A coil is placed in transverse magnetic field of $0.02 \mathrm{T}.$This coil starts shrinking at a rate of $1 \mathrm{mm} {\mathrm{s}}^{-1}$. When its radius $4 \mathrm{cm},$ then what is the value of induced emf-

A uniform magnetic field of induction $B$ is confined to a cylindrical region of radius $R$. The magnetic field is increasing at a constant rate of $\frac{dB}{dt}$ (tesla/second). An electron of charge $q$, placed at the point $P$ on the periphery of the field experiences an acceleration :

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