The magnetic flux through a stationary loop with resistance $R$ varies during an interval of time $T$ as $\phi = at(T - t)$. The heat generated during this time,neglecting the inductance of the loop,will be

$A$ line charge ($\lambda$ per unit length) is in the form of a circular wheel of radius $a$ and moment of inertia $I$,initially at rest. It is free to rotate in a horizontal plane. There is a coaxial magnetic field $B = B_0 \hat{k}$ extending up to a radius $b$ $(b < a)$. If the magnetic field is switched off,the angular velocity $\omega$ of the wheel is given by:

The magnetic flux through a loop of resistance $10 \Omega$ varies according to the relation $\phi = 6t^2 + 7t + 1$,where $\phi$ is in milliweber and time is in seconds. At time $t = 1 \ s$,the induced e.m.f. is:

Consider a metal ring kept on top of a fixed solenoid (say on a cardboard) as per the figure. The center of the ring coincides with the axis of the solenoid. If the current is suddenly switched on,the metal ring jumps up. Explain.

$A$ metal ring is held horizontally and a bar magnet is dropped through the ring with its length along the axis of the ring. The acceleration of the falling magnet is

Assertion : Faraday's laws are a consequence of the conservation of energy.
Reason : In a purely resistive $AC$ circuit,the current lags behind the $emf$ in phase.