The tangent galvanometers having coils of the same radius are connected in series. A current flowing in them produces deflections of 60 0 & 45 0 respectively. The ratio of the number of turns in the coil is
The resistances of three parts of a circular loop are as shown in figure. The magnetic field at the center ‘O’ is (current enters at A and leaves at B and C as shown)
Figure shows a wire PQRS carrying a current I. Portions PQ and RS are straight and QR in a circular arc of radius r subtending an angle α at the centre C. The magnitude of magnetic field due to PQRS at centre C is
A charged particle of specific charge q m = α is released from origin at time t = 0 with velocity V ¯ = V 0 i ^ + j ^ in uniform magnetic field B ¯ = B 0 i ^ . Co-ordinates of the particle at time t = π B 0 α are.
Let two long parallel wires a distance ‘d’ apart, carry equal current ‘ i ’ in the same direction. One wire is at x=0, the other at x=d. Determine magnetic field at any point on x-axis between the wires as a function of ‘x’.
A proton beam moves through a region of space where there exists a uniform magnitude 4.0 T along z-axis. The protons have a velocity of 4 × 10 5 m / s in the x-z plane at an angle 30 0 to the positive z-axis. Then the force acting on the proton is − x × 10 − 14 j ^ N , find x = ?
The rectangular coil having 100 turns is placed in a uniform magnetic field of 0.05 j ^ Telsa as shown in figure. The torque acting on the loop is p × 10 − 3 N m k ^ . find p
Proton with kinetic energy of 1 MeV moves from south to north. It gets an acceleration of 10 12 m / s 2 by an applied magnetic field (west to east). The value of magnetic field: (Rest mass of proton is 1.6 × 10 − 27 k g )
A galvanometer is used in laboratory for detecting the null point in electrical experiments. If, on passing a current of 6 mA it produces a deflection of 2º, its figure of merit is close to :
An α particle is moving along a circle of radius R with a constant angular velocity . Point A lies in the same plane at a distance 2R from the centre. The point A records magnetic field produced by α particle. If the minimum time interval between two successive times at which A records zero magnetic field is ‘t’, the angular speed ω , in terms of t is:
A potential difference of 600 V is applied across the plates of a parallel plate capacitor. The separation between the plates is 3 mm. An electron projected vertically, parallel to the plates, with a velocity of 2 × 10 6 ms − 1 moves undeflected between the plates. What is the magnitude of the magnetic field between the capacitor plates?
The core of a toroid having 3000 turns has inner and outer radii of 11cm and 12cm respectively. The magnetic flux density in the core for a current of 0.70A is 2.5T. What is the relative permeability of the core …….
An electron accelerated through a potential difference V passes through a uniform transverse magnetic field and experiences a force F. If the accelerating potential is increased to 2V, the electron in the same magnetic field will experience a force.
A particle of charge q and mass m starts moving from the origin under the action of an electric field E = E 0 i ^ and B = B 0 i ^ with a velocity v = v 0 j ^ . The speed of the particle will be become 3 v 0 after a time
A circular current carrying coil has a radius R. The distance from the center of the coil on the axis where the magnetic induction will be 1 / 8 th of its value at the center of the coil, is
The magnetic field at center ‘O’ of the arc in figure is
A long cylindrical wire of radius ‘a’ carries a current i distributed uniformly over its cross section. If the magnetic fields at distances r<a and R>a from the axis have equal magnitude, then
Currents I 1 and I 2 flow in the wires shown in figure. The field is zero at distance x to the right of O. Then
A parallel plate capacitor is moving with a velocity of 25 m s − 1 through a uniform magnetic field of 4.0 T as shown in figure. If the electric field within the capacitor plates is 400 N C − 1 and plate area is 25 × 10 − 7 m 2 , then the magnetic force experienced by the positive charge plate is
Infinite wires, each carrying a current 0.5 A, are kept parallel to y-axis and intersecting x-axis at x = ± 1 m , ± 2 m , ± 4 m , ± 8 m ,etc. Wires kept at positive values of x axis carry current in the same direction while wires kept at negative values of x axis carry current successively in opposite directions as shown in figure. A wire is kept parallel to x-axis and intersecting y-axis at y = 2 m . It carries a current i. Assuming this wire to be insulated from others then the current i in it such that magnetic induction at O is zero is: (assume each wire to be infinitely long)
Equal currents i = 1 A are flowing through the wires parallel to y-axis located at x = + 1 m , x = + 2 m , x = + 4 m and so on…,etc. but in alternate opposite directions as shown in figure. The magnetic field(in tesla) at origin would be x × 10 − 7 k ^ , then the find the value of x.
A wire is wound on a long rod of material of relative permeability μ r = 4000 to make a solenoid. If the current through the wire is 5 A and number of turns per unit length is 1000 per metre, then the magnetic field inside the solenoid is
Two circular loops are parallel, coaxial, and almost in contact, 1.00 mm apart, Each loop is 10.0 cm in radius. The top loop carries a clock wise current of 140 A. The bottom loop carries a counterclockwise current of 140 A. Calculate the magnetic force exerted by the bottom loop on the top loop.
A particle of mass ‘m ’ and charge ‘ q’ is projected into a region having a perpendicular uniform magnetic field ‘B’ of width d . Find the angle of deviation ‘ θ ’ of the particle as it comes out of the magnetic field.
A metal wire P Q of mass 10 gm lies at rest on two horizontal metal rails separated by 5 cm. A vertically downward magnetic field of magnitude 0.800 T exists in the pace. The resistance of the circuit is slowly decreased and it is found that when the resistance goes below 20 Ω , the wire P Q starts sliding on the rails . Find the coefficient of friction.
A particle of mass 2 × 10 − 5 kg moving horizontally between two horizontal plates of a charged parallel plate capacitor between which there is an electric field of 200 N C acting upward. A magnetic induction of 2.0 T is applied at right angles to the electric field in a direction normal to both B ¯ and V ¯ . If g is 9.8 m/sec 2 and the charge on the particle is 10 − 6 C , then find the velocity of charge particle, so that it continues to move horizontally.
An electron is moving along positive x-axis. To get it moving on an anticlockwise circular path in xy-plane, a magnetic field is applied.
Calculate the magnetic field at point ‘O’ in the following case.
A square conducting loop of length ‘L’ carries a current ‘i’. the magnetic field at the center of the loop is
A rectangular coil of area 5 . 0 × 10 − 4 m 2 and 60 turns is pivoted about one of its vertical sides. Then coil is in a radial horizontal field of 90 G (radial here means the field lines are in the plane of the coil for any rotation). The torsional constant of hair spring connected to the coil if a current of 2.0 mA produces an angular deflection of is 18 0 is x × 10 − 8 N m / degree
A charged particle of mass ‘m’ and charge ‘q’ moving under the influence of uniform electric field E i and a uniform magnetic field B k follows a trajectory from point P to Q as shown in figure. The velocities at P and Q are respectively, v i and − 2 v j . Then which of the following statements (A,B,C,D) are the correct ? (Trajectory shown is schematic and not to scale) A) E = 3 4 m v 2 q a B) Rate of work done by the electric field at P is 3 4 m v 3 a C) Rate of work done by both the fields at Q is zero D) The difference between the magnitude of angular momentum of the particle at P and Q is 2 m a v
A small circular loop of conducting wire has radius a and carries current I. It is placed in a uniform magnetic field B perpendicular to its plane such that when rotated slightly about its diameter and simple harmonic motion of time period T. If the mass of the loop is m then
An electron gun is placed inside a long solenoid of radius R on its axis. The solenoid has n turns/ length and carries a current I . The electron gun shoots an electron along the radius of the solenoid with speed v . If the electron does not hit the surface of the solenoid, maximum possible value of R is (all symbols have their standard meaning):
The figure shows a region of length ‘l’ with a uniform magnetic filed of 0.3T in it and a proton entering the region with velocity 4 × 10 5 m s – 1 making an angle 60 0 with the field. If the proton completes 10 revolution by the time it cross the region shown, ‘l’ is close to (mass of proton = 1 . 67 × 10 – 27 kg, charge on the proton = 1 . 6 × 10 – 19 C)
For the arrangement as shown in the figure, the magnetic induction at the centre is
A current loop, having two circular arcs joined by two radial lines as shown in the figure. It carries a current of 10 A. The magnetic field at point O will be close to
A charge particle A of charge 2C has velocity 100 m/s. When it passes through point A and has velocity in the direction shown. The strength of magnetic field at point B due to this moving charge is (r = 2m)
A proton, a deuteron and an α particle whose kinetic energies are same enter at right angles to a uniform magnetic field. Then the ratio of the radii of their circular paths is
The radius of curvature of the path followed by a charge particle in magnetic field is proportional to
An electric current passes through a long straight copper wire. At a distance 5cm from the straight wire, the magnetic field is B. The magnetic field at 20cm from the straight wire would be,
A current I flows through a wire of finite length L. The magnetic field at a distance d from the wire on its perpendicular bisector,
Three rings each having equal radius R are placed mutually perpendicular to each other and each having its center at the origin of co-ordinates system. If current I is flowing through each ring then the magnitude of the magnetic field at the common center is
Current i is flowing in hexagonal coil of side a. The magnetic induction at the center of the coil will be
Two similar co-axial coils, separated by some distance, carry the same current I but in opposite directions. The magnitude of the magnetic field B at a point on the axis at the mid point of the line joining the center is
An electron is revolving in a circular orbit of radius r in a hydrogen atom. The angular momentum of the electron is L. The dipole moment associated with it is
A solenoid of 0.4m length with 500 turns carries a current of 3A. A coil of 10 turns and of radius 0.01m carries a current of 0.4A. The torque required to hold the coil with its axis at right angles to that of solenoid in the middle point of it is,
The direction of magnetic force on the electron as shown in the diagram is along,
Two protons move parallel to each other keeping distance r between them, both moving with same velocity V, then the ratio of the electric and magnetic force of interaction between them is,
An electron is projected with velocity V 0 in a uniform electric field E perpendicular to the field. Again it is projected with velocity V 0 perpendicular to a uniform magnetic field B. If r 1 is initial radius of curvature just after entering in the electric field and r 2 is initial radius of curvature just after entering in magnetic field then r 1 / r 2 is
A particle of charge q and mass m starts moving from the origin under the action of an electric field E = E o i ^ a n d B = B o i ^ with velocity V = V o j ^ . The speed of the particle will become 2 V 0 after a time
A charged particle moves in magnetic field B = 10 i ^ with initial velocity u = 5 i ^ + 4 j ^ . The path of the particle will be
Three ions H + , He + and O + 2 having same kinetic energy pass through a region in which there width is a uniform magnetic field perpendicular to their velocity then,
An electron having kinetic energy K is moving in a circular orbit of radius R perpendicular to a uniform magnetic induction B. If kinetic energy is doubled and magnetic induction tripled, the radius will be
Two long conductors, separated by a distance d carry current I 1 and I 2 in the same direction. They exert a force F on each other. Now the current in one of them is increased to two times and direction is reversed. The distance is also increased to 3d. The value of the force between them is
A metal ring of radius 0.5m with its plane normal to a uniform magnetic field B of induction 0.2T carries a current 100A (clockwise). The tension in newton developed in the ring is
A rectangular coil of area 2.5cm x 1.5cm has 100 turns. When a current of 2mA is passed through it, the deflection is 30 0 . The couple per unit twist of the suspended wire is 1 . 44 × 10 – 4 Nmrad – 1 the magnetic induction is nearly……………..T.
A coil of 100 turns and area 2 × 10 – 2 m 2 is pivoted about a vertical diameter in a uniform magnetic field and carries a current of 5A. When the coil is held with its plane in north-south direction, it experiences a couple of 0.3Nm. When the plane is east-west, the corresponding couple is 0.4Nm, the value of magnetic induction is (neglect earth’s magnetic field)…………T.
A straight wire of length 30cm and mass 6mg lies in a direction 30 0 east of north. The earth’s field at this site is horizontal and has a magnitude of 0.8G. The current must be passed through the wire so that it may float in air is ( g = 10 ms – 2 ) ……..A.
An electron revolves in a circle of radius 0 . 4 0 A with a speed of 10 5 m / s . The magnitude of the magnetic field, produced at the center of the circular path due to the motion of the electron in W b / m 2 is
A moving coil galvanometer A has 200 turns and a resistance of 100Ω. Another meter B has 100 turns resistance 40Ω. All the other quantities are same in both the cases. The current sensitivity of A is x times of B, the value of x is
A tangent galvanometer shows no deflection when a current is passed through it, but when the current through it is reversed it gives a deflection of 180 0 , then the plane of the coil
A square loop of edge ‘l’ and carrying a current i , is placed with its edges parallel to the X Y axes. There is a non-uniform magnetic field present in the region B = B 0 1 + x l − k ^ . Find the magnitude of the net magnetic force experienced by the loop.
A coil in the shape of an equilateral triangle of side 0.02 m is suspended from a vertex such that it is hanging in a vertical plane between the pole pieces of permanent magnet producing a horizontal magnetic field of 5 × 10 − 2 T . Find the couple acting on the coil when a current 0.1 A is passed through it (the magnetic field is parallel to its plane).
A particle with charge -5.60 nC is moving in a uniform magnetic field B = − 1.25 T k ^ . The magnetic force on the particle is measured to be F = − ( 3.36 × 10 − 7 N ) i ^ + ( 7.42 × 10 − 7 N ) j ^ . Calculate one of the components of velocity of the particle from this information.
A galvanometer coil is replaced by another coil of diameter 1/4th of the original diameter and the total number of turns as ten times the original number. What will be the new deflection if the same current passes through it? Old deflection is θ .
A potential difference of 600 V is applied across the plates of a parallel plate condenser. The separation between the plates is 3 mm. An electron projected vertically, parallel to the plates, with a velocity of 2×10 6 ms -1 moves undeflected between the plates. Find the magnitude of the magnetic field in the region between the condenser plates. (Neglect the edge effects. Charge of the electron= -1.6 × 10 − 19 C )
An electron gun G emits electrons of energy 2 keV travelling in the positive x-direction. The electrons are required to hit the spot S where GS=0.1 m, and the line GS makes an angle of 60 0 with the x-axis as shown in figure. A uniform magnetic field B parallel to GS exists in the region outside the electron gun. Find the minimum value of ‘B’ needed to make the electron hit S.
An electron is accelerated from rest through a potential difference V. This electron experiences a force F in a uniform magnetic field. On increasing the potential difference to V 1 , the force experienced by the electron in the same magnetic field becomes 2 F . Then, the ratio V 1 V is equal to
The plane of a rectangular loop of wire with sides 0.05 m and 0.08 m is parallel to a uniform magnetic field of induction 1.5 × 10 − 2 T . A current of 10.0 ampere flow through the loop. If the side of length 0.08 m is normal and the side of length 0.05 m is parallel to the lines of induction, then the torque acting on the loop is
A conducting ring of mass 2 kg and radius 0.5 m is placed on a smooth horizontal plane. The ring carries a current of i = 4 A . A horizontal magnetic field B = 10 T is switched on at time t = 0 as shown in figure. The initial angular acceleration of the ring will be
A wire of cross-sectional area A forms three sides of a square and is free to rotate about axis O O 1 . If the structure is deflected by an angle θ from the vertical when current i is passed through it in a magnetic field B acting vertically upwards and density of the wire is ρ , then the value of θ is given by
Five very long, straight insulated wires are closely bound together to form a small cable. Currents carried by the wires are: I 1 = 20 A , I 2 = − 6 A , I 3 = 12 A , I 4 = − 7 A , I 5 = 18 A .(Negative currents are opposite in direction to the positive.) The magnetic field induction at a distance of 10 cm from the cable is
The magnetic field at the center of the circular loop as shown in figure, when a single wire is bent to form a circular loop and also extends to form straight sections, is
From a cylinder of radius R, a cylinder of radius R/2 is removed, as shown in figure. Current flowing in the remaining cylinder is I. Then, magnetic field strength is
A long straight non-conducting string carries a charge density of 40 μC m -1 . It is pulled along its length at a speed of 300 m/sec, then the magnetic field at a normal distance of 5 mm from the moving string is p × 10 − 7 T . Then find the value of p .
A charged particle has acceleration a = 2 i ^ + x j ^ in a magnetic field B = − 3 i ^ + 2 j ^ − 4 k ^ . Find the value if ‘x ’.
A rod of mass 0.720 kg and radius 6 cm rests on two parallel rails that are d=12 cm apart and length of rails is L=49 cm . The rod carries a current of i=48 A in the direction shown in figure. And rolls along the rails without slipping. A uniform magnetic field of magnitude 0.240 T is directed perpendicular to the rod and the rails. If it starts from rest, what is the speed of the rod as it leaves the rails.
A conductor carries a constant current I along the closed path abcdefgha involving 8 of the 12 edges of length l . Find the magnetic dipole moment of the closed path.
An electron is accelerated from rest through a potential difference V . This electron experiences a force F is a uniform magnetic field. On increasing the potential difference to V 1 , the force experienced by the electron in the same magnetic field becomes 6 F . Then the ratio V 1 / V is equal to
A particle of charge ‘q’ and mass ‘m’ starts moving from the origin under the action of an electric field E = 2 E 0 i ^ and B = B 0 i ^ with a velocity v = v 0 j ^ . The speed of the particle will becomes 2 v 0 after a time.
A loop of flexible conducting wire of length l lies in magnetic field ‘B’ which is normal to the plane of loop. A current i is passed through the loop. The tension developed in the wire to open up is
An insulating rod of length L carries a charge ‘ q ’ distributed uniformly on it. The rod is pivoted at its mid point and is rotated at a frequency f about a fixed axis perpendicular to the rod and passing through the pivot. The magnetic moment of the rod system is
A pair of stationary and infinitely long bent wires is placed in he xy plane as shown in figure. Each wire carries current of 10 A. Segments L and M are along the x-axis. Segments P and Q are parallel to the y-axis such that O S = O R = 0.02 m . Find the magnitude and direction of the magnetic induction at origin ‘O’
Three long straight and parallel wires are arranged as shown in figure. The force experienced by 10 cm length of wire ‘Q’ is
A current ‘ i ’ flows through a thin wire shaped as regular polygon of ‘n’ sides which can be inscribed in a circle of radius R. The magnetic field induction at the centre of polygon due to one side of the polygon is
A particle is moving with velocity V ¯ = i ^ + 3 j ^ and it produces an electric field at a point given by E = 2 k ^ . It will produce magnetic field at that point equal to (all quantities are in S.I units)
A beam of protons with a velocity 4.0 × 10 5 ms -1 enters a uniform magnetic field of 0.2 T at an angle of 30 0 to the magnetic field. If the radius of the helical path taken by the proton beam is p × 10 − 2 m , then find p (Take m p r o t o n = 1.6 × 10 − 27 k g )
The magnetic moment of a thin round loop with current in the loop of the radius R = 100 m m is x × 10 − 2 A m 2 , and the magnetic induction at its center is equal to B = 7.0 μ T
A particle of mass m and q has an initial velocity v = v 0 j ^ . If an electric field E = E 0 i ^ and magnetic field B = B 0 i ^ act on the particle, its speed will double after a time:
A very long wire ABDMNDC is shown in figure carrying current I. AB and BC parts are straight, long and at right angle. At D wire forms a circular turn DMND of radius R. AB, BC parts are tangential to circular turn at N and D. Magnetic field at the centre of circle is :
A long, straight wire of radius a caries a current distributed uniformly over its cross-section. The ratio of the magnetic fields due to the wires at distance a 3 and 2a. respectively from the axis of the wire is :
A beam of protons with speed 4 × 10 5 m s − 1 enters a uniform magnetic field of 0.3T at an angle of 60º to the magnetic field. The pitch of the resulting helical path of protons is close to: (Mass of the proton 1.67 × 10 − 27 k g , charge of the proton 1.69 × 10 − 19 C)
A charged particle carrying charge 1 μ C is moving with velocity 2 i ^ + 3 j ^ + 4 k ^ m s − 1 . If an external magnetic field of 5 i ^ + 3 j ^ − 6 k ^ × 10 − 3 T exists in the region where particle is moving , then the force on the particle is F × 10 − 9 N . The vector F is :
Magnitude of magnetic field (in SI units at the center of a hexagonal shape coil of side 10 cm, 50 turns and carrying current I (Ampere) in units of μ 0 I π is :
A galvanometer coil has 500 turns and each turn has an average area of 3 × 10 − 4 m 2 . If a torque of 1.5Nm is required to keep this coil parallel to a magnetic field when a current of 0.5A is flowing through it, the strength of the field (in T) is
A wire A, bent in the shape of an arc of a circle, carrying a current of 2 A and having radius 2 cm and another wire B, also bent in the shape of arc of a circle, carrying a current of 3 A and having radius of 4 cm, are placed as shown in the figure. The ratio of the magnetic fields due to the wires A and B at the common centre O is :
A ring of radius R carries a current i as shown. It is situated in the yz plane with its center at the origin. The current is clockwise when viewed from the side of positive x-axis (right to left). An electron is projected with a velocity 3 i ^ + 4 j ^ − k ^ from the point ‘p’ having coordinates 3 R , 0 , 0 . What is the force experienced by the electron at this moment, if ‘e’ is the magnitude of charge on electron
A particle of charge q and mass m starts moving from the origin under the action of an electric field E = E 0 i ^ and magnetic field B = B 0 i ^ with a velocity v = v 0 j ^ . The speed of the particle will become 2 v 0 after a time.
A particle of charge per unit mass α is released from origin with velocity V = v 0 i ^ in a magnetic field B = − B 0 k ^ for x ≤ 3 2 v 0 B 0 α and B = 0 for x > 3 2 v 0 B 0 α . Then x–coordinate of the particle at time t > π 3 B 0 α would be
An electron experiences no deflection if subjected to an electric field of 3.2 × 10 5 V / m and a magnetic induction of 2.0 × 10 − 3 T . Both the fields are applied perpendicular to the path of electron and also to each other. If the electric field is removed, then the electron will revolve in an orbit of radius (in metres) (mass of the electron = 9 × 10 − 31 kg )
Equal current i flows in two segments of a circular loop in the direction shown in figure. Radius of the loop is r. The magnitude of magnetic field induction at the centre of the loop is
A current path shaped as shown in figure produces a magnetic field at P, the centre of the arc. If the arc subtends an angle of 30° and the radius of the arc is 0.6 m. What is the magnitude of the field at P, if the current is 3.0 A?
A photon with energy of 4.9 eV ejects photoelectrons from tungsten. When the ejected electron enters a constant magnetic field of strength B = 2.5 mT at an angle of 60° with thee field direction, the maximum pitch of the helix described by the electron is found to be 2.7 mm. Find the work-function of the metal in electron-volt. Given that, specific charge of electron is 1.76 × 10 11 C/ kg.
