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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 

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:

A square metallic wire loop of side \(0.1\) 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 \(1\) mA in the loop?
       

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) $\frac{B_0^2\pi r^2}{R}$
(2) $\frac{B_{0}10r^3}{R}$
(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 \(B = 2T\) 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) $\frac{mgR}{Bl}$
(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 4l is rotated about a point O in a uniform magnetic field $\overrightarrow{B}$ directed into the paper. AO = l and OC = 3l. 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 10³ A/s then V_B – V_A is

(1) 5 V
(2) 10 V
(3) 15 V
(4) 20 V

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. $2BL\sin \left(\frac{{\displaystyle \theta }}{{\displaystyle 2}}\right){\left(gL\right)}^{1/2}$
2. $BL\sin \left(\frac{{\displaystyle \theta }}{{\displaystyle 2}}\right){\left(gL\right)}^{\raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$2$}\right.}$
3. $BL\sin \left(\frac{{\displaystyle \theta }}{{\displaystyle 2}}\right){\left(gL\right)}^{3/2}$
4. $BL\sin \left(\frac{{\displaystyle \theta }}{{\displaystyle 2}}\right){\left(gL\right)}^2$

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