A thin ring of radius 'R' metre has charge 'q' coulomb uniformly spread on it. The ring rotates about its axis with a constant frequency of 'f' revolution/s. The value of magnetic induction at the centre of the ring in $\text{Wb/m}^2$ is

( $\mu_0$ = permeability of free space )

Two concentric circular coils having radii $r_1$ and $r_2$ ($r_2 << r_1$) are placed co-axially with centres coinciding. The mutual inductance of the arrangement is (Both coils have single turn, $\mu_0$ = permeability of free space)

Two solenoids A and B of equal number of turns have their lengths and radii in the same ratio $1 : 3$. The ratio of the self-inductance of solenoid A to that of B will be

An electric lamp connected in series with a capacitor and an a.c source is glowing with certain brightness. On reducing the frequency of source the brightness of the lamp