$X$ and $Y$ are two metallic coils arranged in such a way that when the steady change in current flowing in coil $X$ is $4 \ A$,the change in magnetic flux associated with coil $Y$ is $0.4 \ Wb$. The mutual inductance of the system of these coils is . . . . . . $H$.

Two circular coils have their centers at the same point. The mutual inductance between them will be maximum when their axes

$A$ 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.

The dimension of mutual inductance is ............

$A$ solenoid has $2000$ turns wound over a length of $0.30 \ m$. The area of its cross-section is $1.2 \times 10^{-3} \ m^2$. Around its central section,a coil of $300$ turns is wound. If an initial current of $2 \ A$ in the solenoid is reversed in $0.25 \ s$,the emf induced in the coil is equal to

Two coils $P$ and $S$ have a mutual inductance of $3 \times 10^{-3} \ H$. If the current in the coil $P$ is $I = 20 \sin(50 \pi t) \ A$,then the maximum value of the e.m.f. induced in coil $S$ is (in $V$)