The current passing through a coil of 120 turns and inductance 40 mH is 30 mA . The magnetic flux linked with the coil is

$X$ and $Y$ are two circuits having coefficient of mutual inductance 3 mH and resistance $10 \Omega$ and $4 \Omega$ respectively. To have induced current $60 \times 10^{-4} \mathrm{~A}$ in circuit $Y$, the amount of current to be changed in circuit $X$ in 0.02 s is

The ratio of the number of turns per unit length of two solenoids $A$ and $B$ are 1:3 and the lengths of $A$ and $B$ are in the ratio $1: 2$. If the two solenoids have same cross-sectional area, the ratio of the self-inductances of the solenoids $A$ and $B$ is

Magnetic field at a distance of $r$ from $Z$-axis is $B=B_0$ $r t \hat{\mathbf{k}}$ present in the region. $B_0$ is constant and $t$ is time. The magnitude of induced electric field at a distance of $r$ from $Z$-axis is