A rod with a circular cross-section area $2$ cm$^2$ and length $40$ cm is wound uniformly with $400$ turns of an insulated wire. If a current $0.4$ A flows in the wire winding, the total magnetic flux produced inside the winding is $4\pi \times 10^{-6}$ Wb. The relative permeability of the rod is
(Given permeability of vacuum $\mu_0 = 4\pi \times 10^{-7}$ N m A$^{-2}$)

The magnetic moments associated with two closely wound circular coils a and b of radius $r$ and $2r$ respectively are equal if (where $N_a$, $I_a$ and $N_b$, $I_b$ are number of turns and current in A and B respectively)

A conducting loop of radius $10/[\pi]^{1/2}$ cm is placed perpendicular to a uniform magnetic field $0.5$ T. The magnetic field is decreased to zero in $0.5$ s at a steady rate. The induced emf in the circular loop at $0.25$ s is

In the circuit shown, the ratio of the quality factor and the band width is
(Given: band width = R/L)