The mutual inductance of a pair of coils,each of $N$ turns,is $M$ henry. If a current of $I$ ampere in one of the coils is brought to zero in $t$ seconds,the e.m.f. induced per turn in the other coil in volt is:

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 coaxial coils are very close to each other and their mutual inductance is $5 \,mH$. If a current $i = 50 \sin(500t) \,A$ is passed in one of the coils,then the peak value of the induced e.m.f. in the secondary coil will be ........... $V$.

$A$ very long straight conductor and an isosceles triangular conductor lie in a plane and are separated from each other as shown in the figure. If $a = 10 \ cm$,$b = 20 \ cm$,and $h = 10 \ cm$,find the coefficient of mutual induction.

Write the formula for the mutual inductance of two very long coaxial solenoids of length $l$.

$A$ small square loop of wire of side $l$ is placed inside a large square loop of wire of side $(L > l)$. The loops are coplanar and their centres coincide. The mutual inductance of the system is proportional to