The magnetic flux through a coil perpendicular to its plane is varying according to the relation $\phi = (5t^3 + 4t^2 + 2t - 5) \; Wb$. If the resistance of the coil is $5 \; \Omega$,then the induced current through the coil at $t = 2 \; s$ will be $.... \; A$. (in $.6$)

The magnetic flux linked with a coil at any instant $t$ is given by $\phi = 5t^3 - 100t + 300$. The $e.m.f.$ induced in the coil at $t = 2 \ s$ 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?

$A$ circular coil of radius $10 \; cm$, $500$ turns, and resistance $2 \; \Omega$ is placed with its plane perpendicular to the horizontal component of the earth's magnetic field. It is rotated about its vertical diameter through $180^{\circ}$ in $0.25 \; s$. The induced e.m.f. in the coil is (Take $B_H = 3.0 \times 10^{-5} \; T$).

$A$ circular loop of wire is in the same plane as an infinitely long wire carrying a constant current $i$. Four possible motions of the loop are marked by $N, E, W$,and $S$ as shown below. $A$ clockwise current is induced in the loop when the loop is pulled towards:

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 ..... $V$.