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 \(4\times 10^{-3}\) 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. \(\frac{B l v}{\frac{1}{R_{1}} + \frac{1}{R_{2}} + \frac{1}{R_{0}}}\)

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

The coefficient of mutual inductance between two coils depends upon:

Two coils have a mutual inductance of \(5\) mH. The current changes in the first coil according to the equation \(I=I_{0}\cos\omega t,\)where \(I_{0}=10~\text{A}\)and\(\omega = 100\pi ~\text{rad/s}\). The maximum value of emf induced in the second coil is:
1. \(5\pi\) Volt
2. \(2\pi\) Volt
3. \(4\pi\) Volt
4. \(\pi\) Volt