The magnetic potential energy stored in a certain inductor is \(25\) mJ, when the current in the inductor is \(60\) mA. This inductor is of inductance:
1. \(0.138\) H
2. \(138.88\) H
3. \(1.389\) H
4. \(13.89\) H

A long solenoid of diameter \(0.1\) m has \(2 \times 10^4\) turns per meter. At the center of the solenoid, a coil of \(100\) turns and radius \(0.01\) m is placed with its axis coinciding with the solenoid axis. The current in the solenoid reduces at a constant rate to \(0\) A from \(4\) A in \(0.05\) s. If the resistance of the coil is \(10\pi^2~\Omega\), then the total charge flowing through the coil during this time is:
1. \(16~\mu \text{C}\)
2. \(32~\mu \text{C}\)
3. \(16\pi~\mu \text{C}\)
4. \(32\pi~\mu \text{C}\)

A uniform magnetic field is restricted within a region of radius r. The magnetic field changes with time at a rate $\frac{dB}{dt}$. Loop 2 of radius R is outside the region of magnetic field as shown in the figure. Then the emf generated is-

1. zero in loop 1 and zero in loop 2

2. $-\frac{dB}{dt}{\mathrm{\pi r}}^2$ $\mathrm{in}$ $\mathrm{loop}$ $1$ $\mathrm{and}-\frac{\mathrm{dB}}{\mathrm{dt}}{\mathrm{\pi r}}^2$ $\mathrm{in}$ $\mathrm{loop}$ $2$

3. $-\frac{dB}{dt}{\mathrm{\pi r}}^2$ $\mathrm{in}$ $loop$ $1$ $and$ $zero$ $\mathrm{in}$ $\mathrm{loop}$ $2$

4. $\frac{2dB}{dt}{\mathrm{\pi r}}^2$ $\mathrm{in}$ $loop$ $1$ $and$ $zero$ $\mathrm{in}$ $\mathrm{loop}$ $2$