$A$ solenoid has $2000$ turns wound over a length of $0.3\,m$. The area of cross-section is $1.2\times10^{-3}\,m^2$. Around its central section,a coil of $300$ turns is closely wound. If an initial current of $1\,A$ is reversed in $0.25\,s$,find the emf induced in the coil in $mV$.

There are $10$ turns in coil $M$ and $15$ turns in coil $N$. If a current of $2\ A$ is passed through coil $M$,then the flux linked with coil $N$ is $1.8 \times 10^{-3}\ Wb$. If a current of $3\ A$ is passed through coil $N$,then the flux linked with coil $M$ is:

The mutual inductance of a system of two coils does not depend on . . . . . . .

The inductors of two $LR$ circuits are placed next to each other,as shown in the figure. The values of the self-inductance of the inductors,resistances,mutual-inductance,and applied voltages are specified in the given circuit. After both the switches are closed simultaneously,the total work done by the batteries against the induced $EMF$ in the inductors by the time the currents reach their steady-state values is . . . . $mJ$.

Two coils $A$ and $B$ have a coefficient of mutual inductance $M = 2 \ H$. The magnetic flux passing through coil $A$ changes by $4 \ Wb$ in $10 \ s$ due to the change in current in coil $B$. Then:

$A$ short solenoid (length $l$ and radius $r$ with $n$ turns per unit length) lies well inside and on the axis of a very long,coaxial solenoid (length $L$,radius $R$ and $N$ turns per unit length,with $R > r$). Current $I$ flows in the short solenoid. Choose the correct statement.