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

In the given circuit below inductance values of L1, L2 and L3 are same. The magnetic energy stored in the entire circuit is (Ut) and that stored in the L2 inductor is (Ul). Ut/Ul is . (Ignore the mutual inductance if any) [figure]

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 ) ]

A circular loop of radius 20 cm and resistance 2 is placed in a time varying magnetic field B= (2t2+2t+3 ) T. At t=0, for the plane of the loop being perpendicular to the magnetic field and, the induced current in the loop at t=3 s is 50 A. The value of is . (Take =22/7)

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 simple pendulum made of mass 10 g and a metallic wire of length 10 cm is suspended vertically in a uniform magnetic field of 2 T. The magnetic field direction is perpendicular to the plane of oscillations of the pendulum. If the pendulum is released from an angle of 60 with vertical, then maximum induced EMF between the point of suspension and point of oscillation is mV. (Take g = 10 m/s2)