Calculate the self-inductance of a solenoid having \(1000\) turns and length \(1\) m. (The area of cross-section is \(7\) cm² and \(\mu_r=1000).\)

1. \(888\) H

2. \(0.88\) H

3. \(0.088\) H

4. \(88.8\) H

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

The slotting processes in a metallic sheet results in:

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

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

Eddy currents are used in:

1. Induction furnace

2. Electromagnetic brakes

3. Speedometers

4. All of these

A short magnet is allowed to fall along the axis of a horizontal metallic ring. Starting from rest, the distance fallen by the magnet in one second may be: