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.	\({mgR \over Bl}\)	2.	\({mgR \over B^2l^2}\)
3.	\({mgR \over B^3l^3}\)	4.	\({mgR \over B^2l}\)

A coil having number of turns \(N\) and cross-sectional area \(A\) is rotated in a uniform magnetic field \(B\) with an angular velocity \(\omega\). The maximum value of the emf induced in it is:
1. \(\frac{NBA}{\omega}\)
2. \(NBAω\)
3. \(\frac{NBA}{\omega^{2}}\)
4. \(NBAω^{2}\)

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 x 10^-3 Wb. The self-inductance of the solenoid is:

1. 3 H

2. 2 H

3. 1 H

4. 4 H

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

The current I in an inductance coil varies with time t according to the graph shown in the figure. Which one of the following plots shows the variation of voltage in the coil with time?

1.		2.
3.		4.

A bar magnet is released along the vertical axis of the conducting coil. The acceleration of the bar magnet is:

A rod having length \(l\) and resistance \(R_0\) is moving with speed \(v\) as shown in the figure. The current through the rod is:
               

1. \(\frac{B l v}{\frac{R_{1} R_{2}}{R_{1} + R_{2}} + R_{0}}\)

2. \(\frac{Blv}{\left(\frac{1}{R_{1}} + \frac{1}{R_{2}} + \frac{1}{R_{o}}\right)^{2}}\)

3. \(\frac{B l v}{R_{1} + R_{2} + R_{0}}\)

4. \(\frac{B l v}{\frac{1}{R_{1}} + \frac{1}{R_{2}} + \frac{1}{R_{0}}}\)

A solenoid of inductance L and resistance R is connected to a battery of e.m.f. E. Maximum value of magnetic energy stored in the inductor is:

$1.$ $\frac{E^2}{2R}$
$2.$ $\frac{E^{2}L}{2R^2}$
$3.$ $\frac{E^{2}L}{R}$ $$
$4.$ $\frac{E^{2}L}{2R}$

The coefficient of mutual inductance between two coils depends upon:

A small square loop of wire of side 'l' is placed inside a large square loop of side 'L' (L$\gg$l). If the loops are coplanar and their centres coincide, the mutual inductance of the system is directly proportional to:

1. L/l

2. l/L

3. L²/l

4. l²/L