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

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