The coil and magnet are moved in the same direction with the same speed $V$. The induced e.m.f. is

$A$ coil of resistance $8 \Omega$,number of turns $250$,and area $120 \ cm^2$ is placed in a uniform magnetic field of $2 \ T$ such that the plane of the coil makes an angle of $\frac{\pi}{6}$ with the direction of the magnetic field. In a time of $100 \ ms$,the coil is rotated until its plane becomes parallel to the direction of the magnetic field. The current induced in the coil is (in $A$)

Which law is associated with the following equation: $\oint \vec{E} \cdot d\vec{l} = -\frac{d\phi_B}{dt}$?

The magnetic flux $\phi$ (in weber) linked with a closed circuit of resistance $8 \ \Omega$ varies with time (in seconds) as $\phi = 5t^2 - 36t + 1$. The induced current in the circuit at $t = 2 \ s$ is . . . . . . $A$.

Two circular coils $A$ and $B$ are facing each other as shown in the figure. The current $i$ through coil $A$ can be altered.

The magnetic flux through a coil perpendicular to its plane and directed into the paper is varying according to the relation $\phi = (2t^2 + 4t + 6) \, mWb$. The $emf$ induced in the loop at $t = 4 \, s$ is ....... $V$.