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, $r \ll R$ )

A circular coil consists 70 closely wound turns and has a radius of 10 cm . An externally produced magnetic field of magnitude $2 \times 10^{-3} \mathrm{~T}$ is applied perpendicular to the coil. The net flux through the coil is found to vanish when the current in the coil is 2.2 A . The inductance of the coil is

A varying current in a coil changes from 10 A to zero in 1.5 s . If the average emf induced in the coil is 200 V , the self-inductance of the coil is