The magnetic flux through a coil perpendicular to its plane and directed into the paper is varying according to the relation $\phi = 5t^2 + 10t + 5$ milliweber. The $e.m.f.$ induced in the loop after $5 \, s$ is ..... $V$.

Consider the experiment shown in the figure.
$(a)$ What would you do to obtain a large deflection of the galvanometer?
$(b)$ How would you demonstrate the presence of an induced current in the absence of a galvanometer?

The magnitude of flux linked with a coil varies with time as $\phi = 3t^2 + 4t + 7$. The magnitude of the induced e.m.f. at $t = 2 \ s$ is: (in $V$)

Consider a metal ring kept on top of a fixed solenoid (say on a cardboard) as per the figure. The center of the ring coincides with the axis of the solenoid. If the current is suddenly switched on,the metal ring jumps up. Explain.

$A$ coil having effective area $A$ is held with its plane normal to a magnetic field of induction $B$. The magnetic induction is quickly reduced by $25 \%$ of its initial value in $2 \ s$. The e.m.f. induced across the coil will be:

The figure shows certain wire segments joined together to form a coplanar loop. The loop is placed in a perpendicular magnetic field in the direction going into the plane of the figure. The magnitude of the field increases with time. $I_1$ and $I_2$ are the currents in the segments $ab$ and $cd$. Then,