A coil of $100$ turns, having an average area of $100 {\mathrm{cm}}^2$ for each turn, is held in a uniform field of $50 \mathrm{gauss}$. The direction of field is at right angle to the plane of coil. The field is removed in $\frac{1}{100} \mathrm{s}$. Average emf (in $\mathrm{V}$) induced in the coil is,

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