PhysicsPhysics QuestionsElectric Charges And Fields Questions for CBSE Class 12th

Electric Charges And Fields Questions for CBSE Class 12th

Charges q, 2q, 3q and 4q are placed at the comers A, B, C and D of a square as shown in the following figure. The direction of electric field at the centre of the square is along

Separation between two parallel plates facing each other is 2 cm and surface area l 2 = 10 cm 2 . If 10 6 electrons of velocity 10 8 m/s projected into the gap between plates of potential difference ∆ v = 400 V , the deflection of an electron is :

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    A dipole of dipole moment ‘p’ is placed in non-uniform electric field along x-axis. Electric field is increasing at the rate of 1 V /m, then the force on dipole is :

    A uniformly charged ring of charge Q and radius R is folded across its diameter such that two halves make an angle 60° with each other then net electric field at centre ‘O’ of ring is equal to :

    Three point charges+ q, – 2q and+ q are placed at points (x = 0, y = a, z = 0), (x = 0, y = 0, z = 0) and (x = a, y = 0, z = 0), respectively. The magnitude and direction of the electric dipole moment vector of this charge assembly are :

    An electron is moving towards x-axis. An electric field is along y-direction then path of electron is

    Figure shows the electric lines of force emerging from a charged body. If the electric field at A and B are E A a n d E B respectively and if the displacement between A and B is then

    A large plane charge sheet having charge density σ = 2 × 10 − 6 C / m 2 lies in the x − y plane. Find the flux of the electric field through a circular area of radius 1cm lying completely in the region where x ,   y ,   z are all positive and with its normal making an angle of 60 0 with the z − a x i s

    An inclined plane making an angle of 30 0 with the horizontal is placed in a uniform horizontal electric field of 100 V m . A particle of mass 1kg and charge 0.01C is allowed to slide down from rest from height of 1m. If the coefficient of friction is 0.2 , find the time taken by the particle to reach the bottom ( in seconds ) . Take g = 9.8   m / s 2

    A charged particle of radius 5 × 10 − 7 m is located in a horizontal electric field of intensity 6.28 × 10 5 V / m . The surrounding medium has the coefficient of viscosity η = 1.6 × 10 5 N − s / m 2 . The particle start moving under the effect of electric field and finally attains a uniform horizontal speed of 0.02   m / s . Find the × 10 8 number of electrons on it. Assume gravity free space

    A square surface of side L metre in the w plane of the paper is placed in a uniform electric field E (volt/m) acting along the same plane at an angle θ with the horizontal side of the square as shown in Fig. 2.117. The electric flux linked to the surface, in units of volt-m is :

    A charge situated at a certain distance from an electric dipole in the end-on position, experiences a force F If the distance of the charge is doubled, the force acting on the Charge will be

    Two electric dipoles of moment P and 64P are placed in opposite direction on a line at a distance of 25 cm. The electric field will be zero at point between the dipoles whose distance from the dipole of moment P is

    Consider an infinite line charge having uniform linear charge density and passing through the axis of a cylinder. What will be the effect on the flux passing through curved surface if the portions of the line charge outside the cylinder is removed?

    Statement I: A point charge q 0 is kept outside a solid metallic sphere; the electric field inside the sphere is zero. Statement II: Induced charge does not contribute to electric field or potential at a given point.

    Statement I: When a body acquires positive charge, its mass decreases. Statement II: A body acquires positive charge when it looses electrons.

    Four +ve point charges of same magnitude (Q) are placed at four comers of a rigid square frame as shown in figure. The plane of the frame is perpendicular to Z-axis. If a -ve point charge is placed at a distance z away from the above frame (z<<L), then

    A hollow cylinder has a charge q coulomb within it. If ϕ is the electric flux in unit of volt-meter associated with the curved surface B, the flux linked with the plane surface A in unit of volt-metre will be

    A metallic shell has a point charge ‘q’ kept inside its cavity. Which one of the following diagrams correctly represents the electric lines of forces?

    An insulating long light rod of length L pivoted at its centre O and balanced with a weight W at a distance X from the left end as shown in figure. Charges q and 2q are fixed to the ends of the rod. Exactly below each of these charges at a distance h a positive charge Q is fixed. Then x is

    In a region, the intensity of an electric field is given by E = 2 i ^ + 3 j ^ + k ^ in NC − 1 . The electric flux through a surface S = 10 i ^ m 2 in the region is:

    The inward and outward electric flux for a closed surface in units of N-m 2 /C are respectively 8 x 10 3 and 4 x 10 3 . Then the total charge inside the surface is: [where ε 0 = permittivity constant]

    Two point charges q 1 = 2 μ C a n d q 2 = 1 μ C are placed at distances b=1cm and a=2cm from the origin on the Y and X axes as shown in figure. The electric field vector at point P(a,b) will subtend an angle θ with the X-axis is given by tan θ =

    What is the angle (in degrees) between the electric dipole moment and the electric field strength due to it on the equatorial line ?

    There exists an electric field of 1 N/C along y-direction. The flux passing through the square of 1 m placed in xy-plane inside the electric field is :

    Three metallic spheres say X, Y and Z have charges 10 C,-10 C, 10 C, respectively. X, Y and Z are brought in contact such that charge on both X and Y becomes 3 C. What is charge on Z ?

    Consider a uniform electric field E == 3 × 10 3 i ⏜ N / C . What is the flux of this field through a square of 10 cm on a side whose plane is parallel to the yz-plane?

    A cube of side b has a charge q at seven of its vertices. The electric field due to this charge distribution at the centre of this cube will be:

    The ratio of the forces between two small spheres with constant charge (a) in air (b) in a medium of dielectric constant K is

    In the given figure distance of the point from A where the electric field is zero is

    For a dipole q = 2 × 10 − 6 C and d = 0.01  m . Calculate the maximum torque for this dipole if E = 5 × 10 5 N / C .

    The electric field at a point on the equatorial plane at a distance r from the centre of a dipole having dipole moment p is given by, (r >> separation of two charges forming the dipole, ϵ 0 – permittivity of free space)

    The acceleration of an electron due to the mutual attraction between the electron and a proton when they are 1.6 Å apart is, m e ≃ 9 × 10 − 31 kg , e = 1 .6 × 10 − 19 C (Take 1 4 πε 0 = 9 × 10 9 Nm 2 C − 2

    A block having mass m and charge q is resting on a frictionless plane at a distance L from the wall as shown. A uniform electric field E is switched on as shown. If the collision of the block with wall is perfectly elastic, the time taken by the block to return to the initial position is

    An electric field E = x i ^ exist in space. Find work done to move 2C charge particle from A (0, 0) to B (2, 2).

    Two particles each having a Mass of 5g and charge 1 × 10 − 7 C , stays in limiting equilibrium on a horizontal table with a separation of 10cm between them. The coefficient of friction between each particle and the table is same. Find the value of coefficient of friction

    A molecule of a substance has permanent dipole moment p . A mole of this substance is polarised by applying a strong electrostatic field E. The direction of the field is suddenly changed by an angle of 60 o . If N is the Avagadro’s number, the amount of work done by the field is :

    The figure shows electric field lines in which an electric dipole P is placed as shown. Which of the following statements is correct?

    Four electrical charges are arranged on the corners of a 10 cm square as shown. What would be the direction of the resulting electric field at the center point P?

    In finding the electric field using Gauss law the formula E = q e n c ∈ 0 A is applicable. In the formula ∈ 0 is permittivity of free space, A is the area of Gaussian surface and q e n c is charge enclosed by the Gaussian surface. This equation can be used in which of the following situation?

    Two large parallel sheets A and B have charge densities + 2   nC / m 2 and − 5   nC / m 2 . If P is a point in space outside the sheets. Then electric field at P is

    Two identical small charged spheres A and B , each carrying a charge Q are suspended from a point O by two light non-conducting strings each of length l = 1m. Equilibrium separation between the spheres is found to be 10 mm. Now some more charge is supplied to the spheres so that charge on each sphere becomes 8Q. Then new equilibrium separation between the spheres is

    A, B and C are spherical Gaussian surfaces as shown in figure. Then

    Proton and deuteron are placed in a uniform electric field and allowed to move for same time. The ratio of their kinetic energies will be

    There is a uniform electric field of strength 10 3 V /m along y-axis. A body of mass 1 gm and charge 10 – 6 C is projected into the field from origin along the positive x-axis with a velocity 10 m/s. Its speed in m/s after 10 s is (Neglect gravitation)

    What is the electric flux linked with closed surface?

    Electric charge is uniformly distributed along a straight wire of radius 1 mm. The charge per centimetre length of the wire is Q coulomb. Another cylindrical surface of radius 50 cm and length 1 m symmetrically encloses the wire as shown in figure. The total electric flux passing through the cylindrical surface is

    At a point 20 cm from the centre of a uniformly charged dielectric sphere of radius 10 cm, the electric field is 100 V /m. The electric field at 3 cm from the centre of the sphere will be

    An electron moving with the speed 5 x 10 6 m/s is shot parallel to the electric field of intensity 1 x 10 3 N/C. Field is responsible for the retardation of motion of electron. Evaluate the distance travelled by the electron before coming to rest for an instant? (Mass of e = 9 x 10 – 31 kg, charge= 1.6 x 10 – 19 C)

    Electric field at a point varies as r o for

    An electron is released with a velocity of 5 × 10 6 ms – 1 in an electric field of 10 3 N C – 1 which has been applied so as to oppose its motion. How much time could it take before it is brought to rest?

    If the electric flux entering and leaving an enclosed surface respectively is ϕ 1 and ϕ 2 , then the electric charge inside the surface will be

    The electric field in a certain region is acting radially outward and is given by E = Ar. A charge contained in a sphere of radius ‘a’ centred at the origin of the field, will be given by :

    In the following four situations, charged particles are at equal distance from the origin. Arrange them according to the magnitude of the net electric field at origin, greatest being first.

    The number of electrons to be put on a spherical conductor of radius 0.1 m to produce an electric field of 0.036 N/C just above its surface is

    An electric dipole is placed at the origin O and is directed along the x-axis. At a point P, far away from the dipole, the electric field is parallel to y-axis. OP makes an angle θ with the x-axis, then

    Two short dipoles p k ^ and p 2 k ^ are located at (0,0,0) and (1 m, 0, 2 m), respectively. The resultant electric field due to the two dipoles at the point (1 m, 0, 0) is

    Three point charges + q, -2q and +q are placed at points (x = 0, y = a, z = 0), (x = 0, y = 0, z = 0) and (x = a, y = 0, z = 0), respectively. The magnitude and direction of the electric dipole moment vector of this charge assembly are

    Statement I: Vehicle carrying highly inflammable materials have hanging chains, slightly touching the ground. Statement II: The body of a vehicle gets charged when moving through air at high speed.

    Statement I: On going away from a point charge or a small electric dipole, electric field decreases at the same rate in both the cases. Statement II: Electric field is inversely proportional to square of distance from a charge or an electric dipole.

    It has been experimentally observed that the electric field in a large region of earths atinosphere is directed vertically down. At an altitude of 300 m, the electric field is 60 vm -1 . At an altitude of 200 m, the field is 100 vm -1 . Find the net amount of charge contained in the cube of 100 m edge, located between 200 m and 300 m altitude is

    A copper sphere of mass 2.0 g contains about 2 x 10 22 atoms. The charge on the nucleus of each atom is 29 e (e = electronic charge). The mass of an electron is 9.11 x 10 -31 kg.How much mass will the sphere lose or gain if it is given a charge of +2 μ C?

    Two infinitely long parallel wires having linear charge densities λ 1 and λ 2 respectively are placed at a distance of R meters. The force per unit length on either wire will be k = 1 4 π ε 0

    There is a uniform electric field of strength 10 3 V/m along y-axis. A body of mass 1g and charge 10 -6 C is projected into the field from origin along the positive x-axis with a velocity 10 m/s. Its speed in m/s after 10 s is (Neglect gravitation)

    Three identical spheres, each having a charge q and radius R, are kept in such a way that each touches the other two. The magnitude of the electric force on any sphere due to the other two is

    If the flux of the electric field through a closed surface is zero, then

    A positively charged ball hangs from a long silk thread. Electric field at a certain point (at the same horizontal level of ball) due to this charge is E. Let us put a positive test charge q 0 at this point and measure F/q 0 on this charge. Then, E

    An electron falls through a small distance in a uniform electric field of magnitude 2 x 10 4 NC -1 . The direction of the field is reversed keeping the magnitude unchanged and a proton falls through the same distance. The time of fall will be

    Under what conditions can the electric flux ϕ E be found through a closed surface?

    Three charges q 1 = 1 × 10 − 6 C , q 2 = 2 × 10 − 6 C and q 3 = − 3 × 10 − 6 C have been placed as shown in figure. Then the net electric flux will be maximum for the surface

    A ring of charge with radius 0.5 m has 0.002 π m gap. If the ring carries a charge of +1 C, the electric field at the center is

    A positive point charge 50 μ C is located in the plane xy at a point with radius vector r 0 = 2 i ^ + 3 j ^ . The electric field vector, E at a point with radius vector r = 8 i ^ − 5 j ^ , where r 0 and r are expressed in meter, is

    Consider two concentric spherical surfaces S 1 with radius a and S 2 with radius 2a, both centered at the origin. There is a charge +q at the origin and there are no other charges. Compare the flux ϕ 1 through S 1 with the flux ϕ 2 through S 2 .

    An electric dipole of moment p 1 = p i ^ is placed at the origin and the electric field at point. A(r, o) is found to be E.Now another electric dipole of moment p 2 = p j ^ is placed at the origin. Then the resultant electric field at point A will be

    A large charged non-conducting sheet having surface charge density + σ coul / m 2 , is placed to the left of an uncharged matallic plate P as shown in figure. Then the inducted surface charge density on the right face of the plate P is

    A thin copper ring of radius ‘a’ is charged with q units of electricity. An electron is placed at the centre of the copper ring. If the electron is displaced a little, it will have frequency.

    The magnitude of the electric field intensity at point B 2 , 0 , 0 due to a dipole moment, P = i ^ + 5 j ^ kept at origin is n × K (assume that the point B is at large distance from the dipole and K = 1 4 π ε 0 ) (All quantities are in S.I units) Find n.

    A disc having uniform surface charge density + σ in upper half and − σ in lower half is placed on a rough horizontal surface as shown in figure. A uniform electric field is set up as shown. If mass of disc is M and its radius is R, as well sufficient friction is present to prevent slipping, the acceleration of disc is

    A tiny spherical oil drop carrying a net charge q is balanced in still air with a vertical uniform electric field of strength 81 π 7 × 10 5  V / m . When the field is switched off, the drop is observed to fall with terminal velocity 2 × 10 − 3  m / s . Given g = 9.8  m / s 2 , viscosity of the air 1.8 × 10 − 5   Ns / m 2 and the density of oil 900 k g m – 3 . The magnitude of q is:

    Two point charges q 1 and q 2 are placed at (0,0,0) and (1,2,2) m respectively. They repel each other with force of 3 N. The force on q 2 due to q 1 is F 21 = ( x i ^ + y j ^ + z k ^ ) N The value of x+y+z is .

    Two particles of masses in the ratio 1 : 2, with charges in the ratio 1 : 1, are placed at rest in a uniform electric field. They are released and allowed to move for the same time. The ratio of their kinetic energies will be finally

    The electric field on two sides of a large charged plate is shown in figure. The charge density on the plate in SI units is given by ( ε 0 is the permittivity of free space in SI units)

    Figure shows, in cross section, three solid cylinders, each of length L and uniform charge Q. Concentric with each cylinder is a cylindrical Gaussian surface, with all three surfaces having the same radius. Rank the Gaussian surfaces according to the electric field at any point on the surface, greatest first.

    A block of mass m containing a net negative charge -q is placed on a frictionless horizontal table and is connected to a wall through an unstretched spring of spring constant k. If the horizontal electric field E parallel to the spring is switched on, then the maximum compression of the spring is

    A particle of mass m and charge -q moves diametrically through a uniformly charged sphere of radius R with total charge Q. The angular frequency of the particle’s simple harmonic motion, if its amplitude <R, is given by

    A block of mass m is suspended vertically with a spring of spring constant k. The block is made to oscillate in a gravitation field. Its time period is found to be T. Now the space between the plates is made gravity free, and an electric field E is produced in the downward direction. Now the block is given a charge q. The new time period of oscillation is

    A dielectric in the form of a sphere is introduced into a homogeneous electric field. A, B, and C are three points as shown in figure. Then

    A system consists of a thin charged wire ring of radius r and a very long uniformly charged wire oriented along the axis of the ring, with one of its ends coinciding with the center of the ring. The total charge on the ring it q, and the linear charge density on the straight wire is λ . The interaction force between the ring and the wire is

    A positively charged sphere of radius r 0 carries a volume charge density ρ (figure). A spherical cavity of radius r 0 / 2 is then scooped out and left empty. C 1 is the center of the sphere and C 2 that of the cavity. What is the direction and magnitude of the electric field at point B?

    Two identical spheres of same mass and specific gravity (which is the ratio of density of a substance and density of water) 2.4 have different charges of Q and-3Q.They are suspended from two strings of same length l fixed to points at the same horizontal level, but distant l from each other. When the entire set up is transferred inside a liquid of specific gravity 0.8, it is observed that the inclination of each string in equilibrium remains unchanged. Then the dielectric constant of the liquid is

    In a region of space, the electric field is in the x-direction, proportional to x and given by E = αx i ^ , where α is a positive constant. Consider an imaginary cubical volume of edge a, with its edges parallel to the axes of coordinates. The charge inside this cubical volume is

    A positive point charge 50 μ C is located in the plane x-y at the point with radius vector r 0 = 2 i ^ + 3 j ^ where i ^ and j ^ are the unit vectors of the x and y axes. The magnitude of electrostatic force F on a charge of 2 μC placed at the point with radius vector r = 8 i ^ – 5 j ^ is (Here r 0 and r are expressed in meter)

    The distance between the two charges 25 μC and 36 μC IS 11 cm. At what point on the line joining the two, the intensity will be zero?

    The total electric flux emanating from a closed surface enclosing an α -particle (e =electronic charge) is:

    A ball of mass 2 kg, charge 1 C is dropped from top of a high tower. In space electric field exist in horizontal direction away from tower which varies as E = ( 5 − 2 x ) Vm − 1 . Find maximum horizontal distance (in m) that the ball can go from the tower.

    It is required to hold four equal point charges each having a charge Q= 8 7 ( 1 − 2 2 ) C in equilibrium at the corners of a square. Find the point charge, in coulomb, that will do this if placed at the center of the square.

    In a uniformly charged sphere of total charge Q and radius R, the electric field E is plotted as a function of distance from the centre. The graph which would correspond to the above is

    A small mercury drop is charged such that its surface charge density is 2 μC / m 2 . Exactly 125 such drops are combined to form a big drop. What is the surface charge density of the big drop?

    The insulation property of air, breaks at E = 3 x 10 6 N /C. The maximum charge that can be given to a sphere of diameter 5 metre is approximately (in coulomb) :

    Two electric dipoles each of dipole moment p = 6.2 x 10 -3 C cm are placed with their axis along the same line and their centres at a distance d = 10 -8 m. What is force of attraction between dipoles?

    A point particle of mass m is attached to one end of massless rigid non-conducting rod of length l. Another point particle of same mass is attached to the other end of the rod. The two particles carry equal charges +q and -q respectively. This arrangement is held in a region with the field E such that the rod makes an angle θ with the field direction :

    In the given figure distance of the point from A where the electric field is zero is

    A cube of a metal is given a positive charge Q. For the above system, which of the following statements is true

    Two identical charged spheres suspended from a common point by two massless strings of lengths l, are initially at a distance d(d<<l) apart because of their mutual repulsion. The charges begin to leak from both the spheres at a constant rate. As a result, the spheres approach each other with a velocity V. Then V varies as a function of the distance x between the spheres, as

    Two point charges each 10 – 6 C are placed at A ( i ^ + j ^ + k ^ ) m and B ( 2 i ^ + 3 j ^ + 3 k ^ ) m . The force between those charges is

    A hollow metal sphere of radius R is uniformly charged. The electric field due to the sphere at a distance r from the centre

    Two point charges A and B , having charges +Q and -Q respectively, are placed at certain distance apart and force acting between them is F . If 25% charge of A is transferred to B , then force between the charges becomes

    Electric flux through a surface area of 100 m 2 lying in the x y plane is in V − m if E = i ^ + 2 j ^ + 3 k ^

    A point charge Q is placed at the vertex of a cone with height 12 cm and radius 5 cm. Then electric flux through the curved surface of the cone is

    An electric dipole P = p 2 i ^ − j ^ is placed at the origin. Then the angle between electric field vector E at point (a, a) and the positive x-axis is

    A small element Δ l is cut from a circular ring of radius R and λ coulomb charge per unit length. The net electric field at the centre of ring is

    An electric charge Q exerts a force F on a similar electric charge Q separated by a distance γ . A third Q/4 is placed midway between the two charges. Now the force experienced by the charge Q will be

    A is a point on the axis of the electric dipole as shown in figure. Distance O A = γ B is another point at a distance γ from the center O of the Q dipole. If electric potential at A is 1 volts, potential at B is

    A cube has side of length 50 cm. A point charge of +35.4 μ C is kept at the mid point of one edge. The total electric flux over the entire surface of the cube is

    An electric dipole is placed in a non-uniform electric field. Then the electric force on the dipole depends upon

    An electric dipole of moment p = − i ^ − 3 j ^ + 2 k ^ × 10 − 29 C m is at the origin 0 , 0 , 0 . The electric field due to the dipole at r = + i ^ + 3 j ^ + 5 k ^ (note that r . p = 0 ) is parallel to:

    Two point charges +Q and +4Q are kept at a separation l. A third negative point charge is kept at point such that the system of three charges is in equilibrium. Then the third charge is

    In a region of space, the electric field increases radially as E = − 90  r r ^ . The electric charge contained within a sphere of radius 2m centred at origin is

    Electric lines of force are open curves on account of

    A point charge of 100   μ C is placed at 3 i ^ + 4 j ^ m . Find the electric field intensity due to this charge at a point located at 9 i ^ + 12 j ^ m .

    A   body has a charge of -3 μC . If it has 2.5 × 10 13   protons ,   then   how many electrons the body has ?

    A charged particle (mass m and charge q) moves along X axis with velocity V 0 . When it passes through the origin it enters a region having uniform electric field. E = − E j ^ which extends upto x = d . Equation of path of electron in the region x > d is

    Two short dipoles each of dipole moment p are placed at origin. The dipole moment of one dipole is along x-axis, while that of other is along y-axis. The electric field at a point (a, 0) is given by k = 1 4 π ε 0

    An electric dipole p = 8 × 10 − 9 i ^   C − m is placed at the origin. If electric field at a point P ( a , a ) is E, what is the electric field at a point Q ( 0 , 2 a )

    A glass rod rubbed with silk is used to charge a gold leaf electroscope and the leaves are observed to diverge. The electroscope thus charged is exposed to X-rays for a short period. Then

    A positively charged insulator is brought near (but does not touch) two metallic spheres that are in contact. The metallic spheres are then separated. The sphere which was initially farthest from the insulator will

    If a body is charged by rubbing, its weight

    Two point charges placed at a distance r in air experience a certain force. Then the distance at which they will experience the same force in a medium of dielectric constant K is

    If an electric dipole is kept in an uniform electric field then

    The given figure gives electric lines of force due to two charges q 1 and q 2 . What are the signs of the two charges?

    Figure shows the electric field lines around three point charges A, B and C. Which of the following charges are positive?

    Which of the following figure represents the electric field lines due to a combination of one positive and one negative charge?

    Which of the following represents the electric field lines due to a combinations of two negative charges?

    Consider the four field patterns shown. Assuming there are no charges in the regions shown, which of the patterns represents a possible electrostatic field?

    The lines of force of the electric field due to two charges q and Q are sketched in the figure. State if

    Figure shows tracks of three charged particles crossing a uniform electrostatic field with same velocities along horizontal. Which particle has the highest charge to mass ratio?

    The inward and outward electric flux for a closed surface in units of N- m 2 /C are respectively 8 × 10 3 and 4 × 10 3 . Then the total charge inside the surface is (where ε o = permittivity constant)

    A cone lies in a uniform electric field E as shown in figure. The electric flux entering the cone is

    Let there be a spherically symmetric charge distribution with charge density varying as ρ ( r ) = ρ 0 5 4 – r R upto r = R, and ρ (r) = 0 for r > R, where r is the distance from the origin. The electric field at a distance r( r < R) from the origin is given by :

    Three charges of (+2q), (- q) and (- q) are placed at the corners A, B and C of an equilateral triangle of side a as shown in the figure. The magnitude of dipole moment of this combination is

    An electric dipole consisting of two opposite charges of 2 x 10 – 6 C each separated by a distance of 3 cm is placed in an electric field of 2 x 10 5 N/C. The maximum torque on the dipole will be

    An electric dipole is kept in non-uniform electric field. It experiences

    The electric field at a point on equatorial line of a dipole and direction of the dipole moment

    A point Q lies on the perpendicular bisector of an electrical dipole of dipole moment p. If the distance of Q from the dipole is r (much larger than the size of the dipole), then electric field at Q is proportional to

    If E a be the electric field strength of a short dipole at a point on its axial line and E e that on the equatorial line at the same distance, then

    An electric dipole in a uniform electric field experiences (When it is placed at an angle θ ( ≠ 0 ° o r 180 ° with the field)

    An electric dipole consists of two equal and opposite charges placed 2 cm apart. When the dipole is placed in a uniform electric field of strength 10 5 NC – 1 , it experiences a maximum torque of 0 . 2 × 10 – 3 Nm. Find the magnitude of each charge.

    An electric dipole is placed along the x-axis at the origin O. A point P is at a distance of 20 cm from this origin such that OP makes an angle π 3 with the x-axis. If the electric field at P makes an angle θ with x-axis, the value of θ would be

    The electric field due to an electric dipole at a distance r from its centre in axial position is E. If the dipole is rotated through an angle of 90° about “its perpendicular axis, the electric field at the same point will be

    If there are two metallic spheres of same radii but one is solid and the other is hollow, then

    A thin metallic spherical shell contains a charge Q on it. A point charge q is placed at the centre of the shell and another charge q 1 is placed outside it as shown in figure. All the three charges are positive. The force on the charge at the centre is

    A charge Q is fixed at a distance d in front of an infinite metal plate. The lines of force are represented by

    Which of the following curves shown below can possibly represents electrostatic field lines?

    An uncharged sphere of metal is placed in between two charged plates as shown. The lines of force look like

    Three equal charges each having charge +q are placed at the corners of an equilateral triangle of side a. Then the Coulomb force experienced by one charge due to rest of the two is

    A semicircular wire is uniformly charged with linear charge density dependent on the angle θ from y-direction as λ = λ 0 | sin ⁡ θ | , where λ 0 is a constant. The electric field intensity at the centre of the arc is

    A thin non-conducting ring of radius R has a linear charge density λ = λ 0 cos ⁡ θ , where θ is measured as shown. The total electric dipole moment of the charge distribution is

    The diagram shows a uniformly charged hemisphere of radius R. It has volume charge density ρ . If the electric field at a point 2R distance above its centre is E, then what is the electric field at the point which is 2R below its centre?

    Flux passing through shaded surface of sphere when a point charge q is placed at the centre is (radius of the sphere is R)

    Cathode rays travelling from east to west enter into region of electric field directed towards north to south in the plane of paper. The deflection of cathode rays is towards

    A square surface of side L metre is in the plane of the paper. A uniform electric field E (V /m), also in the plane of the paper, is limited only to the lower half of the square surface (see figure). The electric flux in SI units associated with the surface is

    Two infinitely long parallel conducting plates having surface charge densities + σ and – σ , respectively, are separated by a small distance. The medium between the plates is vacuum. If £o is the dielectric permittivity of vacuum, then the electric field in the region between the plates is

    Statement I: When charges are shared between any two bodies, no charge is really lost, but some loss of energy does occur. Statement II: Conservation of energy does not hold in every situation.

    Statement I: A charged particle is free to move in an electric field. It does not move along an electric line of force. Statement II: Charged particle’s initial position decides that it will move along the line of force or not.

    An electric dipole placed in a non-uniform electric field experiences

    Three charges 2q, -q, -q are located at the vertices of an,equilateral triangle. At the centre of the triangle

    A linear charge having linear charge density λ penetrates a cube diagonally and then it penetrates a sphere diametrically as shown. What will be the ratio of flux coming out of cube and sphere

    Two opposite and equal charges 4 x l0 -8 coulomb when placed 2 x 10 -2 cm away, form a dipole. If this dipole is placed in an external electric field 4 x 10 8 newton/ coulomb, the value of maximum torque and the work done in rotating it through 180 ° will be

    Two copper balls, each weighing 20 g are kept in air 10 cm apart. If one electron from every 10 6 atoms is transferred from one ball to the other, the coulomb force between them is (atomic weight of copper is 63.5)

    Five point charges, +q each, are placed at the five vertices of a regular hexagon. The distance of the center of the hexagon from any of the vertices is a. The electric field at the center of the hexagon is

    A and B are two points on the axis and the perpendicular bisector, respectively, of an electric dipole. A and B are far away from the dipole and at equal distances from it. The fields at A and B are E A and E B Then

    Charge on an originally uncharged conductor is separated by holding a positively charged rod very closely nearby, as shown in figure. Assume that the induced negative charge on the conductor is equal to the positive charge q on the rod. Then the flux through surface S 1 is

    A point charge q= -8.0 nC is located at the origin. The electric field (in NC -1 ) vector at the point x = 1.2 m, y = -1.6 m, as shown in figure, is

    In a certain region of space, there exists a uniform electric field of value 20 × 10 2 k ^ Vm − 1 . A rectangular coil of dimension 10 cm x 20 cm is placed in the xy plane. The electric flux through the coil is

    In a region of space, the electric field is given by E = 8 i ^ + 4 j ^ + 3 k ^ . The electric flux through a surface of area 100 units in the xy plane is

    In the arrangement shown in figure, electric flux through the closed surface 1 is Φ, through the closed surface 2 is 2Φ and through the closed surface 3 is 3Φ. Then the electric flux through a closed surface which encloses the charges Q 1 and Q 2 and Q 3 will be

    in a region of space electric charge in uniformly distributed throughout the volume. A cube of edge length l is placed in the region and electric flux from the entire surface of the cube is found to be Φ. If a cube of edge length 3l is placed to that region, the electric flux from the surface of the cube will be

    A proton is projected with a velocity V o towards a large sheet of charge having surface charge density σ coul / m 2 . From what distance should the proton be projected so that it just fails to strike the sheet of charge?

    An electric dipole is placed at the origin as shown in figure. A, B, C and D are four points where the electric fields are perpendicular to the dipole axis. Then which of the following figures is correct?

    The figure shows electric fields lines in a region of space. A positively charged particle is released at some point P on the field line AB. then

    Four positive point charges( +q) are kept at the four corners of a square of a side ‘ l ‘. The net electric field at the mid point of any one side of the square is, take 1 4 πε 0 = K :

    If the electric field lines in a region of space are parallel to each other with equal spacing in between themselves then the field is

    In a gravity free region of space, a charged particle is projected. If the path followed by the particle is a parabola, then in that region

    A particle having charge that of an electron and mass 1.6x 10 -30 kg is projected with an initial speed u at an angle 45° to the horizontal from the lower plate of a parallel plate capacitor as shown in figure. The plates are sufficiently long and have separation 2 cm. The maximum value of velocity of particle not to hit the upper plate is W × 10 6 m/s. Take electric field between the plates = 10 3 V/m directed upward. The value of W is

    A flat, square surface with sides of length L is described by the equations x = L , 0 ≤ y ≤ L , 0 ≤ z ≤ L The electric flux through the square due to a positive point charge q located at the origin (x = 0, y = 0, z = 0) is

    The electric field E 1 at one face of a parallelopiped is uniform over the entire face and is directed out of the face. At the opposite face, the electric field E 2 is also uniform over the entire face and is directed into that face (as shown in figure). The two faces in question are inclined at 30 o from the horizontal, E 1 and E 2 (both horizontal) have magnitudes of 2 . 50 × 10 4 NC − 1 and 7.00 × 10 4 NC − 1 , respectively. Assuming that no other electric field lines cross the surfaces of the parallelopiped, the net charge contained within is

    Two charged particles (M,+Q) and (m,-q) are placed in a gravity free space where a uniform electric field E exists. After the particles are released, they stay at a constant distance from each other. What is this distance? Neglect Gravitational interaction. k is electrostatic constant.

    A thin glass rod is bent into a semicircle of radius r. A charge +Q is uniformly distributed along the upper half, and a charge -Q is uniformly distributed along the lower hall as shown in figure. The electric field E at P, the center of the semicircle, is

    A charged dust particle of radius 5 × 10 − 7 m is moving in a horizontal electric field of intensity 6.28 × 10 5 V / M . The surrounding medium is air with coefficient of viscosity η = 1.6 × 10 − 5 N − s / m 2 . If this particle is moving with a uniform horizontal speed of 0.02 m/s, the number of excess electrons on the drop are 6k. The value of k is .

    S 1 and S 2 are two hollow concentric spheres with charge q and 2q. Space between S 1 and S 2 is filled with a dielectric of dielectric constants. The ratio of flux through S 2 and flux through S 1 is K. Then, the value of 9 K 11 is .

    A nonconducting sphere of radius R is filled with uniform volume charge density – ρ . The center of this sphere is displaced from the origin by d . The electric field E at any point P having position vector inside the sphere is

    Two point charges q 1 = 4 μC and q 2 = 9 μC are placed 20 cm apart. The electric field due to them will be zero on the line joining them at a distance of

    A metallic sphere is placed in a uniform electric field. The lines of force follow the path(s) shown in the figure as

    Two large parallel planes charged uniformly with surface charge density σ and – σ are located as shown in the figure. Which one of the following graphs shows variation of electric field along a line perpendicular to the planes as one moves from A to B ?

    A charge having magnitude Q is divided into two parts q and Q-q which are held a certain distance r apart. The force of repulsion between the two parts will be maximum if the ratio q/Q is

    The flux (in Vm) of electric field E = 200 i ^ N/C through a cube of side 10cm, oriented so that its faces are parallel to the coordinate axes is

    A charge q is located at the centre of a cube, the electric flux through any face is

    A charge q is located at the centre of a cube. The electric flux through any face is :

    Electric field at a point of distance r from a uniform charged wire of infinite length having linear charge density λ is directly proportional to:

    Electric field intensity at a point in between two parallel sheets with like charges of same surface charge densities σ is

    A copper atom consists of copper nucleus surrounded by 29 electrons. The atomic weight of copper is 63.5gmol -1 . Let us now take two pieces of copper each weighing 10 g. Let us transfer one electron from one piece to another for every 1000 atoms in that piece The coulomb force between the two pieces after transfer of electrons if they are 1 cm apart is p × 10 16 N. Find p . (Avogadro number N A = 6 x 10 23 mole -1 , charge on an electron = -1.6 x 10 -19 coulomb)

    Two Point Charges q A =3 μC and q B = − 3 μC are located 20 cm apart in vacuum. What is the electric field at the midpoint O of the line AB joining the two charges?

    A particle of mass m and -q enters the region between the two charged plates initially moving along x-axis with speed V x as shown in the given figure. The length of plate is L and a uniform electric field E is maintained between the plates. Find the vertical deflection of the particle at the far edge of the plate.

    Find the magnitude of the electric field at the point P in the configuration shown in figure for d > > a . Take 2qa = p.

    A hemispherical body is placed in a uniform electric field E. What is the flux linked with curved surface, if field is perpendicular to base in figure.

    A point charge +10 μC is a distance 5cm directly above the centre of a square of side10 cm ,as shown in the figure. What is the magnitude of the electric flux through the square?

    A uniformly charged conducting sphere of 2.4 m diameter has a surface charge density of 80.0 μC / m 2 . What is the total electric flux leaving the surface of the sphere?

    Three positive point charges q 1 , q 2 , and q 3 form an isolated system. Suppose the charges have generated a property due to which like charges also attract. The charges are moving along a circle with same speed maintaining angles as shown in the figure. The charge q 1 experiences a force f 1 due to other two charges. Similarly, q 2 experiences a force f 2 and q 3 , a force f 3 . The ratio f 1 : f 2 : f 3 , the ratio of masses of the charge particles q 1 , q 2 , and q 3 is

    The law, governing the force between electric charges is known as

    A body can be negatively charged by

    An isolated solid metallic sphere is given + Q charge. The charge will be distributed on the sphere

    Dielectric constant of pure water is 81. Its permittivity will be

    Three equal charges are placed on the three corners of a square. If the force between q 1 and q 2 is F 12 and that between q 1 and q 3 is F 13 , the ratio of magnitudes F 12 F 13 is

    With the rise in temperature, the dielectric constant K of a liquid

    Force of attraction between two point charges Q and – Q separated by d metre is F e . When these charges are placed on two identical spheres of radius R = 0.3d whose centres are d metre apart, the force of attraction between them is

    Two charges each equal to 2 μC are 0.5 m apart. If both of them exist inside vacuum, then the force between them is

    A charge Q is divided into two parts of q and Q – q . If the coulomb repulsion between them when they are separated is to be maximum, the ratio of Q q should be

    Two point charges 3 × 10 − 6 C and 8 × 10 − 6 C repel each other by a force of 6 × 10 − 3 N . If each of them is given an additional charge – 6 × 10 6 C , the force between them will be

    Two small conducting spheres of equal radius have charges + 10 μC and – 20 μC respectively and placed at a distance R from each other experience force F 1 . If they are brought in contact and separated to the same distance, they experience force F 2 . The ratio of F 1 to F 2 is

    Two charges +4e and +e are at a distance x apart. The distance, a charge q must be placed from charge +e so that it is in equilibrium, is nx . The value of n is

    Three identical point charges, as shown are placed at the vertices of an isosceles right angled triangle. Which of the numbered vectors coincides in direction with the electric field at the mid-point M of the hypotenuse

    The electric field inside a spherical shell of uniform surface charge density is

    The number of electrons to be put on a spherical conductor of radius 0.1 m to produce an electric field of 0 .036 N / C just above its surface is

    Equal charges q are placed at the vertices A and B of an equilateral triangle ABC of side a. The magnitude of electric field at the point C is

    An electron of mass m e initially at rest moves through a certain distance in a uniform electric field in time t 1 . A proton of mass m p also initially at rest takes time t 2 to move through an equal distance in this uniform electric field. Neglecting the effect of gravity, the ratio of t 2 / t 1 is nearly equal to

    Two charges + 5 μC and + 10 μC are placed 20 cm apart. The net electric field at the mid-Point between the two charges is

    The electric field due to a charge at a distance of 3 m from it is 500 N/coulomb. The magnitude of the charge is 1 4 πε 0 = 9 × 10 9 N − m 2 coulomb 2

    If q is the charge per unit area on the surface of a conductor, then the electric field intensity at a point on the surface is

    An electron enters in an electric field with its velocity in the direction of the electric lines of force. Then

    There are two equally charged identical metal spheres A and B repel each other with a force 3 × 10 -5 N. Another identical uncharged sphere C is touched with A and then placed at the mid-point between A and B. Net force on C is

    Four point charges 1 μ C , – 2 μ C , 3 μ C and – 2 μ C are arranged on the four vertices of a square of side 1 cm. The dipole moment of this charge assembly is

    A uniformly charged non-conducting hemispherical shell is shown in figure. What is correct direction of net electric field at point A on its open plane surface.

    Two charges q and – 3q are fixed on x-axis separated by distance d. Where should a third charge 2q be placed from A such that it will not experience any force?

    The electric field in a region of space is given by E = 5 i ^ + 2 j ^     NC − 1 . The electric flux due to this field through an area 2 m 2 lying in the Y Z plane in S.I. units is

    A bob of a simple pendulum of mass 40 gm with a positive charge 4 x 10 – 6 C is oscillating with time period ‘ T 1 ‘. An electric field of intensity 3.6 x 10 4 N/c is applied vertically upwards now time period is T 2 . The value of T 2 T 1 is (g=10 m / s – 2 )

    An electron falls from rest through a vertical distance h in a uniform and vertically upward directed electric field E . The direction of electric field is now reversed, keeping its magnitude the same. A proton is allowed to fall from rest in it through the same vertical distance h . The time of fall of the electron, in comparison to the time of fall of the proton is

    A conducting sphere of radius R is given a charge Q. The electric potential and the electric field at the centre of the sphere respectively are

    An electric field is acting vertically upwards. A small body of mass 1 gm and charge – 1 μ C is projected with a velocity 10 m/s at an angle 45 0 with horizontal. Its horizontal range is 2m then the intensity of electric field is : (g = 10 m / s 2 )

    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 and y = 0 in the XY plane

    Two similar point charges q 1 and q 2 are placed at a distance r apart in air. Assume that a slab of thickness one third the separation between the charges is placed between the charges and it is observed that the ratio of Coulomb’s repulsive force before and after placement of dielectric is 25:9. Then the dielectric constant K of such a slab is

    The total electric flux leaving spherical surface of radius 1cm and surrounding an electric dipole is

    Two parallel infinite line charges with linear charge densities + λC / m and – λC / m are placed at a distance of 2R in free space. What is the electric field mid-way between the two line charges?

    A ring of charge with radius 0.5 m has 0.002   π m gap. If the ring carries a charge of + 1 C, the electric field at the center is nearly

    Two pith balls carrying equal charges are suspended from a common point by strings of equal length, the equilibrium separation between them is r. Now the strings are rigidly clamped at half the height. The equilibrium separation between the balls now become:

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

    Which one of the following statement is correct

    The electric field in a certain region is acting radially outward and is given by E = A r . A charge contained in a sphere of radius ‘a’ centred at the origin of the field, will be given by

    An electric dipole is placed at an angle of 30 0 with an electric field intensity 2 × 10 5 N C – 1 . It experiences a torque equal to 4 N m . The charge on the dipole, if the dipole length is 2 c m

    An electric dipole of dipole moment p is aligned parallel to a uniform electric field E. The energy required to rotate the dipole by 90 o is

    A charge ‘q’ is placed at the centre of the line joining two equal charges ‘Q’. The system of the three charges will be in equilibrium if ‘q’ is equal to

    A thin glass rod is bent into a semicircle of radius r. A charge +Q is uniformly distributed along the upper half, and a charge –Q is uniformly distributed along the lower half, as shown in the figure. The resultant electric field E at P, the center of the semicircle, is

    One-fourth of a sphere of radius R is removed as shown in figure. An electric field E exists parallel to the xy plane. Find the flux through the remaining curved part

    Which of the following four figures correctly show the forces that three charged particle exert on each other

    Four charges equal to – Q are placed at the four corners of a square and a charge q is at its centre. If the system is in equilibrium, the value of q is

    For an equipotential surface the direction of electric field is

    Suppose the charge of a proton and an electron differ slightly. One of them is -e, the other is ( e + Δ e ) . If the net of electrostatic force and gravitational force between two hydrogen atoms placed at a distance d (much greater than atomic size) apart is zero, then Δ e is of the order of Given mass of hydrogen m h = 1 . 67 × 10 – 27 kg

    Figure shows the electric lines of force emerging from a charged body. If the electric fields at A and B are E A and E B respectively and the distance between A and B is r then

    Two infinite planes each with uniform surface charge density + σ are kept in such a way that the angle between them is 30 o . The electric field in the region shown between them is given by

    In finding the electric field using gauss law the formula E = Q e n c l o s e d ∈ 0 A is applicable. In the formula ∈ 0 is permittivity of free space, A is the area of Gaussian surface and Q e n c l o s e d is charge enclosed by the Gaussian surface . The equation can be used in which of the following situation

    Three charged particles A, B and C with charges − 4 q ,   2 q and − 2 q are present on the circumference of a circle of radius d . The charged particles A, C and centre O of the circle formed an equilateral triangle and point B is diametrically opposite to point C as shown in figure. Electric field at O along X – direction is

    Consider a sphere of radius R which carries a uniform charge density ‘ ρ ‘ . If a sphere of radius R 2 is carved out of it, as shown. The ratio E A E B of magnitude of electric field E A and E B , respectively at points A and B due to the remaining portion is

    It has been experimentally observed that the electric field in a large region of earth’s atmosphere is directed vertically down wards. At an altitiude of 300m, the electric field is 60 V / m . At an altitude of 200m, the field is 100 V / m . Calculate the net amount of charge contained in the cube of 100m edge, located between 200m and 300m altitude

    An electric dipole of moment P = − i ^ − 3 j ^ + 2 k ^ × 10 − 29 C − m is at the origin 0 ,   0 ,   0 . The electric field due to this dipole at r = + i ^ + 3 j ^ + 5 k ^ n o t e   r . p = O is parallel to

    For uniformly charged ring of radius R, the electric field on its axis has the largest magnitude at a distance ‘ h ‘ from its centre. The value of h is

    Three charges + Q ,    q , + Q   are placed respectively at a distance O ,   d 2 and d from the origin. If the net force experienced by + Q , placed at x = 0 , is zero then the value of q is

    Two point charges q 1 10 μ c and q 2 − 25 μ c are placed on the x − a x i s at x = 1 m and x = 4 m respectively the electric field i n   V / m at point y = 3 m on y − a x i s is t a k e 1 4 π ∈ 0 = 9 × 10 9   N − m 2 / C 2

    Determine the electric dipole moment of the system of three charges, placed on the vertices of an equilateral triangle, as shown in the figure

    An electric field of 1000   V / m is applied to an electric dipole at angle of 45 o . The value of electric dipole moment is 10 − 29 C . m . What is the potential energy of the electric dipole?

    A bob of simple pendulum has mass 2 g and a charge 5 μ c . It is at rest in a uniform horizontal electric field of intensity 2000   V / m . At equilibrium, the angle that the pendulum makes with the vertical is

    An electric dipole is formed by two equal and opposite charges q with separation ‘ d ‘ . The charges have same mass(m). It is kept in a uniform electric field E. If it is slightly rotated from its equilibrium orientation, then its angular frequency ‘ ω ‘ is

    Two small equally charged spheres each of Mass ‘ m ‘ are suspended from the same point by silk threads of length L. The distance between the spheres x < < L . Find the rate d q d t with which the charges leak off each sphere if their approach velocity varies as V = a x when ‘ a ‘ is constant

    A pendulum of bob of Mass 80 m g and carrying a charge of 2 × 10 − 8 C is at rest in a uniform horizontal electric field of 20 k V m − 1 . Find the tension in the string

    A proton and an α – particle start from rest in a uniform electric field, then the ratio of times of flight to travel same distance in the field is

    The electric field in a region is given by E = 3 5 E 0 i ^ + 4 5 E 0 j ^ with E 0 = 2 × 10 3   N / C . Find the flux of this field through a rectangular surface of area 0.2 m 2 parallel to y − z plane in N − m 2 C − 1

    A cube of side 10 cm encloses a charge of 0.1 μ C at its centre. Calculate the number of lines of force through each face of the cube

    A spherical shell of radius R = 1.5   c m has a charge q = 20 μ C uniformly distributed over it. The force exerted by one half over the other half is

    At a point 20cm from the centre of a uniformly charged dielectric sphere of radius 10cm , the electric field is 100 V / m . The electric field at 3cm from the centre of the sphere will be

    The energy required to break one bond in DNA is 10 − 20 J . This value in eV is nearly :

    A spherical conductor of radius 10cm has a charge of 3 .2 × 10 − 7 C distributed uniformly. What is the magnitude of electric field at a point 15 cm from the centre of the sphere 1 4 π ∈ 0 = 9 × 10 9 N   m 2 / C 2  

    An electric dipole is situated in an electric field of uniform intensity E/4 whose dipole moment is 2p and moment of inertia is I. If the dipole is displaced slightly from the equilibrium position, then the angular frequency of its oscillations is

    If electric field lines of two charges are shown. Choose correct option.

    A sphere encloses an electric dipole with charges ± 3 × 10 – 6 C. What is the total electric flux across the sphere?

    A charge of 4 × 10 − 9 C is uniformly distributed over the surface of ring shape conductor of radius 0.3 m . Calculate the intensity of electric field at a point on the axis of the ring at a distance of 0.4 m from the plane of the conductor V / m

    ABC is a right angle triangle with sides AB=3 cm BC=4 cm and AC=5 cm . Charges +15, +12 and -20 esu are placed at A,B,C respectively. Magnitude of force experienced by the charge at B in dyne is

    Two parallel large thin metal sheets have equal surface charge densities σ = 26.4 × 10 − 12 C m 2 of opposite signs. The electric field between these sheets (in V/m) is

    An externally long wire is uniformly charged an electron is resolving about the wire and making 10 8 revolutions per second in an orbit of radius 2cm . Linear charge density of wire in n C / m is

    Two small spherical ball each carrying a charge Q = 10 μ C (10 micro coulomb) are suspended by two insulating of equal lengths 1m each from a point fixed in the ceiling it is found that in equilibrium threads are separated by angle 60 o between them as shown in the figure . What is the tension in the threads N. Take 1 4 π ε 0 = 9 × 10 9   N m / C 2 )

    An electric dipole P   =   p i ^ is placed at the origin. A point charge +Q is placed at point A (–a, b). Then the ratio b a for which the electric field at B(0,b) will be zero is

    A charged particle of mass m and charge Q is released from rest from the position x 0 ,    0 in a uniform electric field ‘ E 0 j ^ ‘ . The angular momentum of the particle about origin

    A positively charged very large sheet has a charge density of ‘ σ ‘    coul / m 2 . An electric dipole of moment ‘P’ is placed near the sheet of charge at right angles to the sheet as shown in figure. Find the work done in rotating the dipole through an angle of 180 0 .  

    In a region of space the electric field is given by E = 8 i ^ + 4 j ^ + 3 k ^ unit. The electric flux through a surface of area of 100 unit in xy plane is

    A spherical charged conductor has σ as the surface density of charge. The electric field on its surface is ‘E’. If the radius of the sphere is doubled, keeping surface density of charge unchanged, What will be the electric field on the surface of the new spheres?

    A point charge of 100 μ C, is placed at 3 i ^ + 4 j ^ m. Find the electric field intensity due to this charge at a point located at 9 i ^ + 12 j ^ m.

    In a certain region of space, there exists a uniform electric field of value 2 × 10 2 k ^ V m − 1 . A rectangular coil of dimension 10 cm × 20 cm is placed in the xy plane. The electric flux through the coil is

    A hollow spherical shell of radius r has a uniform charge density σ π . It is kept in a cube of edge 3 r such that the centre of the cube coincides with the centre of the shell. The electric flux that comes out of a face of the cube is

    A cone lies in a uniform electric field E as shown in figure. The electric flux entering the cone is

    Three identical charges each of magnitude 3 q 0 are kept at vertices of an equilateral triangle. What should be charge at the centre to obtain system in equilibrium?

    Consider two concentric spherical surfaces S 1 with radius a and S 2 with radius 2a, both centered at the origin. There is a charge +q at the origin and there are no other charges. Compare the flux φ 1 through S 1 with the flux φ 2 through S 2 .

    Find the flux through the cube if point charge q is placed at the corner of cube

    Two infinite planes each with uniform surface charge density + σ are kept in such a way that the angle between them is 30 0 . The electric field in the region shown between them is given by

    ABCD is a square of side Length l and O is its centre. The line OP is perpendicular to the plane of the square and OP= l /2. A point charge Q is placed at point P. Then electric flux through the square ABCD is

    A point charge + 2 μ C is placed at the centre of a sphere of radius 10cm. Another charge − 2 μ C is kept at a distance of 20 cm from the centre of the sphere. Then electric flux through the surface of the sphere is

    Three charged particles A,B and C with charges – 4q, 2q and -2q are present on the circumference of a circle of radius d. The charged particles A,C and centre O of the circle formed an equilateral triangle as shown in figure, Electric field at O along x-direction is:

    A particle of mass m and charge q is released from rest in a uniform electric field. If there is no other force on the particle, the dependence of its speed ν on the distance x travelled by it is correctly given by (graphs are schematic and not drawn to scale)

    Consider a sphere of radius R which carries a uniform charge density ρ . If a sphere of radius R 2 is carved out of it, as shown , the ratio E A E B of magnitude of electric field E A and E B . respectively, at points A and B due to the remaining portion is:

    An electric field E = 4 x i ^ − y 2 + 1 j ^ N / C passes through the box shown in figure. The flux of the electric field through surfaces A B C D and B C G F are marked as ϕ 1    a n d    ϕ 2 respectively .The difference between ϕ 1 − ϕ 2 is in Nm 2 / C

    A small point mass carrying some positive charge on it, is released from the edge of a table. There is a uniform electric filed in this region in the horizontal direction. Which of the following options then correctly describe the trajectory of the mass? (Curves are drawn schematically and are not to scale).

    Two charged thin infinite plane sheets of uniform surface charge density σ + and σ − , where σ + > σ − , intersect at right angle. Which of the following best represents the electric field lines for this system :

    A particle of charge q and mass m is subjected to an electric field E = E 0 1 − a x 2 in the x-direction, where a and E 0 are constants. Initially the particle was at rest at x = 0. Other than the initial position the kinetic energy of the particle becomes zero when the distance of the particle from the origin is:

    Intensity of electric field at a distance of 1m from an infinitely long line of charge is 100 V/m. What will be the electric flux through a 1m long cylindrical Gaussian surface with its axis on the line of charge?

    A, B and C are three large sheets having charge densities + 3 σ   C / m 2 ,   − σ   C / m 2 and + 2 σ   C / m 2 respectively. Then electric field at P is

    An uncharged metal object M is insulated from its surroundings. A positively charged metal sphere S is then brought near to M. Which diagram best illustrates the resultant distributions of charge on S and M ?

    Which of the following figure represents the electric field lines due to a single negative charge?

    Which of the following figure represents the electric field lines due to a single negative charge?

    Which of the following figures correctly shows the top view sketch of the electric field lines for a uniformly charged hollow cylinder as shown in figure?

    Figure shows the electric lines of force emerging from a charged body. The electric field at A and B are EA and En, respectively. If the distance between A and B is r, then

    An electron enters in an electric field with its velocity in the direction of the electric lines of force. Then

    An electron of mass m e initially at rest moves through a certain distance in a uniform electric field in time t 1 . A proton of mass m p also initially at rest takes time t 2 to move through an equal distance in this uniform electric field. Neglecting the effect of gravity, the ratio of t 2 / t 1 is nearly equal to

    A cylinder of radius r and length l is placed in an uniform electric field in such a way that the axis of the cylinder is parallel to the field. The flux of the field through the cylindrical surface is

    A charge q is enclosed by an imaginary Gaussian surface. If radius of surface is increasing at the rate dr dt = K, then

    q 1 , q 2 , q 3 and q 4 are point charges located at points as shown in the figure and S is a spherical Gaussian surface of radius R. Which of the following is true according to the Gauss’s law?

    Consider the charge configuration and spherical Gaussian surface as shown in the figure. When calculating the flux of the electric field over the spherical surface, the electric field will be due to

    A point charge q is placed at a distance a/2 directly above the centre of a square of side a. The electric flux through the square is

    An electric field given by E = 4 i ^ + 3 y 2 + 2 j ^ pierces Gaussian cube of side 1 m placed at origin such that its three sides represents x, y and z axes. The net charge enclosed within the cube is

    Three infinitely long charged sheets are placed as shown in figure. The electric field at point P is

    The electric flux for Gaussian surface A that encloses the charged particles in free space is (Given: q 1 = -14 nC, q 2 = 78.85 nC, q 3 = -56 nC)

    An infinite number of charges, each of charge 1 μC, are placed on the x-axis with co-ordinates x = 1, 2, 4, 8, ···· ∞ meters· If a charge of 1 C is kept at the origin, then what is the net force acting on 1 C charge?

    In the diagram shown, electric flux over the surface of Gaussian surface (1) is 8 × 10 4   V − m and the flux over the Gaussian surface (2) is 12 × 10 4   V − m . Then the charge Q 1 is equal to

    The electric field at 20 cm from the centre of a uniformly charged sphere of radius IO cm is E. Then at a distance 5 cm from the centre it will be :

    The electric field inside a spherical shell of uniform surface charge density is :

    An electron q = − 1.6 × 10 − 19 ,    m e = 9.1 × 10 − 31   k g is projected out along the + x axis with an initial speed of 2.0 × 10 6   m / s . It goes 20 cm and stops due to a uniform electric field in the region. Find the magnitude and direction of the field.

    A charge Q is distributed uniformly in a sphere (solid). Then the electric field at any point r where r < R (r is radius of sphere) varies as :

    The maximum electric field intensity on the axis of a uniformly charged ring of charge q and radius R will be :

    An insulating solid sphere of radius ‘R’ is charged in a non uniform manner such that volume charge density ρ = A r where A is a positive constant and r the distance from centre. Electric field strength at any inside point at distance r 1 is:

    A uniformly charged ring of radius 15 cm carries a total charge 60 µC. Where should a point charge 3 µC be kept on the axis of the ring so that it experiences maximum force?

    A ring of radius 20 cm is given some charge that distributes in a uniform manner along the length of ring. It is observed that maximum field strength along the axis of ring is 650 N/C. Field strength at the centre of ring will be :

    Charge is distributed non-uniformly in the volume of a solid insulating sphere of radius ‘a’ such that volume charge density ( ρ ) varies with distance from the centre (r) as ρ (r) = Cr 2 , r ≤ a here C is a constant. Magnitude of electric field strength outside the sphere, i.e., for r > a, is :

    Three charges are placed at the vertices of an equilateral triangle of side ‘a’ as shown in the following Fig. The force experienced by the charge placed at the vertex A in a direction normal to BC is :

    The electric field due to a uniformly charged sphere of radius R as a function of the distance from its centre is represented graphically by :

    A thin conducting ring of radius R is given a charge +Q. The electric field at the centre O of the ring due to the charge on the part AKB of C the ring is E. The electric field at the centre due to the charge on the part ACDB of the ring, (Fig. 2.101) is :

    Two infinitely long uniformly charged non-conducting sheets of charge density σ = 2 E 0 x 10 – 3 each are placed perpendicular to each other as shown in figure. What is the resultant electric field intensity at point P ?

    A infinitely long non-conducting cylinder of inner radius 5 cm and outer radius 7 cm has uniform volume charge density ρ = 8 . 85 x 10 – 9 C / m 3 . The magnitude of electric field at a distance of 10 cm from axis of the cylinder is

    Two point charges ( +Q) and (-2Q) are fixed on the x-axis at positions a and 2a from origin, respectively. At what positions on the axis, the resultant electric field is zero?

    Two point charges Q and-3Q are placed at some distance apart. If the electric field at the location of Q is E, then at the locality of -3Q, it is

    An infinite number of electric charges each equal to 5 nC (magnitude) are placed along x-axis at x =1 cm, x = 2 cm, x = 4 cm, x = 8m ………. and so on. In the setup, if the consecutive charges have opposite sign, then the electric field in newton/coulomb at x = 0 is 1 4 πε 0 = 9 × 10 9 N − m 2 / C 2

    An electric dipole of moment 3 × 10 − 8 coul-m is placed at a distance of 10 cm from a + 10 μ C point charge with the charge on its axis. Then magnitude of force experienced by the dipole is

    A point charge + 12 μ C is placed at the centre of a thin charged metallic shell of radius 10 cm. It charge on the shell is − 2 μ C , intensity of electric field at a distance 30 cm from the centre of the shell is

    Two charges q 1 and q 2 are kept on x-axis and electric field at different points on x-axis is plotted against x. Choose correct statement about nature and magnitude of q 1 and q 2 .

    In a regular polygon of n sides, each comer is at a distance r from the centre. Identical charges each of magnitude q are placed at comers. The field at the centre is

    Equal charges q are placed at the vertices A and B of an equilateral triangle ABC of side a. The magnitude of electric field at the point C is

    A charge Q is situated at the centre of a cube. The electric flux through one of the faces of the cube is :

    Three identical point charges, as shown, are placed at the vertices of an isosceles right angled triangle. Which of the numbered vectors coincides in direction with the electric field at the mid-point M of the hypotenuse?

    A charged conducting sphere has diameter 2.4m and surface charge density 10 μC / m 2 . Electric flux passing through its surface will be :

    A square surface of side L metres is in the plane of the paper. A uniform electric field E (volt/m) also in the p I an e of the paper, is limited only to the lower half of the square surface (see Fig. 2.115). The electric flux in SI units associated with the surface is :

    Five point charges each having magnitude q are placed at the corner of hexagon as shown in figure. Net electric field at the centre O is E . To get net electric field at O be 6 E , charge placed on the remaining sixth comer should be

    Infinite charges of magnitude q each are lying at x =l , 2, 4, 8 … meter on x-axis. The value of intensity of electric field at point x = 0 due to these charges will be

    A charge of 12 pC is placed at a distance of I0 cm directly above the centre of a square of side 20 cm. What is the magnitude of electric flux through the square?

    Charge q is uniformly distributed over a thin half ring of radius R. The electric field at the centre of the ring is

    Two infinitely long line of charge carrying charges + λ C m and – λ C m are kept at a separation r . Then the electric field at a distance r from each line of charge is

    A spherical space of radius R is uniformly charged and electric flux through the surface of this spherical space is ϕ . What will be the electric field at a point on the surface of a concentric spherical space of radius R 2 ?

    l g of cork with a charge 1 μC floats motionless 1 cm above a large uniformly charged plane near the surface of the earth. The surface charge density of the plane, assuming it to be an infinite sheet, is

    Two concentric rings, one of radius R and total charge +Q and the second of radius 2R and total charge -✓8Q, lie in x-y plane (i.e., z = 0 plane). The common centre of rings lies at origin and the common axis coincides with z-axis. The charge is uniformly distributed on both the rings. At what distance from origin is the net electric field on z-axis zero?

    In a region of space the electric field is in the x-direction and proportional to x, i.e., E = E 0 x i ^ . Consider an imaginary cubical volume of edge a with its edges parallel to the axes of coordinates. The charge inside this volume will be

    The electric intensity due to a dipole of length 10 cm and having a charge of 500 μC, at a point on the axis 20 cm from one of the charges in air is :

    Fig. shows an electric dipole. A point charge 4 μC is placed on the axial line of dipole at a large distance from the centre of dipole where electric field strength due to dipole is I 00 N/C. The dipole is also present in the electric field of 4 μC charge. Assuming that the charges that make the dipole are fixed relative to each other, but the dipole, as a whole, is free to move :

    An electric dipole is placed at an angle of 30° with an electric. field intensity 2 x 10 5 N / C . It experiences a torque equal to 4 Nm. The charge on the dipole, if the dipole length is 2 cm, is :

    A point charge 25 μC is located in the XY-plane at the point of position vector r 0 = i ^ + j ^ m . What is the magnitude of electric field at the point of position vector r 1 = 4 i ^ + 5 j ^ m ?

    Following figure shows for Gaussian surface S 1 , S 2 , S 3 and S 4 Now, match the following columns and mark the correct code given below. Column-I Column-II i. ϕ S 1 p. + Q ε 0 ii. ϕ S 2 q. 0 iii. ϕ S 3 r. – Q ε 0 iv. ϕ S 4 s. 2 Q ε 0 Codes:

    A point charge 8.85 μ C is placed at the centre of a cube. Then electric flux through one of the focus of the cube is

    Two charges + 3 . 2 × 10 – 19 and -3.2×10 -19 C placed at 2.4A apart form an electric dipole. It is placed in a uniform electric field of intensity 4 × 10 5 V/m . The electric dipole moment is

    An electric dipole is placed in an electric field generated by a point charge. Then which of the following statements is true?

    If the magnitude of intensity of electric field at a distance x on axial line and at a distance y on equatorial line on a given dipole are equal, then x : y is

    For a dipole, q = 2 × 10 – 6 C and d = 0.0 l m . Calculate the maximum torque for this dipole if E = 5 × 10 5 N/C.

    What is the angle between the electric dipole moment and the electric field strength due to it on the equatorial line?

    A neutral water molecule ( H 2 0 ) in its vapour state has an electric dipole moment of magnitude 6 . 4 × 10 – 30 C-m. How far apart are the molecules’ centres of positive and negative charge?

    The locus of the points (in the xy-plane) where the electric field due to a dipole (dipole axis is along x-axis and its equatorial is along y-axis) is perpendicular to its axis, is

    An electric dipole is situated in an electric field of uniform intensity E whose dipole moment is p and moment of inertia is I. If the dipole is displaced slightly from the equilibrium position, then the angular frequency of its oscillations is

    An electric dipole is kept on the axis of a uniformly charged ring at distance 2 R from the centre of the ring. The direction of the dipole moment is along the axis. The dipole moment is p, charge of the ring is Q and radius of the ring is R. The force on the dipole is

    Four metal conductors having different shapes such that of 1. a sphere 3. a pear 2. a cylinder 4. a lightning conductor are mounted on insulating stands and charged. The one which is best suited to retain the charges for a longer time is

    A metallic solid sphere is placed in a uniform electric field. The lines of force follow the path(s) shown in figure as

    Two identical charges, 5   μ C each, are in the air. What is the largest charge to be transferred from one charge to another, so that their interaction force decreases to 2.5 times?

    Conduction electrons are almost uniformly distributed within a conducting plate. When placed in an electrostatic field E , the electric field within the plate.

    If a spherical charged conductor comes out from the closed surface of the sphere, then total flux emitted from the surface will be

    Two infinitely long parallel wires having linear charge densities λ 1 and λ 2 respectively, are placed at a distance of R metres. The force per unit length on either wire will be k = 1 4 πε 0

    A soap bubble (surface tension = T) is charged to a maximum surface density of charge = σ When it is just going to burst, its radius R is given by

    A particle of charge -q and mass m moves in a circle of radius r around an infinitely long line charge of linear charge density + λ . Then its time period is where k = 1 4 πε 0

    Six charges are placed at the vertices of a regular hexagon as shown in the figure. The electric field on the line passing through point O and perpendicular to the plane of the figure as a function of distance x from point O is (assume x >>a)

    Four very large metal plates are given the charges as shown in figure. The middle two are then connected through a wire. Find the charge that will flow through the wire.

    A conic surface is placed in a uniform electric field E as shown such that field is perpendicular to the surface on the side AB. The base of the cone is of radius R and height of the cone is h. The angle of cone is θ as shown. Find the magnitude of that flux which enters the cone curved surface from left side. Don’t count the outgoing flux. ( θ < 45°)

    A uniformly charged and infinitely long line having a liner charge density )., is placed at a normal distance y from a point 0. Consider a sphere of radius R with O as centre and R > y. Electric flux through the surface of the sphere is

    Two infinite sheets having charge densities σ 1 and σ 2 are placed in two perpendicular planes whose two dimensional view is shown in the figure. The charges are distributed uniformly on sheets in electrostatic equilibrium condition. Four points are marked I, II, Ill and IV. The electric field intensities at these points are E 1 , E ¯ 2 , E 3 and E ¯ 4 respectively. The correct expression for electric field intensities is

    The electric field intensity due to a dipole of length 10 cm and having a charge of 500 μC, at a point on the axis at a distance 20 cm from one of the charges in air, is

    A charge q is located at the centre of a cube. The electric flux through any face is

    An infinitely long wire is kept along z-axis from z = – ∞ to z = + ∞ having uniform near charge density 10 9 nC / m . The electric field at point (6 cm, 8 cm, 10 cm) will be

    An electric dipole of moment P is lying along a uniform electric field E . The work done in rotating the dipole by 90° is

    A thin conducting ring of radius R is given a charge +Q. The electric field at the centre O of the ring due the to the charge on the part AKB of the ring is E. The electric field at the centre due to the charge on the part ACDB of the ring is

    Statement I: If the medium between two charges is replaced by another medium of greater dielectric constant, then the electric force between them decreases. Statement II: Electric dipole moment varies inversely as the dielectric constant.

    Statement I: The electric field due to a dipole on its axial line at a distance r is E. Then, electric field due to the same dipole on the equatorial line and at the same distance will be E 2 . Statement II: Electric field due to dipole varies inversely as the square of distance.

    A charge is given velocity perpendicular to uniform electric field, then Statement-l: Initial power delivered by electric field is zero. Statement II: Path of charged particle is circular.

    Statement I: Electric lines of force do not cross each other. Statement II: Electric field at a point superimpose to give one resultant electric field.

    Statement I: Coulomb’s law can be derived from Gauss’s law. Statement II: Gauss’s law can be derived from Coulomb’s law.

    Three identical dipoles are arranged as shown below. What will be the net electric field at P k = 1 4 π ε 0 ?

    The magnitude of electric field intensity at point B (2, 0, 0) due to a dipole of dipole moment, p = i ^ + 3 j ^ kept at origin is (assume that the point B is at large distance from the dipole and k = 1 4 πε 0 )

    An electric dipole is placed in a uniform electric field E of magnitude 40 N/C. Graph shows the magnitude of the torque on the dipole versus the angle θ between the field E and the dipole moment p . The magnitude of dipole moment p is equal to

    Two infinitely large charged planes having uniform surface charge density + σ and – σ are placed along x-y plane and y-z plane, respectively, as shown in the figure. Then the nature of electric lines of forces in x-z plane is given by

    In the figure shown, find the ratio of the linear charge densities λ 1 (on semi-infinite straight wire) and λ 2 (on semi-circular part), that is λ 1 / λ 2 so that the field at O is along y direction.

    A ring of radius R has charge -Q distributed uniformly over it. A charge q is placed at the centre of the ring such that the electric field becomes zero at a point on the axis of the ring distant R from the centre of the ring. The value of charge q is

    A sphere of radius R carries charge such that its volume charge density is proportional to the square of the distance from the centre. What is the ratio of the magnitude of the electric field at a distance 2R from the centre to the magnitude of the electric field at a distance of R/2 from the centre (i.e., E r=2R / E r=R/2 )?

    A metallic shell has a point charge q kept inside its cavity. Which one of the following diagrams correctly represents the electric lines of forces?

    Shown below is a distribution of charges. The flux of electric field due to these charges through the surface S is

    The electric field due to a uniformly charged sphere of radius R as a function of the distance from its centre is represented graphically by

    A cube of a metal is given a positive charge Q. For the above system, which of the following statements is true?

    If two conducting spheres are separately charged and then brought in contact. Then

    An uncharged conducing large plate is placed as shown. Now an electric field E towards right is applied. Find the induced charge density on right surface of the plate.

    Two copper balls, each weighing 10 g are kept in air 10 cm apart. If one electron from every 10 6 atoms is transferred from one ball to the other, the coulomb force between them is (atomic weight of copper is 63.5)

    In the given figure two tiny conducting balls of identical mass m and identical charge q hang from non-conducting threads of equal length L. Assume that θ is so small that t a n ⁡ θ ≈ s i n ⁡ θ then for equilibrium x is equal to

    Two charges each equal to η q η − 1 < 3 are placed at the corners of an equilateral triangle of side a. The electric field at the third corner is E 3

    In the following four situations charged particles are at equal distance from the origin. Arrange them as per the magnitude of the net electric field at origin greatest first

    An electric dipole is situated in an electric field of uniform intensity E whose dipole moment is p and moment of inertia is I. If the dipole is displaced slightly from the equilibrium position, then the angular frequency of its oscillations is

    Three positive charges of equal value q are placed at the vertices of an equilateral triangle. The resulting lines of force should be sketched as in

    A small sphere carrying a charge ‘q’ is hanging in between two parallel plates by a string of length L. Time period of pendulum is T 0 . when parallel plates are charged, the time period changes to T. The ratio T/T 0 is equal to

    Three identical dipoles are arranged as shown below. What will be the net electric field at P k = 1 4 π ε 0 ?

    A charge Q is fixed at a distance d in front of an infinite metal plate. The lines of force are represented by

    A charged metallic ball is lowered into an insulated metal can. The ball is made to touch bottom of the can, then it, is placed on the disc of electroscope shown below. Final observation must be

    An electrically isolated hollow (initially uncharged), conducting sphere has a small positively charged ball suspended by an insulating rod from its inside surface, see diagram. This causes the inner surface of the sphere to become negatively charged. When the ball is centered in the sphere the electric field outside the conducting sphere is

    Two identical balls having like charges and placed at a certain distance apart repel each other with a certain force. They are brought in contact and then moved apart to a distance equal to half their initial separation. The force of repulsion between them increases 4.5 times in comparison with the initial value. The ratio of the initial charges of the balls is

    Two identical simple pendulums, A and B, are suspended from the same point. The bobs are given positive charges, with A having more charge than B. They diverge and reach equilibrium, with A and B making angles θ 1 and θ 2 with the vertical respectively. Which of the following is correct?

    Two identical conducting spheres having unequal positive charges q 1 and q 2 separated by distance r. If they are made to touch each other and then separated again to the same distance. The electrostatic force between the spheres in this case will be (neglect induction of charges)

    Three similar charges +q are placed on 3 corners of an equilateral triangle ABC of side a. How many minimum charges should be placed on a circle of radius a with the center at A so that resultant force on the charge placed at the center is q 2 4 π ε 0 a 2 along x-axis?

    Which of the following four figures correctly show the forces that three charged particles exert on each other?

    Three charges +Q 1 , +Q 2 , and q are placed on a straight line such that q is somewhere in between +Q 1 and +Q 2 . If this system of charges is in equilibrium, what should be the magnitude and sign of charge q?

    Three positive charges of equal magnitude q are placed at the vertices of an equilateral triangle of side l . How can the system of charges be placed in equilibrium?

    Five point charges, each of value +q, are placed on five vertices of a regular hexagon of side L. The magnitude of the force on a point charge of value -q coulomb placed at the center of the hexagon is

    In figure, two equal positive point charges q 1 = q 2 = 2.0 μ C interact with a third point charge Q = 4.0 μ C. The magnitude, as well as direction, of the net force on Q is

    An electric charge q exerts a force F on a similar electric charge q separated by a distance r. A third charge q/4 is placed midway between the two charges. Now, the force F will

    Three charges (each Q) are placed at the three corners of an equilateral triangle. A fourth charge q is placed at the center of the triangle. The ratio ‘ q/Q’ so as to make the system in equilibrium is

    A point charge of 100 μ C is placed at 3 i ^ + 4 j ^ m. Find the electric field intensity due to this charge at a point located at 9 i ^ + 12 j ^ m.

    Four electrical charges are arranged on the corners of a 10 cm square as shown. What would be the direction of the resulting electric field at the center point P?

    Two charges Q 1 = 18 μ C and Q 2 = -2 μ C are separated by a distance R, and Q 1 is on the left of Q 2 . The distance of the point where the net electric field is zero is

    Three equal charges, each +q, are placed on the corners of an equilateral triangle. The electric field intensity at the centroid of the triangle is

    Four point charges are placed at the corners of a square with diagonal 2a as shown. What is the total electric field at the center of the square?

    The maximum electric field at a point on the axis of a uniformly charged ring is E 0 . At how many points on the axis will the magnitude of the electric field be E 0 /2.

    Find the electric field vector at P (a, a, a) due to three infinitely long lines of charges along the x-, y- and z-axes, respectively. The charge density, i.e., charge per unit length of each wire is λ .

    A thin metallic spherical shell contains a charge Q on its surface. A point charge q 1 is placed at the center of the shell, and another charge q 2 is placed outside the shell. All the three charges are positive. Then the force on charge q 1 is

    The lines of force of the electric field due to two charges q and Q are sketched in the figure. State if

    A positively charged particle moving along x-axis with a certain velocity enters a uniform electric field directed along positive y-axis. Its

    Figure shows four charges q 1 , q 2 , q 3 , and q 4 fixed in space. Then the total flux of the electric field through a closed surface S, due to all the charges, is

    The electric flux from a cube of edge l is ϕ . If an edge of the cube is made 2 l and the charge enclosed is halved, its value will be

    Eight charges, 1 μ C , − 7 μ C , − 4 μ C , 10 μ C , 2 μ C , − 5 μ C , − 3 μC , and 6 μC , are situated at the eight corners of a cube of side 20 cm. A spherical surface of radius 80 cm encloses this cube. The center of the sphere coincides with the center of the cube. Then, the total outgoing flux from the spherical surface (in units of Vm) is

    The following diagram shows the electric field lines between two opposite charges. The positive charge is indicated by the black circle, the negative charge by the white circle. An electron starting from rest at the indicated position (X), and accelerated to high speed by the electric field will follow most likely which trajectory?

    There are three concentric thin spheres of radius a, b, c (a > b > c). The total surface charge densities on their surfaces are σ , – σ , σ respectively. The magnitude of electric field at r ( distance from centre) such that a > r > b is

    The point charges Q and -2Q are placed at some distance apart. If the electric field at the location of Q is E, the . electric field at the location of -2Q will be

    There exists a uniform electric field in the space as shown. Four points A, B, C and D are marked which are equidistant from the origin. If V A , V B , V C and V D are their potentials, respectively, then

    Two identical point charges are placed at a separation of d. P is a point on the line joining the charges, at a distance x from any one charge. The field at P is E. E is plotted against x for values of x from close to zero to slightly less than d. Which of the following represents the resulting curve

    Two concentric conducting thin spherical shells A, and B having radii r A and r B r B > r A are charged to Q A a n d − Q B Q B > Q A The electrical field along a line, (passing through the centre) is

    An isolated charge q 1 of mass m is suspended freely by a thread of length l . Another charge q 2 is brought near it (r >> l). When q 1 is in equilibrium tension in thread will be

    It is required to hold equal charges q in equilibrium at the corners of a square. What charge when placed at the center of the square will do this?

    Two charges q 1 and q 2 are kept on the x-axis, and the electric field at different points on the x-axis is plotted against x. Choose the correct statement about the nature and magnitude of q 1 and q 2 .

    Two concentric rings, one of radius R and total charge +Q and the second of radius 2R and total charge − 8 Q , lie in x-y plane (i.e., z = 0 plane). The common center of rings lies at origin and the common axis coincides with z-axis. The charge is uniformly distributed on both rings. At what distance from origin is the net electric field on z-axis zero

    An uncharged sphere of metal is placed in between two charged plates as shown. The lines of force look like

    Two semicircular rings lying in the same plane of uniform linear charge density λ have radii r and 2r. They are joined using two straight uniformly charged wires of linear charge density λ and length r as shown in the figure. The magnitude of electric field at common center of semi-circular rings is

    An electron of mass m e , initially at rest moves through a certain distance in a uniform electric field in time t 1 . A proton of mass m p also initially at rest takes time t 2 to move through an equal distance in this uniform electric field. Neglecting the effect of gravity, the ratio of t 2 /t 1 is nearly equal to

    A region of space contains some, charge uniformly distributed through out the space. When a spherical Gaussian surface of radius R is placed in the region electric flux through its surface is 12 volt-m. When a spherical Gaussian surface of radius 2R is placed in that region, electric flux through its surface will be

    If an electric dipole is kept in a uniform electric field then which of the following quantities will be zero

    A point charge is placed on the axis of an electric dipole at a distance r from its centre. Magnitude of force experienced by the charge is F. Now the dipole is rotated through an angle of 45°, then the magnitude of force experienced by the dipole will be

    An electric dipole is placed in a uniform electric field. Torque experienced by the dipole is 8 x 10 -6 N-m and the magnitude of potential energy stored in the system is 8 3 µJ. Then the angle between the dipole moment vector and the electric field vector is

    Three electric dipoles p 1 , p 2 and p 3 are placed along three sides of on equilateral triangle ABC as shown in figure If p 1 = p 2 = p 3 = p and the dipole p 3 is removed from the system, then the resultant dipole moment of the system will be

    A point charge Q is placed at the centre of a cube, another point charge Q is placed at one edge of the cube and a third charge is placed at one corner of the cube. Then the net electric flux over the entire surface of the cube is

    A large sheet of charge having charge density ‘p’ coul/m 2 passes through a cube having length of side ‘l’. Then maximum electric flux over the surface of the cube is

    If the net electric flux over a Gaussian surface is zero, then select the correct option

    In the arrangement shown, electric flux through surface 1 is ϕ . Then what will be the electric flux through the closed surface 2 ?

    The electric flux over closed surface can be calculated if

    A then spherical shell A of radius R is concentrically placed inside another then spherical shell B of radius 2R. Electric flux through the surface of shell A is +2 volt-m and that through the surface of B is +8 volt-m. The electric charge enclosed bt the region bounded by the shells A and B is

    A uniform electric field E exists in a region of space. Three squares having areas 2 m 2 , 3 m 2 and 4 m 2 lie in xy, yz and zx planes respectively. If the electric flux through the areas are 4 V-m, 9 V-m and 8 V-m respectively, then the electric field may be

    For a point charge kept a long distance away from a charged conducting solid sphere, the charged sphere behaves as

    For an electric dipole, the equipotential surface having zero potential is

    If E a be the electric field strength of a short dipole at a point on its axial line and E e that on the equatorial line at the same distance, then

    A ring of charge with radius 0.5 m has 0.002 π m gap. If the ring carries a charge of +1 C, the electric field at the centre is

    Two electric dipoles each of dipolemoment P = 6.2×10 –30 C-m are placed with their axis along the same line and their centres at a distanced = 10 –8 cm. The force of attraction between dipoles is

    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 o will be

    In a region, electric field depends on X-axis as E = E 0 x 2 . There is a cube of edge a as shown. Then find the charge enclosed in that cube.

    An electric dipole has the magnitude of its charge as q and its dipole moment is p. It is placed in a uniform electric field E. If its dipole moment is along the direction of the field, the force on it and its potential energy are respectively.

    Three identical spheres A, B and C of radius r and each carrying charge q are placed on the vertices of an equilateral triangle of side l l > > r The resultant force on B is F. Now an uncharged identical sphere is first touched with A and then with B and then removed. Now the resultant force on B is:

    A given charge situated at a certain distance from a short electric dipole on its axis and experiences a force F. If the distance of the charge from the dipole is doubled the force acting on the charge will be

    The electric field in a region is radially outward with magnitude E = α r. If α = 100 V/m 2 and R = 0.30 m, then the value of charge contained in a sphere of radius R centered at the origin is W x 10 -10 Coulomb. The value of W is

    The magnitude of the electric field intensity at point B 2 , 0 , 0 due to a dipole moment, P = i ^ + 5 j ^ kept at origin is n × K (assume that the point B is at large distance from the dipole and K = 1 4 π ε 0 ) (All quantities are in S.I units) Find n .

    Consider an infinite line charge having uniform linear charge density and passing through the axis of a cylinder. What will be the effect on the flux passing through the curved surface if the portions of the line charge outside the cylinder is removed.

    A uniformly charged and infinitely long line having a liner charge density λ is placed at a normal distance y from a point O. Consider a sphere of radius R with O as the center and R > y. Electric flux through the surface of the sphere is

    Flux passing through the shaded surface of a sphere when a point charge q is placed at the center is (radius of the sphere is R)

    A charge q is placed at some distance along the axis of a uniformly charged disc of surface charge density σ . The flux due to the charge q through the disc is ϕ . The electric force on charge q exerted by the disc is

    A point charge +Q is positioned at the centre of the base of a square pyramid as shown. The flux through one of the four identical upper faces of the pyramid is

    An oil drop, carrying six electronic charges and having a mass of 1.6 × 10 − 12 g , falls with some terminal velocity in a medium. What magnitude of vertical electric field is required to make the drop move upward with the same speed as it was formerly moving downward with? Ignore buoyancy.

    A spherical shell of radius R = 1.5 cm has a charge q = 20 μ C uniformly distributed over it. The force exerted by one half over the other half is

    Two pith balls each with mass m are suspended from insulating threads. When the pith balls are given equal positive charge Q, they hang in equilibrium as shown. We now increase the charge on the left pith ball from Q to 2Q while leaving its mass essentially unchanged. Which of the following diagrams best represents the new equilibrium configuration?

    A sphere of radius R carries charge such that its volume charge density is proportional to the square of the distance from the center. What is the ratio of the magnitude of the electric field at a distance 2R from the center to the magnitude of the electric field at a distance of R/2 from the center?

    Three identical point charges, each of mass m and charge q, hang from three strings as shown in figure. The value of q in terms of m, L, and q is

    An uncharged conducting large plate is placed as shown. Now an electric field E toward right is applied. Find the induced charge density on the right surface of the plate.

    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?

    Figure shows a uniformly charged hemisphere of radius R. It has a volume charge density ρ . If the electric field at a point 2R, above its center is E, then what is the electric field at the point 2Rbelow its center?

    A soap bubble (surface tension = T) is charged to a maximum surface density of charge = σ . When it is just going to burst? Its radius R is given by

    Four point positive charges are held at the vertices of a square in a horizontal plane. Their masses are 1 kg, 2kg,3kg and 4kg. Another point positive charge of mass 10 kg is kept on the axis of the square. The weight of this fifth charge is balanced by the electrostatic force due to those four charges. If the four charges on the vertices are released such that they can freely move in any direction (vertical, horizontal etc.) then the acceleration of the centre of mass of the four charges immediately after the release is (use g = 10 m / s 2 )

    Two identical small equally charged conducting balls are suspended from long threads secured at one point. The charges and masses of the balls are such that they are in equilibrium when the distance between them is a (the length of thread L >> a).One of the balls is then discharged. Again for the certain value of distance b (b << l) between the balls the equilibrium is restored, The value of a 3 b 3 is .

    A simple pendulum is suspended in a lift which is going up with an acceleration of 5 m/s 2 . An electric field of magnitude 5 N/C and directed vertically upward is also present in the lift. The charge of the bob is 1 μ C and mass is 1 mg. Taking g = π 2 and length of the simple pendulum I m, the time period of the simple pendulum (in sec) is .

    A ring of radius R has charge -Q distributed uniformly over it. Calculate the charge (q) that should be placed at the centre of the ring such that the electric field becomes zero at a point on the axis of the ring distant ‘R’ from the centre of the ring. If the value of q = Q 4 Ω . The value of Ω is .

    Electric field in a region is given by E = − 4 x i ^ + 6 y j ^ . The charge enclosed in the cube of side 1 m oriented as shown in the diagram is given by α ∈ 0 . The value of α is .

    Six charges are kept at the vertices of a regular hexagon as shown in the figure. If magnitude of force applied by +Q on +q charge is F, then net electric force on the +Q is nF. The value of n is .

    Four charge particles each having charge Q=1 C are fixed at corners of base (at A, B, C and D) of a square pyramid with slant length ‘a’ ( A P = B P = D P = P C = a = 2 m ) , a charge -Q is fixed at point P. A dipole with dipole moment p= 1 C-m is placed at centre of base and perpendicular to its plane as shown in figure. If the force on dipole due to charge particles is Ω 4 π ε 0 N . The value of Ω is .

    In Bohr’s theory of the hydrogen atom, an electron moves in a circular orbit about a proton of radius 0.53 A o . Speed of electron in Bohr’s orbit is about 1 N × 69 × speed of light The value of N is .

    Two small metal spheres having equal charge and mass are suspended from some point on the ceiling of a damp room with silk threads of equal length. Let centre to centre distance between sphere be x, x << l, l is length of silk thread. Due to ionization of medium, charge leaks off from each sphere and they keep on coming closer to each other at a constant rate. Let their approach velocity y varies as v ∝ x − 1 / 2 If mass of each sphere is m then the rate at which charge varies with respect to time is d q d t ∝ N 2 2 π ε 0 m g l . The value of N is .

    Consider a uniform charge distribution with charge density 2 C/m 3 throughout in space. If a Gaussian sphere has a variable radius which changes at the rate of 2 m/s, then value of rate of charge of flux is proportional to r k , (r= radius of sphere). Then, the value of k is .

    There exists a uniform electric field E in horizontal direction. A particle having mass m and charge q is projected with a velocity u in upward direction in uniform gravitational field g as shown in the figure. The radius of curvature of path of particle at the highest point is

    The angle θ such that the electric field (vector) at A is perpendicular to dipole moment (vector) is

    A molecule of water appear as shown in figure. Its dipole moment, assuming that all the electrons in the molecule rotate symmetrically about the oxygen nucleus is nearly (Take cos 52 0 = 0.616).

    Three point charges + q each are fixed at A ( L / 2 , L / 2 , 0 ) , B ( − L / 2 , L / 2 , 0 ) , C ( 0 , − L , 0 ) . A fourth point charge – q and mass ‘m’ is kept on z-axes at D (0,0,Z) with Z<<L and released, the minimum time taken by the fourth charge to cross the xy-plane is nearly (neglect effect of gravity)

    A positive charge ‘Q’ is distributed uniformly throughout an insulated sphere of radius R, centered at origin. A positive charge ‘Q’ is placed at x = 2R on the x-axis. The magnitude of the electric filed at x = R 2 on the x-axis will be

    The point charges 3 μ C and 4 μ C are placed at a separation of 7 m. The medium between them is of two types as shown in figure, the electric force acting between them is

    Gauss’s law cannot be used to find electric field strength near an electric dipole near a triangle with point charges at its corners, this is because

    A small block of mass m, charge +q is kept at the top of a smooth inclined plane of angle 30° placed in an elevator moving upward with an acceleration a 0. Electric field E exits between the vertical side walls of the elevator. The time taken by the block to come to the lowest point of inclined plane is ( assuming the surface to be smooth).

    An electron of mass m, initially at rest moves through a certain distance in a uniform electric field in time t. A proton of mass M, also initially at rest, takes time T to move through an equal distance in this uniform electric field. Neglecting the effect of gravity, the ratio T t is nearly equal to

    An electron enters the region between the charged plates as shown in figure with some initial velocity at an angle θ to the plates. The plate width is I and plate separation is d. The electron follows the path shown, just missing the upper plate. Neglect gravity.

    An electron is projected from a distance d and with initial velocity u parallel to a uniformly charged flat conducting plate as shown. It strikes the plate after travelling a distance l along the direction of projection. The surface charge density σ of the conducting plate is.

    A solid metallic sphere has a charge +3Q. Concentric with this sphere is a conducting spherical shell having charge -Q. The radius of the sphere is a and that of the spherical shell is b(b>a). What is the electric field at a distance R(a<R<b) from the centre.

    Six charges, three positive and three negative of equal magnitude are to be placed at the vertices of a regular hexagon such that the electric field at O is double the electric field when only one positive charge of same magnitude is placed at R. Which of the following arrangements of charge is possible for, P, Q, R, S, T and U respectively?

    A disk of radius a 4 having a uniformly distributed charge 6 C is placed in the x-y plane with its centre at − a 2 , 0 , 0 . A rod of length ‘a’ carrying a uniformly distributed charge 8C is placed on the x-axis from x = a 4 to x = 5 a 4 . Two point charges -7C and 3C are placed at a 4 , − a 4 , 0 and − 3 a 4 , 3 a 4 , 0 respectively. Consider a cubical surface formed by six surfaces x = ± a 2 , y = ± a 2 , z = ± a 2 . The electric flux through this cubical surface is

    A tiny spherical oil drop of radius r carrying a net charge q is balanced in still air with a vertical uniform electric field of strength E. When the field is switched off, the drop is observed to fall with terminal velocity v , viscosity of the air = η and the density of oil = d. The magnitude of q is

    Three charges, each of +4 μC are placed at the corners B, C and D of a square ABCD of side 1 m. The electric field at the center O of the square is

    Three identical spheres each having a charge 2q and radius R are kept such that each touches the other two. Find the magnitude of the electric force on any sphere due to the other two

    The block shown in the diagram has a mass of 2 microgram and a charge of 2×10 -9 coulomb. If the block is given an initial velocity of 2 ms -1 in X direction at t = 0 and an electric field of 2 NC -1 in X direction is switch on at that moment, then R Will be (g= 10 ms -2 )

    A cavity of radius r is made inside a solid sphere. The volume charge density of the remaining sphere is ρ . The centre of sphere and centre of cavity are separated by a distance a. The magnitude of electric field inside the cavity is

    Two charges Q 1 and Q 2 are distance d apart. Two dielectrics of thickness t 1 and t 2 and dielectric constant k 1 and k 2 are introduced as shown. Find the force between the charges

    The wrong statement about electric lines of force is:

    A cylinder of radius R and length L is placed in a uniform electric field E parallel to the cylinder axis. The total flux for the surface of the cylinder is given by:

    An isolated solid metallic sphere is given +Q charge. The charge will be distributed on the sphere:

    If the uniform surface charge density on the infinite plane sheet is σ , electric field near the surface will be :

    Two positively charged particles each of mass 1.7 x 10 -27 kg having charge of 1.6 x 10 -19 C are placed at separation r. Calculate r (in cm ), to the nearest integer if each one experiences a repulsive force equal to its weight. (Take g = 10 ms -2 ).

    A charged dust particle of radius 5×10 -7 m is located in a horizontal electric field having an intensity of 6.28 x 10 5 Vm -1 . The surrounding medium is air with coefficient of viscosity η = 1 .6 × 10 − 5 Nsm − 2 . If this particle moves with a uniform horizontal speed 0.02 ms -1 , find the number of electrons in it.

    Consider an electric field E = E 0 x ^ , where E 0 is a constant. The flux through the area (as shown in the figure) due to this field is :

    The bob of a simple pendulum has a mass of 40 g and a positive charge of 4×10 -6 C. It makes 20 oscillation in 45 s. A vertical electric field pointing upward and of magnitude 2.5×10 4 NC -1 is switched on. How much time, in seconds will it now take to complete 20 oscillations? Take g = 10 m / s 2

    A polythene piece rubbed with wool is found to have negative charge of 3.2 x 10 -7 C. Estimate the number of electrons transferred from wool to polythene.

    A conductor A with a cavity as shown in the figure is given a charge Q. Find the net charge appear on the inner surface of the cavity.

    An early model for an atom considered to have a positively charged point nucleus of charge Z e surrounded by a uniform density of negative charge up to a radius R. The atom as a whole is neutral. For this model, what is the electric field at a distance r from the nucleus, where r>R ?

    Two point charges placed at a certain distance r in air exert a force F on each other. Then, the distance r’ at which these charges will exert the same force in a medium of dielectric constant k is given by

    Two charges are at a distance ‘d’ apart. If a copper plate (conducting medium) of thickness d 2 is placed between them, the effective force will be

    Two identical charged spheres are suspended by strings of equal lengths. The strings make an angle of 30 o with each other. When suspended in a liquid of density 0.8 g cm -3 , the angle remains the same. If density of the material of the sphere is 1.6 g cm -3 , the dielectric constant of the liquid 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?

    When the distance between the charged particles is halved, the force between them becomes

    There are two charges +1 microcoulombs and +5 microcoulombs. The ratio of the forces acting on them will be

    A charge q 1 exerts some force on a second charge q 2 . If third charge q 3 is brought near, the force of q 1 exerted on q 2

    F g and F e represents gravitational and electrostatic force respectively between electrons situated at a distance 10 cm. The ratio of F g / F e is of the order of

    A soap bubble is given a negative charge, then its radius

    Four charges are arranged at the corners of a square ABCD, as shown in the adjoining figure. The force on the charge kept at the centre O is

    A total charge Q is broken in two parts Q 1 and Q 2 and they are placed at a distance R from each other. The maximum force of repulsion between them will occur, when

    Out of gravitational, electromagnetic, Vander Waals, electrostatic and nuclear forces; which two are able to provide an attractive force between two neutrons

    The minimum charge on an object is

    Two small spheres each having the charge + Q are suspended by insulating threads of length L from a hook. This arrangement is taken in space where there is no gravitational effect, then the angle between the two suspensions and the tension in each will be

    Three charges 4q, Q and q are in a straight line in the position of 0, l/2 and l respectively. The resultant force on q will be zero, if Q =

    Two charges each of 1 coulomb are at a distance 1km apart, the force between them is

    + 2 C and + 6 C two charges are repelling each other with a force of 12N. If each charge is given – 2 C of charge, then the value of the force will be

    There are two metallic spheres of same radii but one is solid and the other is hollow, then

    Two charges q 1 and q 2 are placed in vacuum at a distance d and the force acting between them is F. If a medium of dielectric constant 4 is introduced around them, the force now will be

    When 10 14 electrons are removed from a neutral metal sphere, the charge on the sphere becomes

    Two similar spheres having + Q and – Q charge are kept at a certain distance. F force acts between the two. If in the middle of two spheres, another similar sphere having + Q charge is kept, then it experience a force in magnitude and direction as

    A glass rod rubbed with silk is used to charge a gold leaf electroscope and the leaves are observed to diverge. The electroscope thus charged is exposed to X-rays for a short period. Then

    Number of electrons in one coulomb of charge will be

    When 10 19 electrons are removed from a neutral metal plate, the electric charge on it is

    Two charges are at a distance ‘d’ apart. If a copper plate (conducting medium) of thickness d 2 is placed between them, the effective force will be

    Two electrons are separated by a distance of 1 A ∘ . What is the coulomb force between them

    Two copper balls, each weighing 10g are kept in air 10 cm apart. If one electron from every 10 6 atoms is transferred from one ball to the other, the coulomb force between them is (atomic weight of copper is 63.5)

    Three charges are placed at the vertices of an equilateral triangle of side ‘a’ as shown in the following figure. The force experienced by the charge placed at the vertex A in a direction normal to BC is

    Two particle of equal mass m and charge q are placed at a distance of 16 cm. They do not experience any force. The value of q m is

    When a glass rod is rubbed with silk, it

    Dielectric constant for metal is

    When air is replaced by a dielectric medium of constant k, the maximum force of attraction between two charges separated by a distance

    Two point charges placed at a certain distance r in air exert a force F on each other. Then the distance r’ at which these charges will exert the same force in a medium of dielectric constant k is given by

    Two charges placed in air repel each other by a force of 10 − 4 N . When oil is introduced between the charges, the force becomes 2 .5 × 10 − 5 N . The dielectric constant of oil is

    A body has – 80 micro coulomb of charge. Number of additional electrons in it will be

    The charges on two sphere are +7 μ C and – 5 μ C respectively. They experience a force F. If each of them is given and additional charge of – 2 μ C, the new force of attraction will be

    The ratio of electrostatic and gravitational forces acting between electron and proton separated by a distance 5 × 10 − 11 m , will be (Charge on electron = 1 .6 × 10 − 19 C , mass of electron = 9 .1 × 10 − 31 kg , mass of proton = 1 .6 × 10 − 27 kg , G = 6 .7 × 10 − 11 Nm 2 / kg 2

    Two charges of equal magnitudes and at a distance r exert a force F on each other. If the charges are halved and distance between them is doubled, then the new force acting on each charge is

    Equal charges q are placed at the four corners A, B, C, D of a square of length a. The magnitude of the force on the charge at B will be

    One metallic sphere A is given positive charge whereas another identical metallic sphere B of exactly same mass as of A is given equal amount of negative charge. Then

    Two point charges Q and – 3Q are placed at some distance apart. If the electric field at the location of Q is E then at the locality of – 3Q, it is nE . The value of n is

    The intensity of electric field required to balance a proton of mass 1 .7 × 10 − 27 kg and charge 1 .6 × 10 − 19 C is nearly

    The intensity of the electric field required to keep a water drop of radius 10 − 5 cm just suspended in air when charged with one electron is approximately g = 10 newton / kg , e = 1 .6 × 10 − 19 coulomb

    The electric field near a conducting surface having a uniform surface charge density σ is given by

    The unit of intensity of electric field is

    The figure shows some of the electric field lines corresponding to an electric field. The figure suggests

    A hollow insulated conducting sphere is given a positive charge of 10   μC . What will be the electric field at the centre of the sphere if its radius is 2 meters

    A cube of side b has a charge q at each of its vertices. The electric field due to this charge distribution at the centre of this cube will be

    Four charges are placed on corners of a square as shown in figure having side of 5 cm. If Q is one microcoulomb, then electric field intensity at centre will be

    Point charges +4q, -q and +4q are kept on the x-axis at points x = 0 , x = a and x = 2 a respectively, then

    Two point charges of 20 μC and 80 μC are 10 cm apart. Where will the electric field strength be zero on the line joining the charges from 20 μC charge

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

    What is the magnitude of a point charge which produces an electric field of 2 N/C at a distance of 60 cm 1 / 4 πε 0 = 9 × 10 9 N − m 2 / C 2

    There is a solid sphere of radius ‘R’ having uniformly distributed charge. What is the relation between electric field ‘E’ (inside the sphere) and radius of sphere ‘R’ is

    A metallic shell has a point charge q kept inside its cavity. Which one of the following diagrams correctly represents the electric lines of force ?

    A charged oil drop is suspended in a uniform field of 3×10 4 v/m so that it neither falls nor rises .The charge on the drop will be (take mass of the charge =9.9 x10- 15 kg and g = 10m /s 2

    Which of the following is deflected by electric field

    A charged particle of mass 5 × 10 − 5 kg is held stationary in space by placing it in an electric field of strength 10 7 NC − 1 directed vertically downwards. The charge on the particle is

    Consider the points lying on a straight line joining two fixed opposite charges. Between the charges there is

    Figures below show regular hexagons, with charges at the vertices. In which of the following cases the electric field at the centre is not zero

    Two point charges + 3 μ C and + 8 μ C repel each other with a force of 40 N. If a charge of − 5 μ C is added to each of them, then the force between them will become

    Two small conducting sphere of equal radii have charges + 10 μ C and – 20 μ C respectively and placed at a distance R from each other experience force F 1 . If they are brought in contact and separated to the same distance, they experience force F 2 . The ratio of F 1 to F 2 is

    A pith ball A of mass 9 × 10 -5 kg carries a charge of 5 μ C. What must be the magnitude and sign of the charge on a pith ball B held 2 cm directly above the pith ball A, such that the pith ball A, remains stationary?

    An electron is moving towards x-axis. An electric field is along y-direction then path of electron is

    A charged particle of mass 5 × 10 − 5 kg is held stationary in space by placing it in an electric field of strength 10 7 NC − 1 directed vertically downwards. The charge on the particle is

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