A flat circular coil has 100 turns of wire of radius 10 cm . A uniform magnetic field exists in a direction perpendicular to the plane of the coil and it grows at a rate of $0.1 \mathrm{~T} / \mathrm{s}$. The induced emf in the coil is

A long solenoid has 20 turns per cm. A small loop of area $4 / \pi \mathrm{cm}^2$ is placed inside the solenoid normal to its axis. If the current carried by the solenoid changed steadily from 1.0 A to 3.0 A in 0.2 s , what is the magnitude of the induced emf in the loop while the current is changing?

Consider two solenoids $X$ and $Y$ such that the area and length of $Y$ are twice that of $X$ respectively and the magnetic energy stored in both the solenoids is same, then the ratio of magnitude of magnetic fields of the two solenoids $\frac{\left|\mathbf{B}_X\right|}{\left|\mathbf{B}_Y\right|}$ is

Two concentric circular coils, one of small radius $r$ and the other of large radius $R$ are placed co-axially with centres coinciding. If the radius $r$ is changed by $2 \%$, then the change in mutual inductance of the arrangement is (assume, $r \ll R$ )