Electromagnetic Induction - 10 Jan 2021Contact Number: 9667591930 / 8527521718

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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 $\mathrm{\omega}=100\mathrm{\pi}$ rad/s. Maximum value of e.m.f. induced in the second coil is

1. 5$\pi $ volt

2. 2$\pi $ volt

3. 4$\pi $ volt

4. $\pi $ 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) $\frac{1}{2}B\omega {l}^{2}$

(2) $\frac{3}{4}B\omega {l}^{2}$

(3) $B\omega {l}^{2}$

(4) $2B\omega {l}^{2}$

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) *R*_{1}/*R*_{2}

(2) *R*_{2}/*R*_{1}

(3) ${R}_{1}^{2}/{R}_{2}$

(4) ${R}_{2}^{2}/{R}_{1}$

A square metallic wire loop of side 0.1 *m* and resistance of 1 Ω is moved with a constant velocity in a magnetic field of 2 *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 *mA* in the loop?

1. 1 *cm*/*sec*

2. 2 *cm*/*sec*

3. 3 *cm*/*sec*

4. 4 *cm*/*sec*

Shown in the figure is a circular loop of radius *r* and resistance *R*. A variable magnetic field of induction *B* = *B*_{0}*e*^{–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) $\frac{{B}_{0}^{2}\pi {r}^{2}}{R}$

(2) $\frac{{B}_{0}10{r}^{3}}{R}$

(3) $\frac{{B}_{0}^{2}{\pi}^{2}{r}^{4}R}{5}$

(4) $\frac{{B}_{0}^{2}{\pi}^{2}{r}^{4}}{R}$

A rectangular loop with a sliding connector of length *l* = 1.0 *m* is situated in a uniform magnetic field *B* = 2 *T* perpendicular to the plane of the loop. Resistance of connector is *r* = 2 Ω. Two resistance of 6 Ω and 3 Ω 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 *N*

2. 4 *N*

3. 2 *N*

4. 1 *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) $\frac{mgR}{Bl}$

(2) $\frac{mgR}{{B}^{2}{l}^{2}}$

(3) $\frac{mgR}{{B}^{3}{l}^{3}}$

(4) $\frac{mgR}{{B}^{2}l}$

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

(1) ${V}_{A}-{V}_{O}=\frac{B\omega {l}^{2}}{2}$

(2) ${V}_{O}-{V}_{C}=\frac{7}{2}B\omega {l}^{2}$

(3) ${V}_{A}-{V}_{C}=4B\omega {l}^{2}$

(4) ${V}_{C}-{V}_{O}=\frac{9}{2}B\omega {l}^{2}$

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 10^{3} *A*/*s* then *V _{B}* –

(1) 5

(2) 10

(3) 15

(4) 20

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

(1) $2BL\mathrm{sin}\left(\frac{{\displaystyle \theta}}{{\displaystyle 2}}\right){\left(gL\right)}^{1/2}$

(2) $BL\mathrm{sin}\left(\frac{{\displaystyle \theta}}{{\displaystyle 2}}\right){\left(gL\right)}^{\raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$2$}\right.}$

(3) $BL\mathrm{sin}\left(\frac{{\displaystyle \theta}}{{\displaystyle 2}}\right){\left(gL\right)}^{3/2}$

(4) $BL\mathrm{sin}\left(\frac{{\displaystyle \theta}}{{\displaystyle 2}}\right){\left(gL\right)}^{2}$

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

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) (4)

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/x^{2}

2.1/(2x-a)^{2}

3.1/(2x+a)^{2}

4. 1/(2x-a) x (2x+a)

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