A uniform but time-varying magnetic field $B\left(t\right)$ exists in a circular region of radius $a$ and is directed into the plane of the paper, as shown figure. The magnitude of the induced electric field at point $P$ at a distance $r$ from the centre of the circular region-

In a uniform magnetic field of inductance $B$, a wire in the form of semicircular of radius $r$ rotates about the diameter of the circle with angular frequency $\omega$. If the total resistance of the circuit is $R$, the mean power generated per period of rotation is

In the figure magnetic energy stored in the coil is (in steady state)