Electromagnetic Induction

A 30 cm long solenoid has 10 turns per cm and area of 5 cm2. The current through the solenoid coil varies from 2 A to 4 A in 3.14 s. The e.m.f. induced in the coil is 10-5 V. The value is .

1. 60
2. 12
3. 120
4. 34

An inductor of inductance 10 mH having resistance of 100 is connected to battery of E.M.F. 1.0 V through a switch as shown in the figure below. After switch is closed, the ratio of instantaneous voltages across the inductor when the current passing through it is 2 mA and 4 mA is . [figure]

1. 4/3
2. 3/4
3. 5/3
4. 3/5

A square loop of side 2 cm is placed in a time varying magnetic field with magnitude as B=0.4 (300t) Tesla. The normal to the plane of loop makes an angle of 60° with the field. The maximum induced emf produced in the loop is mV.

1. 12
2. 18
3. 21
4. 24

A metal rod of length L rotates about one end at origin with a uniform angular velocity . The magnetic field radially falls off as B(r)=B0e- r; being a positive constant. The emf induced (neglecting the centripetal force on electrons in the rod) is :

1. B0 [ 1 2-e- L ( 1 2+ L ) ]
2. B0 [ 1 2+e- L ( 1 2+ L ) ]
3. B0 [ 4 2-e-2 L ( 1 2+ 2L ) ]
4. B0 [ 3 2-e-3 L ( 3 2+ L ) ]

When a coil is placed in a time dependent magnetic field the power dissipated in it is P. The number of turns, area of the coil and radius of the coil wire are N, A and r respectively. For a second coil number of turns, area of the coil and radius of the coil wire are 2N, 2A and 3r respectively. When the first coil is replaced with second coil the power dissipated in it is 2 P. The value of is .

1. 36
2. 128 2
3. 16
4. 64

A circular current loop of radius R is placed inside square loop of side length L (L R) such that they are co-planar and their centers coincide. The permeability of free space is 0. The mutual inductance between circular loop and square loop is .

1. 2 2 0 L2R
2. 2 0 L2R
3. 2 0 R2L
4. 2 2 0 R2L

A 20 m long uniform copper wire held horizontally is allowed to fall under the gravity (g = 10 m/s2) through a uniform horizontal magnetic field of 0.5 Gauss perpendicular to the length of the wire. The induced EMF across the wire when it travels a vertical distance of 200 m is mV.

1. 200 10
2. 0.2 10
3. 20 10
4. 2 10

A circular loop of radius 7 cm is placed in uniform magnetic field of 0.2 T directed perpendicular to plane of loop. The loop is converted into a square loop in 0.5 s . The EMF induced in the loop is mV.

1. 13.2
2. 6.6
3. 1.32
4. 8.25

Suppose a long solenoid of 100 cm length, radius 2 cm having 500 turns per unit length, carries a current I = 10 ( t) A, where = 1000 rad/s. A circular conducting loop (B) of radius 1 cm coaxially slid through the solenoid at a speed v = 1 cm/s. The r.m.s. current through the loop when the coil B is inserted 10 cm inside the solenoid is 2 . The value of is . [Resistance of the loop = 10 ]

1. 80
2. 280
3. 100
4. 197

XPQY is a vertical smooth long loop having a total resistance R where PX is parallel to QY and separation between them is l. A constant magnetic field B perpendicular to the plane of the loop exists in the entire space. A rod CD of length L(L > l) and mass m is made to slide down from rest under the gravity as shown in figure. The terminal speed acquired by the rod is m/s. (g = acceleration due to gravity) [figure]

1. mgRB2l2
2. 2mgRB2L2
3. 2mgRB2l2
4. 8mgRB2l2

Three identical coils C1, C2 and C3 are closely placed such that they share a common axis. C2 is exactly midway. C1 carries current I in anti-clockwise direction while C3 carries current I in clockwise direction. An induced current flows through C2 will be in clockwise direction when

1. C1 and C3 move with equal speeds away from C2
2. C1 moves towards C2 and C3 moves away from C2
3. C1 and C3 move with equal speeds towards C2
4. C1 moves away from C2 and C3 moves towards C2

Figure shows the circuit that contains three resistances (9 each) and two inductors (4 mH each). The reading of ammeter at the moment switch K is turned ON, is A. [figure]

1. 2
2. 3
3. 1
4. zero

A conducting circular loop of area 1.0 m2 is placed perpendicular to a magnetic field which varies as B = (100t) Tesla. If the resistance of the loop is 100 , then the average thermal energy dissipated in the loop in one period is J.

1. 2
2. 2
4. 2

A 1 m long metal rod AB completes the circuit as shown in figure. The area of circuit is perpendicular to the magnetic field of 0.10 T. If the resistance of the total circuit is 2 then the force needed to move the rod towards right with constant speed (v) of 1.5 m/s is N. [figure]

1. 5.7 10-2
2. 7.5 10-3
3. 5.7 10-3
4. 7.5 10-2

A solenoid having area A and length 'l' is filled with a material having relative permeability 2. The magnetic energy stored in the solenoid is :

1. B2Al4 0
2. B2Al2 0
3. B2Al 0
4. B2Al

A coil of area A and N turns is rotating with angular velocity in a uniform magnetic field B about an axis perpendicular to B. Magnetic flux and induced emf across it, at an instant when B is parallel to the plane of coil, are :

1. = AB, = NAB
2. = AB, = 0
3. = 0, = 0
4. = 0, = NAB

Consider I1 and I2 are the currents flowing simultaneously in two nearby coils 1 & 2, respectively. If L1 = self inductance of coil 1, M12 = mutual inductance of coil 1 with respect to coil 2, then the value of induced emf in coil 1 will be :

1. e1 = -L1 dI2dt - M12 dI1dt
2. e1 = -L1 dI1dt + M12 dI2dt
3. e1 = -L1 dI1dt - M12 dI1dt
4. e1 = -L1 dI1dt - M12 dI2dt

A uniform magnetic field of 0.4 T acts perpendicular to a circular copper disc 20 cm in radius. The disc is having a uniform angular velocity of 10 rad s-1 about an axis through its centre and perpendicular to the disc. What is the potential difference developed between the axis of the disc and the rim? ( = 3.14)

1. 0.5024 V
2. 0.0628 V
3. 0.2512 V
4. 0.1256 V

Regarding self-inductance: Choose the correct answer from the options given below:

1. A, B, C, E only
2. A, B, C, D only
3. A, C, D, E only
4. B, C, D, E only

A rectangular metallic loop is moving out of a uniform magnetic field region to a field free region with a constant speed. When the loop is partially inside the magnetic field, the plot of magnitude of induced emf ( ) with time (t) is given by

1. [figure]
2. [figure]
3. [figure]
4. [figure]