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 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 $10{\mathrm{\pi }}^2$ $\mathrm{\Omega ,}$ then the total charge flowing through the coil during this time is:-

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