitance between A and B .

    A 3  μF capacitor is charged to a potential of 300  V and a 2  μF capacitor is charged to 200  V . The capacitors are then connected in parallel with plates of opposite polarity joined together. What amount of charge will flow through the connecting wire when the plates are so connected?

    Variation of electrostatic potential along x-direction is shown in the graph. The correct statement about electric field is:-

    If Electric field directed parallel to axis is represented by graph, and potential at origin is taken as zero. Find potential at x = 8 m

    In the circuit shown switch S is kept open for long time. Switch is closed at t = 0, find total heat produced after closing the switch

    The linear charge density on a dielectric ring of radius R is varying with θ as λ = λ 0 cos ⁡ θ 2 , where λ 0 is constant. The potential at the centre O of ring [in volt] is

    An electric field E = A x i ^ exists in the space, where A =10 V/m 2 . Consider the potential at (10 m, 20 m) to be zero. The potential (in V) at the origin is

    An electron beam accelerated from rest through a potential difference of 5000 V in vacuum is allowed to impinge on a surface normally. The incident current is 50 μ A and if the electrons come to rest on striking the surface, the force on it is

    In the circuit shown in figure, magnitude of instantaneous power consumed by the capacitor is

    How does the potential difference change with the effect of the dielectric when the battery is kept disconnected from the capacitor?

    Consider an arrangement of six plates of effective area A and separated from each other by distance d as shown. The capacitance between terminals of A and B

    Two capacitors with capacitance 2C and C are joined in parallel and charged up to potential V. The battery is removed and the capacitor of capacity C is filled completely with a medium of dielectric constant K. The potential difference across the capacitors equals:

    Two spherical conductors A and B of radii a and b(b > a) are placed concentrically in air. The two are connected by a copper wire as shown in figure. Then the equivalent capacitance of the system is

    The plates in a parallel plates capacitor are separated by a distance d with air as the medium between the plates. In order to increase the capacity by 66% a dielectric slab of thickness 3d/5 is introduced between the plates. What is the dielectric constant of the dielectric slab?

    A parallel plate capacitor of plate area A and plate separation d is charged to potential difference V and then battery is disconnected. A slab of dielectric constant K is then inserted between the plates. If q, E and W denotes the magnitude of charge on each plate, electric field between the plates (After the slab insertion) and work done on the system, then

    What is the magnitude of charge that will reside in the parallel plate capacitor formed by these two plates.

    Calculate the amount of energy released on discharging a capacitor which has a potential difference of 200 V across its plates and 0.1 C charge is stored in it.

    When an alpha-particle is accelerated by a PD of 3 volt, its energy is:

    An arc of radius R is shown in the figure, find the potential at its centre :

    A glass slab is put with in the plates of a charged parallel plates condenser. (not connected to battery) Which of the following quantities does not change.

    A capacitor of charge 100 μC , 2 μF is connected another uncharged capacitor of capacity 6 μ F then common potential of both the capacitors is

    Five identical capacitor plates are arranged such that they make four capacitors each of 2 μ F . The plates are connected to a source of voltage 10 V. The total charge on plate C is:

    From A conducting sphere of radius R a cavity of radius R/2 is cut out as shown in the figure. At the centre of cavity a point charge q is placed then, the potential and field at point P as shown in the figure is

    Initial charge on conducting sphere of radius r is Q 0 . If S is closed at t = 0 then charge on the sphere at any time t is

    Two identical thin rings, each of radius R metres, are coaxially placed at a distance of R metres from each other. If Q 1 coulombs and Q 2 coulombs are the charges uniformly spread on the two rings, the work done in moving a charge q from the centre of first ring to that of the second is

    A potential field is shown by its equipotential surfaces. At point P, the electric field E is

    16. The work done in carrying a particle of a charge 2C from B (1m, 0, 1m) to A(0.8m, 0.6m, 1m) in a non-uniform electric field E = ( i ^ + x j ^ + k ^ ) N / m along the straight line path from B to A is

    Two capacitors C 1 and C 2 having capacitance 2 μ F and 4 μ F respectively are connected as shown in the figure. Initially C 1 has charge 4 μ C and C 2 is uncharged. After long time closing the switch S :

    Consider a capacitor charging circuit. Let Q 1 be the charge given to the capacitor in a time interval of 10 ms and Q 2 be the charge given in the next time interval of 10 ms. Let 10 μ C charge be deposited in a time interval t 1 and the next 10 μ C charge is deposited in the next time interval t 2 .

    A charge particle, having mass m and charge –q is thrown from the center of charged ring, having linear charge density λ and radius r fixed in a stationary space, along its axis. The minimum speed v for which it will escape this isolated ring is

    In circuit diagram capacitance of capacitor C 1 = 3 μ F and C 2 = 1 μ F . It is given that time constant of circuit between A and B is 3 millisecond. Value of R will be

    The equation of an equipotential line in an electric field is y = 2x, then the electric field Strength vector at (1, 2) may be

    In a certain region of space, the potential is given by : V = K 2 x 2 − y 2 + z 2 The electric field at the point (1,1, 1) has magnitude =

    Uniform electric field of magnitude 100 V/m in space is directed along the line y = 3 + x. Find the potential difference between point (3, 1) & (1, 3)

    A point charge Q is moved along a circular path around another fixed point charge. The work done is zero.

    A solid sphere of radius R is charged uniformly through out the volume. At what distance from its surface is the electrostatic potential half of the potential at the centre.

    An electric line of force in the xy plane is given by equation x 2 + y 2 = 1 . A particle with unit positive charge, initially at rest at the point x = 1 , y = 0 in the xy plane

    What is the equivalent capacity of combination of capacitors ?

    A half ring of radius R has charge λ per unit length. The potential at its centre is :

    The work done in carrying a charge of 5 μ C from point A to a point B in an electric field is 10mJ. The potential difference V B – V A is then

    Two charged spherical conductors of radii R 1 and R 2 are connected by a wire. Then the ratio of surface charge densities of the spheres σ 1 / σ 2 is:

    Three concentric spherical shells have radii a, b and c (a<b<c) and have surface charge densities σ , – σ and σ respectively. If V A , V B and V C denote the potential of the three shells, then for c = a + b we have

    The electric A potential at a point (x, y, z) is given by V = − x 2 y − xz 3 + 4 The electric field E at that point is

    Two spheres A and B of radius 4 cm and 6 cm are given charges of 80 μ C and 40 μ C respectively. If they are connected by a fine wire, the amount of charge flowing from one to the other is

    A capacitor of capacitance C 1 = 4 μ F is charged to V 1 = 80V and another capacitor of capacitance C = 6 μ F is charged to V 2 = 30V. When they are connected together, the energy lost by the 4 μ F capacitor is

    A uniform electric field pointing in positive r-direction exists in a region. Let A be the origin, B be the point on the r-axis at r =+ 1 cm and C be the point on the y-axis at y = + 1 cm. Then the potentials at the points A, B and C satisfy:

    The potential difference between points P and Q in the circuit shown is :

    A capacitor of capacitance C is charged by connecting it to a battery. The battery is now removed and this capacitor is connected to a second uncharged capacitor of capacitance C’. If the charge distributes equally on the two capacitors, the ratio of the total energy stored in the capacitors after connection to the total energy stored in them before connection is:

    Charges are placed on the vertices of a square as shown. Let E be the electric field and V the potential at the centre. If the charges on A and B are interchanged with those D on D and C respectively, then

    A 2 μ F capacitor is charged as shown in the figure. The percentage of its stored energy dissipated after the switch S is turned to position 2 is :

    If on the concentric hollow spheres of radii r and R (> r) the charge Q is distributed such that their surface densities are same then the potential at their common centre is:

    The radii of two metallic spheres P and Q are r 1 and r 2 respectively. They are given the same charge. If r 1 > r 2 Then on connecting them with a thin wire, the charge will flow:

    64 drops of mercury each charged to a potential of 10V are combined to form one bigger drop. The potential of this drop will be (Assume all the drops to be spherical):

    The capacity of a spherical conductor in MKS system is:

    Consider two concentric spherical metal shells of radii r 1 and r 2 (r 2 > r 1 ). If the outer shell has a charge q and the inner one is grounded, the charge on the inner shell is :

    The capacity of parallel plate condenser depends on:

    The true statement on increasing distance between the plates of an isolated parallel plate condenser

    The distance between the plates of a parallel plate Condenser is 4mm and potential difference is 60olts. If the distance between the plates is increased to12mm, then

    Consider the situation shown in the figure. The capacitor A has a charge q on it whereas Bis uncharged. The charge appearing on the capacitor B a long time after the switch is closed is:

    Three plates of common surface area A are connected as shown. The effective capacitance will be:

    In the figure a potential of +1200V is given to point A and point B is earthed, what is the potential at the point P?

    The charge on 4 μ F capacitor in the given circuit is…in μ C:

    The capacitance between the points A and B in the given circuit will be:

    In the figure shown, the effective capacitance between the points A and B, if each has capacitance C, is:

    In the given circuit, charge Q 2 on the 2 μ F capacitor changes as C is varied from 1 μ F to 3 μ F. Q 2 as a function of ‘C’ is given properly by :(figures are drawn schematically and are not to scale)

    A combination of capacitors is set up as shown in the figure. The magnitude of the electric field due to a point charge Q(having a charge equal to the sum of the charges on the 4 μ F and 9 μ F capacitors), at a point distance 30m from it, would equal :

    Assume that an electric field E = 30 x 2 i exists in space. Then the potential difference V A − V O , where V O is the potential at the origin and V A the potential at x = 2 m is :

    Two capacitors C 1 , and C 2 , are charged to 120 V and 200 V respectively. It is found that by connecting them together the potential on each one can be made zero. Then,

    Two charged particles having charges 1 μC and – 1 μC and of mass 50 g each are held at rest while their separation is 2 m. Now the charges are released. Find the speed of the particles when their separation is 1 m.

    In the given circuit, a charge of +80 μ C is given to the upper plate of the 4 μ F capacitor. Then in the steady state, the charge on the upper plate of the 3 μ F capacitor is :

    A point charge q is placed inside a conducting spherical shell of inner radius 2R and outer radius 3R at a distance of R from the center of the shell. Find the electric potential at the center of the shell.

    Mark the correct statement:

    For circuit the equivalent capacitance between points, P and Q is

    A parallel plate capacitor is made of two circular plates separated by a distance of 5 mm and with a dielectric of dielectric constant 2.2 between them. When the electric field in the dielectric is 3 x 10 4 V/m, the charge density of the positive plate will be close to:

    Four identical capacitors are connected in series with a 10 V battery as shown in the figure. Potentials at A and B are

    In the given circuit, a potential difference of 60 V is applied across AB. The potential difference between points M and N is:

    An electron having charge e and mass m starts from the lower plate of two metallic plates separated by a distance d. If the potential difference between the plates is V, the time taken by the electron to reach the upper plate is given by

    A solid sphere of radius R is charged uniformly. The electrostatic potential V is plotted as a function on distance r from centre of sphere. Which of the following best represents the resulting curve ?

    Two parallel plate capacitors of capacitance C and 2C are connected in parallel and charged to a potential difference V by a battery. The battery is then C disconnected and the space between the plates of capacitor C is completely filled with a material of dielectric constant K. The potential difference across the capacitors now becomes:

    Figure shows three circular arcs, each of radius R and total charge as indicated. The net electric potential at the center of curvature is

    A unit positive point charge of mass m is projected with a velocity V inside the tunnel as shown. The tunnel has been made inside a uniformly charged nonconducting sphere. The minimum velocity with which the point charge should be projected such that it can reach the opposite end of the tunnel is equal to

    Find the potential V of an electrostatic field E = a ( y i ^ + x j ^ ) , where a is a constant.

    Inside a hollow conducting sphere, which is uncharged, a charge q is placed at its center. Let electric field at a distance x from center at point p be E and potential at this point be V. Now, some positive charge Q is given to this sphere, then

    A parallel plate air capacitor is connected to a battery. The quantities charge, voltage, electric field and energy associated with this capacitor are given by Q 0 , V 0 , E 0 and U 0 respectively. A dielectric slab is now introduced to fill the space between the plates with battery still in connection. The corresponding quantities now given by Q,V,E and U are related to the previous quantities as :

    Two large identical plates are placed infront of each other at x = d and x = 2d as shown in the figure. If charges on plates are Q and -5Q, the potential versus distance graph for region x = 0 to x = 3d is (d is very small and potential at x = 0 is v 0 )

    Seven capacitors, a switch S and a source of e.m.f are connected as shown in the figure. Initially, S is open and all capacitors are uncharged. After S is closed and steady state is attained, the potential difference in volt across the plates of the capacitor 7 μ F is :

    Two uniformly charged large plane sheets S 1 and S 2 having charge densities σ 1 & σ 2 ( σ 1 > σ 2 ) are placed at a distance (d) parallel to each other. A charge q is moved along a line of length (a < d) at 45° with normal to S 1 . Then, work done by electric field is:

    An electron travelling in a uniform electric field passes from a region of potential V 1 to a region of higher potential V 2 . Then

    The given fig. shows two identical parallel plate capacitors connected to a battery with switch S is closed. The switch is now opened and free space between the plates of the capacitors is now filled with dielectric of K = 3. Then, ratio of energy stored in both capacitors before and after introduction of dielectric is ;

    The potential of a point B ( − 20 m , 30 m ) taking the potential of a point A (30 m, -20 m) to be zero in an electric field E = 10 x i ^ − 20 j ^ NC − 1 is

    A parallel plate capacitor with air between the plates has a capacitance of 9 pF. The separation between its plates is d. The space between the plates is now filled with two dielectrics. One of the dielectric has dielectric constant k 1 = 3 and thickness d/3 while the other one has dielectric constant k 2 = 6 and thickness 2d/3. Capacitance of the capacitor is now

    Uniform electric field exists in a region and is given by E = E 0 i ^ + E 0 j ^ . There are four points A(-a, 0), B(0 , -a), C(a, 0), and D(0, a) in the xy plane. Which of the following is the correct relation for the electric potential?

    A spherical capacitor has an inner sphere of radius 12 cm and an outer sphere of radius 13 cm. The outer sphere is earthed, and the inner sphere is given a charge of 2.5 μ C. The space between the concentric spheres is filled with a liquid of dielectric constant 32. Determine the potential of the inner sphere

    A 600 pF capacitor is charged by a 200 V supply. It is then disconnected from the supply and is connected to another uncharged 600 pF capacitor. What is the common potential (in V) and energy lost (in J) after reconnection?

    Effective capacitance between A and B in the figure shown is (all capacitance are in μF ):

    An uncharged parallel plate capacitor having a dielectric of dielectric constant K is connected to a similar air cored parallel plate capacitor charged to a potential V 0 . The two share the charge, and the common potential becomes V. The dielectric constant K is

    A capacitor of capacitance C 0 is charged to a potential V 0 and then isolated. A small capacitor C is then charged from C 0 , discharged and charged again; the process being repeated n times. Due to this, the potential of the larger capacitor is decreased to V. The value of C is

    Two square plates ( l × l ) and dielectric l 2 × t 2 × l arranged as shown in figure. Find the equivalent capacitance of the structure.

    In figure, the battery has a potential difference of 20 V. The charge in the capacitor marked as C is

    Find the equivalent capacitance across A and B.

    A 16 μF capacitor, initially charged to 5 V, is started charging at t = 0 by a source at the rate of 40 t μCs − 1 . How long will it take to raise its potential to 10V?

    In the circuit shown (figure), the equivalent capacitance between the points X and Y is

    In the given arrangement of capacitors, 6 μC charge is added to point a. Find the charge on upper capacitor.

    The capacitor plates are fixed on an inclined plane and connected to a battery of emf E. The capacitor plates have plate area a, length l, and the distance between them is d. A dielectric slab of mass m and dielectric constant K is inserted into the capacitor and tied to mass M by a massless string as shown in the figure. Find the value of M for which the slab will stay in equilibrium. There is no friction between slab and plates.

    Three large plates are arranged as shown. How much charge will flow through the key k if it is closed?

    Figure shows two capacitors C 1 and C 2 connected with 10 V battery and terminal A and B are earthed. The graph shows the variation of potential as one moves from left to right. Then the ratio C 1 /C 2 is

    A uniform electric field of magnitude 325 V/m is directed in the negative y direction in figure. The coordinates of point A are (-0.2 m, -0.3 m) and those of point B are (0.4 m, 0.5 m). Calculate the potential difference V B − V A (in volts), along the path shown in the figure.

    A uniform field of magnitude E = 2000 N/C is directed θ = 37 ∘ below the horizontal. Find the potential difference between P and R V P − V R (in volts).

    Two point charges q 1 and q 2 are fixed at a distance 3.0 cm as shown in the figure. A dust particle with mass m = 5 .0 × 10 − 9 kg and charge q 0 = 2 .0 nC starts from rest at point ‘a’ and moves in a straight line to point ‘b’. What is its speed v at point b (in m/s) ? (round off to nearest integer)

    A particle of mass m carrying charge ‘q’ is projected with velocity ‘v’ from point ‘A’ towards an infinite line of charge from a distance ‘a’. Its speed reduces to zero momentarily at point ‘B’ which is at a distance a/2 from the line of charge. If another particle with mass m and charge ‘-q’ is projected with the same velocity ‘v’ from ‘A’ towards the line of charge. If v = 10 2 m / s , what will be its speed (in m/s) at ‘B’ ?

    A 100 eV proton is projected directly towards a large metal plate that has surface charge density of 2 .2 × 10 − 6 C / m 2 . From what distance (in mm) must the proton be projected, if it is to just fail to strike that plate?

    A source in the form of a metal sphere of diameter 10 -3 m emits electrons at a constant rate of 6.25 x 10 10 particles per second. If the source is electrically insulated, how long (in μ s) will it take for its potential to rise by 1.0 volt, assuming that 80% of emitted electrons escape from the surface.

    The plates of a capacitor are charged to a potential difference of 100 V and then connected across a resistor. The potential difference across the capacitor decays exponentially with respect to time. After one second the potential difference between the plates of the capacitor is 80 V. What is the fraction of the stored energy which has been dissipated?

    A circuit has a section AB shown in figure. The emf of the cell is 10 V and the capacitors have capacitances C 1 = 1 μF and C 2 = 2 μF . The potential difference V AB = 5 V . Find the charges on the capacitors (in μ C).

    Three plates A, B and C each of area 0.1 m 2 are separated by 0.885 mm from each other as shown in the figure. A 10 V battery is used to charge the system. Find the energy stored in the system (in μ J).

    A conducting body 1 has some initial charge Q, and its capacitance is C. There are two other conducting bodies, 2 and 3, having capacitance: C 2 = 2C and C 3 = ∞ . Bodies 2 and 3 are initially uncharged. Body 2 is touched with body 1. Then, body 2 is removed from body 1 and touched with body 3, and then removed. This process is repeated for N times. If the charge on body 1 at the end is found to be Q x N , find the value of x.

    The potential at a point x (measured in μ m) due to some charges situated on the x-axis is given by V ( x ) = 20 / x 2 − 4 volt. The electric field E at x = 4 μ m is given by:

    In the absence of other conductors, the surface charge density

    A charge of Q coulomb is placed on a solid piece of metal of irregular shape. The charge will distribute itself

    When a body is earth connected, electrons from the earth flow into the body. This means the body is…..

    The electric potential V at any point O (x, y, z all in metres) in space is given by V = 4 x 2 volt . The electric field at the point ( 1 m , 0 , 2 m ) in volt/metre is

    A hollow metal sphere of radius 5 cm is charged so that the potential on its surface is 10 V. The potential at the centre of the sphere is

    A metallic sphere has a charge of 10 μC . A unit negative charge is brought from A to B both 100 cm away from the sphere but A being east of it while B being on west. The net work done is

    Two plates are 2 cm apart, a potential difference of 10 volt is applied between them, the electric field between the plates is

    Three particles, each having a charge of 10 μC are placed at the corners of an equilateral triangle of side 10 cm. The electrostatic potential energy of the system is (Given 1 4 πε 0 = 9 × 10 9 N − m 2 / C 2 )

    There is an electric field E in X-direction. If the work done on moving a charge 0.2 C through a distance of 2 m along a line making an angle 60 ∘ with the X-axis is 4.0, what is the value of E

    In the figure the charge Q is at the centre of the circle. Work done is maximum when another charge is taken from point P to

    Four identical charges + 50 μC each are placed, one at each corner of a square of side 2m. How much external energy is required to bring another charge of + 50 μC from infinity to the centre of the square Given 1 4 πε 0 = 9 × 10 9 Nm 2 C 2

    In Millikan’s oil drop experiment an oil drop carrying a charge Q is held stationary by a potential difference 2400 V between the plates. To keep a drop of half the radius stationary the potential difference had to be made 600 V. What is the charge on the second drop

    A charge of 5C experiences a force of 5000N when it is kept in a uniform electric field. What is the potential difference between two points separated by a distance of 1cm

    Two insulated charged conducting spheres of radii 20 cm and 15 cm respectively and having an equal charge of 10C are connected by a copper wire and then they are separated. Then

    Equal charges are given to two spheres of different radii. The potential will

    Two point charges 100   μC and 5 μC are placed at points A and B respectively with AB = 40 cm. The work done by external force in displacing the charge 5 μC from B to C, where BC = 30 cm, angle ABC = π 2 and 1 4 πε 0 = 9 × 10 9 Nm 2 / C 2

    A charge of 5C is given a displacement of 0.5m. The work done in the process is 10J. The potential difference between the two points will be

    Two metal pieces having a potential difference of 800 V are 0.02 m apart horizontally. A particle of mass 1 .96 × 10 − 15 kg is suspended in equilibrium between the plates. If e is the elementary charge, then charge on the particle is

    Two spheres of radius a and b respectively are charged and joined by a wire. The ratio of electric field of the spheres is

    A particle of mass m and charge q is placed at rest in a uniform electric field E and then released. The kinetic energy attained by the particle after moving a distance y is

    A charged water drop whose radius is 0 .1   μm is in equilibrium in an electric field. If charge on it is equal to charge of an electron, then intensity of electric field will be ( g = 10   ms − 2 )

    A sphere of radius 1 cm has potential of 8000 V, then energy density near its surface will be

    What is the potential energy of the equal positive point charges of 1 μC each held 1 m apart in air

    The ratio of momenta of an electron and an α -particle which are accelerated from rest by a potential difference of 100 volt is

    An oil drop having charge 2e is kept stationary between two parallel horizontal plates 2.0 cm apart when a potential difference of 12000 volts is applied between them. If the density of oil is 900 kg/m 3 , the radius of the drop will be

    A proton is accelerated through 50,000 V. Its energy will increase by

    When a proton is accelerated through 1V, then its kinetic energy will be

    Two metal spheres of radii R 1 and R 2 are charged to the same potential. The ratio of charges on the spheres is

    Two positive point charges of 12 μC and 8 μC are 10cm apart. The work done in bringing them 4 cm closer is

    Eight mercury droplets having a radius of 1 mm and a charge of 0.066 pC each merge to form one droplet. Its potential is

    A charge Q is distributed over two concentric hollow spheres of radii r and R (>r) such that the surface densities are equal. The potential at the common centre is

    n small drops of same size are charged to V volt each. If they coalesce to form a single large drop, then its potential will be

    A condenser of capacity 50 μ F is charged to 10 volts. Its energy is equal to

    A parallel plate condenser is filled with two dielectric as shown in fig. Area of each plate is A metre 2 and the separation is d metre. The dielectric constants are K 1 and K 2 respectively. Its capacitance is farad will be

    A parallel plate condenser with plate area A and separation d is filled with dielectrics as shown in fig. The dielectric constants are K 1 and K 2 respectively. The capacitance will be

    Two spherical conductors A and B of radii a and b (b > o) are placed con-centrically in air as shown in fig. B is given a charge + Q and A is earthed. The equivalent capacitance of the system is

    Five capacitors 10 μ F capacity each are connected to a D.C. potential of 100 volts as shown in fig. The equivalent capacitance between the points A and B will be equal to

    The effective capacitance between points X and Y shown in fig. assuming C 2 = 10 μ F and that the other capacitors are all 4.00 μ F is

    Referring to fig. the effective capacitance between A and B will be

    Four metallic plates, each with a surface area of one side A, are placed at a distance d apart from each other. The two inner plates are connected to point A and the other two plates to another point A as shown in fig. Then the capacitance of the system is

    Four metallic plates of each with a surface area of one side A, are placed at a distance d from each other. The alternate plates are connected to points A and B as shown in fig. The equivalent capacitance of the system will be

    Four metallic plates, each with a surface area of one side A, are placed at a distance d apart from each other. The two inner plates are connected to point A and the other two plates to another point A as shown in fig. Then the capacitance of the system is

    Four metallic plates, each with a surface area of one side A, are placed at a distance d apart from each other. The two inner plates are connected to point A and the other two plates to another point A as shown in fig. Then the capacitance of the system is

    In the circuit of fig. capacitors A and B have identical geometry, but a material of dielectric constant 3 is present between the plates of B. The potential difference across A and B are, respectively

    Thee plates A, B, C each of area 50 cm 2 have separation 3 mm between A and B and 3 mm between B and C fig. The energy stored when the plates are fully charged is

    A parallel plate capacitor with air as dielectric is charged to a potential V. It is then connected to an uncharged parallel plate capacitor filled with wax of dielectric constant K. The common potential of both capacitor is

    The plate separation in a parallel plate condenser is d and plate area is A. If it is charged to V volts, then the work done in increasing the plate separation to 2 d will be

    A condenser of capacity C 1 is charged to V volt. The energy stored in it is U. It is connected in parallel to another condenser of capacity C 2 . The energy loss in this process will be

    A potential difference of 2000 V is established between the parallel plates of a capacitor with air between the plates. If the air becomes conducting when the electric field exceeds 3 x 10 6 N/C, the minimum separation between the plates should be

    A capacitor of capacitance 160 μ F is charged to a potential difference of 200 V and then connected across a discharge tube which conducts until the potential difference across it has fallen to 100 V. The energy dissipated in the tube is

    An automobile spring extends 0.2 m for 5000 N load. The ratio of potential energy stored in the spring when it has been compressed by 0.2 m to the potential energy stored in a 10 μ F capacitor at a potential difference of 10,000 V is

    Capacitor A is charged to a potential of 100 V and, capacitor B is charged to a potential of 75 V. What are the charges on A and B after key is closed Fig.

    Two concentric spheres of radii R and r have similar charges with equal surface densities ( σ ). What is the electric potential at their common centre

    Twenty seven identical drops of mercury are charged simultaneously to the same potential of 10 units, Assuming the drops are made to combine to form one large drop, then its potential is

    Two spheres A and B of radii 17 cm each and having charges of 1 and 2 coulomb respectively are separated by a distance of 80 cm. The electric field at a point on the Iine joining the centres of two spheres is approximately zero at some distance from the sphere A. The electric potential at this point is

    A ring of radius I caries a charge +q. A test charge -q o is released on its axis at a distance 3 R from its centre. How much kinetic energy will be acquired by the test charge when it reaches the centre of the ring ?

    The electric potential at a point (x, y) in x-y plane is given by V = – k (xy). The field intensity at a distance r from the origin varies as

    A thin spherical conducting shell of radius fi has a charge q. Another charge Q is place at the centre of the shell. The electrostatic potential at a point P a distance R/2 from the centre of the shell is

    A point charge + q is placed at the origin as shown in fig. Work done in taking another point charge -Q from point A (0,a) to another point B (a,0) along the straight paths AB is

    The work done required to put the four charges together at the corners of a square as shown in fig. is

    A positive charge q and a negative charge -q are placed at x = -0 and x = + a respectively. The variation of V along X – axis is represented by the graph.

    Three point charges of equal value q are placed at the vertices of al equilateral triangle. The resulting lines of force should be sketch as in

    Two equal point charges are fixed at x = – α and x = + α on the X-axis . Another point charge Q is placed at the origin. The change in electrical potential energy of Q when it is displaced by a small distance x along the X-axis, is approximately proportional to

    Two identical capacitors are joined in parallel and charged to a potential V. They are then disconnected from the battery and connected to each other in series. The positive plate of one being connected to the negative of the other and two outer plates left unconnected. Which of the following statements is correct ?

    Force acting upon a charged particle kept between the plates of a charged capacitor is E If one of the plates of the capacitor is removed, force acting on the same particle will become

    An electron is accelerated through a potential difference of 2oo volts. If e I m for electron be 1.6×10 11 coulomb/kg, the velocity acquired by the electron will be

    The force of attraction between the plates of air filled capacitor having charge Q and area of each plate A is given by

    A parallel plate condenser with plate area A and separation d filled with dielectric as shown in fig. The dielectric constants are K 1 and K 2 respectively. The capacitors will be

    There is an air filled 1 pF parallel plate capacitor. When the plate separation is doubled and the space is filled with wax, the capacitance increases to 2 pF. The dielectric constant of wax is

    A parallel plate condenser having a plate separation of d is charged to a potential V. It is then isolated. The intensity of electric field between the plates is then found to be E. The separation between the plates is doubled. The new electric field intensity is

    If the potential of a capacitor having capacity 6 μ F is increased from t0 volt to 20 volt, thon increase in energy will be

    When two capacitors one of 3 μ F and the other of 6 μ F arc connected in series and the combination is charged to a potential difference of 120 volt, the potential difference across 3 μ F capacitor is

    The capacity of a parallel plate condenser is 10 μ F when the distance between its plate is 8 cm. If the distance between the plates is reduced to 4 cm, the capacity will be

    The plates of a parallel plate capacitor are charged up to 100 volt. A 2 mm thick plate is inserted between the plates, then to maintain the same potential difference, the distance between the capacitor plates is increased by 1.6 m.m. The dielectric constant of the plate is

    A capacitor of capacitance 1 μ F withstands a maximum voltage of 6 kV while another capacitor of capacitance 2 μ F, the maximum voltage 4 kV If they are connected in series, the combination can withstand a maximum of

    Two capacitors 2 μ F and 4 μ F are connected in parallel. A third capacitor of 6 μ F capacity is connected in series. The combination is then connected across a 12 V battery. The voltage across 2 μ F capacity is

    What is effective capacitance between points X and Y ?

    A parallel plate capacitor has plate area A and separation d. It is charged to a potential difference V o . The charging battery is disconnected and the plates are pulled apart to three times the initial separation. The work required to separate the plate is

    A capacitor is charged to store an energy U. The charging battery is disconnected. An identical capacitor is now connected to the first capacitor in parallel. The energy in each of the capacitor is

    Two capacitors A and B are connected in series with a battery as shown in fig. When the switch S is closed and the capacitors get charged fully, then

    Consider the situation shown in fig. The capacitor A has a charge q on it whereas B is uncharged. The charge appearing on the capacitor B a long time after the switch is closed is

    Two capacitors of capacitances 3 μ F and 6 μ F are charged to a potential to 12 v each. They are now connected to each other, with the positive plate of each joined to the negative plate of the other. The potential difference across each will be

    Four metallic plates, each with a surface area of one side A, are placed at a distance d from each other. The plates reconnected as shown in the fig. Then the capacitance of the system between A and B is

    In the circuit as shown in figure, the effective capacitance between A and B is

    ln the circuit shown in figure the potential difference across the 4.5 μ F capacitor is

    A 40 μ F capacitor is a defibrillator is charged to 3000 V The energy stored in the capacitance is sent through the patient during a pulse of duration 3 ms. The power delivered to the patient is

    Six metallic plates of each with a surface area of one side A, are placed at a distance d from each other. The alternate plates are connected to points P and Q as shown in fig. The capacitance of the system is

    In question , the capacitor is connected to a battery with terminal voltage V This connection is maintained while the dielectric slab is held in place by the application of a force F. The required force is plates of one of the capacitors so as to fill the gap, the battery remaining connected. The charge on each capacitor will be

    For the circuit shown, which of the following statements is true ?

    Two identical capacitors, have the same capacitance C. One of them is charged to potential V 1 and the other to V 2 . The negative ends of the capacitors are connected together. When the positive ends are also connected, the decrease in energy of the combined system is

    A fully charged capacitor has a capacitance C. It is discharged through a small coil of resistance wire embedded in a thermally insulated block of specific heat capacity s and mass n. If the temperature of the block is raised by ∆ T, the potential difference V across the capacitor is

    A condenser of 2 μ F capacity is charged steadily from o to 5 coulomb. Which of the following graphs correctly represents the variation of potential difference across its plates with respect to charge on the condenser

    Two insulating plates are both uniformly charged in such a way that potential difference between them is (V 2 -V 1 = 20 V) (i.e., plate 2 is at higher potential). The plates are separated by d = 0.1 m and can be treated as infintely large. An electron is released from rest on the inner surface of plate 1. What is its speed when it hits plate 2 ? (e = 1.6 x 10 -19 C, m e = 9.11x 10 -31 kg)

    As shown in the figure, charges + q and – q are placed at the vertices B and C of an isosceles triangle. The potential at the vertex A is

    Three charges Q, + q and +q are placed at the vertices of a right-angled isosceles triangle as shown. The net electrostatic energy of the configuration is zero if Q is equal to

    A hollow conducting sphere of radius R has a charge ( + Q ) on its surface. What is the electric potential within the sphere at a distance r = R 3 from its centre

    Two electric charges 12 μC and – 6 μC are placed 20 cm apart in air. There will be a point P on the line joining these charges and outside the region between them, at which the electric potential is zero. The distance of P from – 6 μC charge is

    The radius of a soap bubble whose potential is 16V is doubled. The new potential of the bubble will be

    In the rectangle, shown below, the two corners have charges q 1 = − 5 μC and q 2 = + 2 .0 μC . The work done in moving a charge + 3 .0 μC from B to A is (take 1 / 4 πε 0 = 10 10 N – m 2 ​ / C 2 )

    Two electric charges 12 μC and − 6 μC are placed 20 cm apart in air. There will be a point P on the line joining these charges and outside the region between them, at which the electric potential is zero. The distance of P from − 6 μC charge is

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