Self and mutual inductance

AB is a part of an electrical circuit (see figure). The potential difference "\(V_A - V_B\)", at the instant when current i = 2 A and is increasing at a rate of 1 amp / second is:

The magnetic energy stored in an inductor of inductance \(4\,\mu\mathrm{H}\) carrying a current of 2 A is :

Two conducting circular loops of radii \(R_1\) and \(R_2\) are placed in the same plane with their centres coinciding. If \(R_1 >> R_2\), the mutual inductance M between them will be directly proportional to :

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

Figure shows a circuit that contains three identical resistors with resistance R = 9.0 \(\Omega\) each, two identical inductors with inductance L = 2.0 mH each, and an ideal battery with emf \(\varepsilon\) = 18 V. The current 'i' through the battery just after the switch closed is,.....

A long solenoid of diameter 0.1 m has \(2\times10^4\) turns per meter. At the centre 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 0A from 4 A in 0.05 s. If the resistance of the coil is \(10\pi^2\,\Omega\), the total charge flowing through the coil during this time is :

A long solenoid has 1000 turns. When a current of 4A flows through it, the magnetic flux linked with each turn of the solenoid is \(4\times10^{-3}\) Wb. The self-inductance of the solenoid is :