The planar concentric rings of metal wire having radii $r_1$ and $r_2$ (with $r_1>r_2$ ) are placed in air. The current $I$ is flowing through the coil of larger radius. The mutual inductance between the coils is given by ( $\mu_0=$ permeability of free space)

A magnetic field of $2 \times 10^{-2} \mathrm{~T}$ acts at right angles to a coil of area $100 \mathrm{~cm}^2$ with 50 turns, The average e.m.f. induced in the coil is 0.1 V , when it is removed from the field in time $t$. The value of ' $t$ ' is (in second)

A current of 0.5 A is passed through winding of a long solenoid having 400 turns. The magnetic flux linked with each turn is $3 \times 10^{-3} \mathrm{~Wb}$. The self inductance of the solenoid is

A square loop of area $25 \mathrm{~cm}^2$ has a resistance of $10 \Omega$. The loop is placed in uniform magnetic field of magnitude 40 T . The plane of loop is perpendicular to the magnetic field. The work done in pulling the loop out of the magnetic field slowly and uniformly in 1 second, will be