Two coils $P$ and $Q$ are kept near each other. When no current flows through coil $P$ and current increases in coil Q at the rate of $10 \mathrm{~A} / \mathrm{S}$, the e.m.f. in coil P is 15 mV . When coil Q carries no current and current of 1.8 A flows through coil $P$, the magnetic flux linked with coil Q is

To manufacture a solenoid of length ' $l$ ' and inductance ' $L$ ', the length of the thin wire required is (Diameter of the solenoid is very less than length, $\mu_0=$ permeability of free space)

Initially a rectangular coil with length vertical is moving out with constant velocity ' $v$ ' in a constant magnetic field ' $B$ ' towards right. Now the same coil is rotated through $90^{\circ}$ in same plane in same magnetic field B and the coil is moving with same velocity $\mathbf{v}$. The magnitude of induced e.m.f. is now

A simple pendulum with bob of mass m and conducting wire of length $L$ swings under gravity through an angle $\theta$. The component of earth's magnetic field in the direction perpendicular to swing is B . Maximum e.m.f. induced across the pendulum is ( $\mathrm{g}=$ acceleration due to gravity)