Electromagnetic Induction

A rectangular wire loop of sides 8 cm and 3 cm with a small cut, is moving out of a region of uniform magnetic field of magnitude 0.3 T directed normal to the plane of the loop. The emf developed across the cut, if the velocity of the loop is 2 cm s-1, in a direction normal to the shorter side of the loop, will be :

1. 1.8 10-4 volt
2. 1.3 10-4 volt
3. 1.2 10-4 volt
4. 4.8 10-4 volt

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

The magnetic flux linked to a circular coil of radius R is = 2t3 + 4t2 + 2t + 5 Wb The magnitude of induced emf in the coil at t = 5 s is

1. 192 V
2. 108 V
3. 197 V
4. 150 V

Two conducting circular loops of radii R1 and R2 are placed in the same plane with their centres coinciding. If R1 >> R2, the mutual inductance M between them will be directly proportional to :

1. R22R1
2. R1R2
3. R2R1
4. R12R2

A 800 turn coil of effective area 0.05 m2 is kept perpendicular to a magnetic field 5 10-5 T. When the plane of the coil is rotated by 90 around any of its coplanar axis in 0.1 s, the emf induced in the coil will be :

1. 0.2 V
2. 0.02 V
3. 2 V
4. 2 10-3 V

In which of the following devices, the eddy current effect is not used?

1. magnetic braking in train
2. electromagnet
3. electric heater
4. induction furnace

The magnetic potential energy stored in a certain inductor is 25 mJ, when the current in the inductor is 60 mA. This inductor is of inductance

1. 0.138 H
2. 138.88 H
3. 1.389 H
4. 13.89 H

A long solenoid of diameter 0.1 m has 2 104 turns per meter. At the centre of the solenoid, a coil of 100 turns and radius 0.01 m is placed with its axis coinciding with the solenoid axis. The current in the solenoid reduces at a constant rate to 0 A from 4 A in 0.05 s. If the resistance of the coil is 10 2 , the total charge flowing through the coil during this time is

1. 16
2. 32
3. 16
4. 32

Figure shows a circuit that contains three identical resistors with resistance R = 9.0 each, two identical inductors with inductance L = 2.0 mH each, and an ideal battery with emf = 18 V. The current i through the battery just after the switch is closed is [figure]

1. 0.2 A
2. 4 A
3. 0 ampere
4. 2 mA

A long solenoid has 1000 turns. When a current of 4 A flows through it, the magnetic flux linked with each turn of the solenoid is 4 10-3 Wb. The self-inductance of the solenoid is

1. 2 H
2. 1 H
3. 4 H
4. 3 H

A uniform magnetic field is restricted within a region of radius r. The magnetic field changes with time at a rate d Bdt. Loop 1 of radius R > r encloses the region r and loop 2 of radius R is outside the region of magnetic field as shown in the figure. Then the e.m.f. generated is [figure]

1. zero in loop 1 and zero in loop 2
2. - d Bdt r2 in loop 1 and - d Bdt r2 in loop 2
3. - d Bdt R2 in loop 1 and zero in loop 2
4. - d Bdt r2 in loop 1 and zero in loop 2

An electron moves on a straight line path XY as shown. The abcd is a coil adjacent to the path of electron. What will be the direction of current, if any, induced in the coil ? [figure]

1. The current will reverse its direction as the electron goes past the coil
2. No current induced
3. abcd
4. adcb

A conducting square frame of side 'a' and a long straight wire carrying current I are located in the same plane as shown in the figure. The frame moves to the right with a constant velocity 'V'. The emf induced in the frame will be proportional to [figure]

1. 1(2x+a)2
2. 1(2x-a)(2x+a)
3. 1x2
4. 1(2x-a)2

A thin semicircular conducting ring (PQR) of radius r is falling with its plane vertical in a horizontal magnetic field B, as shown in the figure. [figure] The potential difference developed across the ring when its speed is v, is

1. zero
2. Bv r22 and P is at higher potential
3. rBv and R is at higher potential
4. 2rBv and R is at higher potential

A wire loop is rotated in a magnetic field. The frequency of change of direction of the induced e.m.f. is

1. four times per revolution
2. six times per revolution
3. once per revolution
4. twice per revolution

A current of 2.5 A flows through a coil of inductance 5 H. The magnetic flux linked with the coil is

1. 0.5 Wb
2. 12.5 Wb
3. zero
4. 2 Wb

In a coil of resistance 10 , the induced current developed by changing magnetic flux through it, is shown in figure as a function of time. The magnitude of change in flux through the coil in weber is [figure]

1. 8
2. 2
3. 6
4. 4

A coil of resistance 400 is placed in a magnetic field. If the magnetic flux (Wb) linked with the coil varies with time t (sec) as = 50t2 + 4. The current in the coil at t = 2 sec is

1. 0.5 A
2. 0.1 A
3. 2 A
4. 1 A

The current (I) in the inductance is varying with time according to the plot shown in figure. [figure] Which one of the following is the correct variation of voltage with time in the coil ?

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

The current i in a coil varies with time as shown in the figure. The variation of induced emf with time would be [figure]

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

A conducting circular loop is placed in a uniform magnetic field, B = 0.025 T with its plane perpendicular to the field. The radius of the loop is made to shrink at a constant rate of 1 mm s-1. The induced emf when the radius is 2 cm, is

1. 2
3. 2
4. 2