Two coils have a mutual inductance $0.005 \, H$. The current changes in the first coil according to the equation $I = I_0 \sin(\omega t)$,where $I_0 = 10 \, A$ and $\omega = 100\pi \, rad/s$. The maximum value of the $e.m.f.$ in the second coil is:

$A$ pair of adjacent coils have a mutual inductance, $M$. The current in one coil changes from $0 \,A$ to $16 \,A$ in $0.3 \,s$, and the change of flux linkage with the other coil is $40 \,Wb$. The value of $M$ is: (in $\,H$)

Two coaxial solenoids are made by winding thin insulated wire over a pipe of cross-sectional area $A = 10 \ cm^2$ and length $\ell = 20 \ cm$. If one of the solenoids has $N_1 = 300$ turns and the other has $N_2 = 400$ turns,their mutual inductance is (given $\mu_0 = 4\pi \times 10^{-7} \ T \ m \ A^{-1}$):

If a change in current of $0.01\, A$ in one coil produces a change in magnetic flux of $1.2 \times 10^{-2}\,Wb$ in the other coil,then the mutual inductance of the two coils in henries is.....$H$

Consider $I_1$ and $I_2$ are the currents flowing simultaneously in two nearby coils $1$ and $2$,respectively. If $L_1$ is the self-inductance of coil $1$ and $M_{12}$ is the mutual inductance of coil $1$ with respect to coil $2$,then the value of the induced emf in coil $1$ will be:

Find the mutual inductance in the arrangement,when a small circular loop of wire of radius $R$ is placed inside a large square loop of wire of side $L$ $(L \gg R)$. The loops are coplanar and their centres coincide: