$A$ coil has $200$ turns and an area of $70 \ cm^2$. The magnetic field perpendicular to the plane of the coil is $0.3 \ Wb/m^2$ and it takes $0.1 \ s$ to rotate through $180^o$. The value of the induced $e.m.f.$ will be ...... $V$.

$A$ line charge ($\lambda$ per unit length) is in the form of a circular wheel of radius $a$ and moment of inertia $I$,initially at rest. It is free to rotate in a horizontal plane. There is a coaxial magnetic field $B = B_0 \hat{k}$ extending up to a radius $b$ $(b < a)$. If the magnetic field is switched off,the angular velocity $\omega$ of the wheel is given by:

The area of a coil is $A$. The coil is placed in a magnetic field which changes from $B_{0}$ to $4 B_{0}$ in time $t$. The magnitude of the induced e.m.f. in the coil will be:

Lenz's law is expressed by the following formula (here $e$ = induced $e.m.f.$,$\phi$ = magnetic flux in one turn and $N$ = number of turns).

$A$ conducting ring of certain resistance is falling towards a current-carrying straight long conductor. The ring and conductor are in the same plane. Then

$A$ coil of resistance $400 \,\Omega$ is placed in a magnetic field. If the magnetic flux $\phi \,(Wb)$ linked with the coil varies with time $t \,(s)$ as $\phi = 50t^2 + 4$,the current in the coil at $t = 2 \,s$ is.....$A$.