Electromagnetic Induction · Question 1

Consider a long solenoid of length l and radius r. If n is the number of turns per unit length and 0 is the permeability of free space, the inductance of the solenoid is :

1. 2 0 n2 r2 l
2. 0 n2 r2 l
3. 0 n2 r2 l
4. ( 0/2 )n2 r2 l

Two identical inductors are connected in two different configurations P and Q, where a time varying current I(t) is flowing, as shown in the figure. The induced emf between points a and b for configuration P is EP and that for configuration Q is EQ. The ratio EP/EQ is: [Neglect the effect of mutual inductance.] [figure]

1. 2
2. 1/4
3. ½
4. 1

A conducting loop of finite resistance lies on the x-y plane. There is a constant magnetic field in the z direction. The area of the loop varies with time t, as A = A0(1 + t) in appropriate units. The figure that correctly indicates the qualitative behaviour of the power P dissipated in the loop as a function of time is:

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

AB is a part of an electrical circuit (see figure). The potential difference "VA - VB", at the instant when current i = 2 A and is increasing at a rate of 1 amp/ second is: [figure]

1. 9 volt
2. 10 volt
3. 5 volt
4. 6 volt

[figure] In the above diagram, a strong bar magnet is moving towards solenoid-2 from solenoid-1. The direction of induced current in solenoid-1 and that in solenoid-2, respectively, are through the directions:

1. AB and DC
2. BA and CD
3. AB and CD
4. BA and DC

A sheet is placed on a horizontal surface in front of a strong magnetic pole. A force is needed to: Choose the correct statement(s) from the options given below:

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

Let us consider two solenoids A and B, made from same magnetic material of relative permeability r and equal area of cross-section. Length of A is twice that of B and the number of turns per unit length in A is half that of B. The ratio of self inductances of the two solenoids, LA : LB is

1. 1 : 2
2. 2 : 1
3. 8 : 1
4. 1 : 8

The magnetic energy stored in an inductor of inductance 4 carrying a current of 2 A is :

1. 4 mJ
2. 8 mJ
3. 8
4. 4

A square loop of side 1 m and resistance 1 is placed in a magnetic field of 0.5 T. If the plane of loop is perpendicular to the direction of magnetic field, the magnetic flux through the loop is

1. 2 weber
2. 0.5 weber
3. 1 weber
4. Zero weber

A big circular coil of 1000 turns and average radius 10 m is rotating about its horizontal diameter at 2 rad s-1. If the vertical component of earth's magnetic field at that place is 2 10-5 T and electrical resistance of the coil is 12.56 , then the maximum induced current in the coil will be

1. 0.25 A
2. 1.5 A
3. 1 A
4. 2 A