Electromagnetic Induction

Two coils have a mutual inductance of 5 mH. Current changes in the first coil according to the equation I = $I_{0}$ cos wt, where $I_{0}$ = 10 A and $ω = 100 π$ rad/s. Maximum value of e.m.f. induced in the second coil is
1. 5 $π$ volt
2. 2 $π$ volt
3. 4 $π$ volt
4. $π$ volt

One conducting U tube can slide inside another as shown in figure, maintaining electrical contacts between the tubes. The magnetic field B is perpendicular to the plane of the figure. If each tube moves towards the other at a constant speed v then the emf induced in the circuit in terms of B, l and v where l is the width of each tube, will be

1. Zero
2. 2 Blv
3. Blv
4. – Blv

The adjoining figure shows two bulbs $B_1$ and $B_2$ resistor $R$ and an inductor $L$. When the switch $S$ is turned off

1.	Both $B_1$ and $B_2$ die out promptly.
2.	Both $B_1$ and $B_2$ die out with some delay.
3.	$B_1$ dies out promptly but $B_2$ with some delay.
4.	$B_2$ dies out promptly but $B_1$ with some delay.

A copper rod of length l is rotated about one end perpendicular to the magnetic field B with constant angular velocity ω. The induced e.m.f. between the two ends is
1. $\frac{1}{2} B ω l^{2}$
2. $\frac{3}{4} B ω l^{2}$
3. $B ω l^{2}$
4. $2 B ω l^{2}$

Two conducting circular loops of radii $R_1$ and $R_2$ are placed in the same plane with their centres coinciding. If $R_1>>R_2$, the mutual inductance $M$ between them will be directly proportional to:

1.	$\dfrac{R_1}{R_2}$	2.	$\dfrac{R_2}{R_1}$
3.	$\dfrac{R^2_1}{R_2}$	4.	$\dfrac{R^2_2}{R_1}$

A square metallic wire loop of side $0.1~\text m$ and resistance of $1~\Omega$ is moved with a constant velocity in a magnetic field of $2~\text{wb/m}^2$ as shown in the figure. The magnetic field is perpendicular to the plane of the loop and the loop is connected to a network of resistances. What should be the velocity of the loop so as to have a steady current of $1~\text{mA}$ in the loop?

1. $1~\text{cm/s}$
2. $2~\text{cm/s}$
3. $3~\text{cm/s}$
4. $4~\text{cm/s}$

Shown in the figure is a circular loop of radius r and resistance R. A variable magnetic field of induction B = B₀e^–t is established inside the coil. If the key (K) is closed, the electrical power developed right after closing the switch, at t=0, is equal to

1. $\frac{B_{0}^{2} π r^{2}}{R}$
2. $\frac{B_{0} 10 r^{3}}{R}$
3. $\frac{B_{0}^{2} π^{2} r^{4} R}{5}$
4. $\frac{B_{0}^{2} π^{2} r^{4}}{R}$

A rectangular loop with a sliding connector of length $l= 1.0$ m is situated in a uniform magnetic field $B = 2T$ perpendicular to the plane of the loop. Resistance of connector is $r=2~\Omega$. Two resistances of $6~\Omega$ and $3~\Omega$ are connected as shown in the figure. The external force required to keep the connector moving with a constant velocity $v = 2$ m/s is:

1. $6~\text{N}$
2. $4~\text{N}$
3. $2~\text{N}$
4. $1~\text{N}$

A wire cd of length l and mass m is sliding without friction on conducting rails ax and by as shown. The vertical rails are connected to each other with a resistance R between a and b. A uniform magnetic field B is applied perpendicular to the plane abcd such that cd moves with a constant velocity of

1. $\frac{m g R}{B l}$
2. $\frac{m g R}{B^{2} l^{2}}$
3. $\frac{m g R}{B^{3} l^{3}}$
4. $\frac{m g R}{B^{2} l}$

10.

A conducting rod AC of length 4l is rotated about a point O in a uniform magnetic field $\vec{B}$ directed into the paper. AO = l and OC = 3l. Then

1. $V_{A} - V_{O} = \frac{B ω l^{2}}{2}$
2. $V_{O} - V_{C} = \frac{7}{2} B ω l^{2}$
3. $V_{A} - V_{C} = 4 B ω l^{2}$
4. $V_{C} - V_{O} = \frac{9}{2} B ω l^{2}$

11.

The network shown in the figure is a part of a complete circuit. If at a certain instant the current i is 5 A and is decreasing at the rate of 10³ A/s then V_B – V_A is

1. 5 V
2. 10 V
3. 15 V
4. 20 V

12.

A simple pendulum with bob of mass m and conducting wire of length L swings under gravity through an angle 2θ. The earth’s magnetic field component in the direction perpendicular to swing is B. Maximum potential difference induced across the pendulum is

1. $2 B L \sin (\frac{θ}{2}) {(g L)}^{1 / 2}$
2. $B L \sin (\frac{θ}{2}) {(g L)}^{\frac{1}{2}}$
3. $B L \sin (\frac{θ}{2}) {(g L)}^{3 / 2}$
4. $B L \sin (\frac{θ}{2}) {(g L)}^{2}$

13.

Some magnetic flux is changed from a coil of resistance 10 ohm. As a result an induced current is developed in it, which varies with time as shown in figure. The magnitude of change in flux through the coil in webers is

1. 2
2. 4
3. 6
4. None of these

14.

A rectangular loop is being pulled at a constant speed v, through a region of certain thickness d, in which a uniform magnetic field B is set up. The graph between position x of the right-hand edge of the loop and the induced emf E will be-

1. 2.
3. 3.

15.

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

1.1/x²
2.1/(2x-a)²
3.1/(2x+a)²
4. 1/(2x-a) x (2x+a)

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1.	Both \(B_1\) and \(B_2\) die out promptly.
2.	Both \(B_1\) and \(B_2\) die out with some delay.
3.	\(B_1\) dies out promptly but \(B_2\) with some delay.
4.	\(B_2\) dies out promptly but \(B_1\) with some delay.

1.	\(\dfrac{R_1}{R_2}\)	2.	\(\dfrac{R_2}{R_1}\)
3.	\(\dfrac{R^2_1}{R_2}\)	4.	\(\dfrac{R^2_2}{R_1}\)

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