A circular coil of area $200 \mathrm{~cm}^2$ and 50 turns is rotating about its vertical diameter with an angular speed of $\theta$ $40 \mathrm{rads}^{-1}$ in a uniform horizontal magnetic field of magnitude $2 \times 10^{-2} \mathrm{~T}$. The maximum emf induced in the coil is

A train with an axle of length 1.66 m is moving towards north with a speed of $90 \mathrm{kmh}^{-1}$. If the vertical component of the earth's magnetic field is $0.2 \times 10^{-4} \mathrm{~T}$, the emf induced across the ends of the axle of the train is

Two circular coils of radii $r_1$ and $r_2\left(r_1 \ll r_2\right)$ are placed coaxially with their centres coinciding. The mutual inductance of the arrangement is

When a current $i$ through a solenoid is increasing at a constant rate, then the induced current is