The magnetic flux through a loop of resistance $10 \Omega$ varies according to the relation $\phi = 6t^2 + 7t + 1$,where $\phi$ is in milliweber and time is in seconds. At time $t = 1 \ s$,the induced e.m.f. is:

Whenever a magnet is moved towards or away from a conducting coil,and an e.m.f. is induced,the magnitude of which is independent of:

Predict the direction of induced current in the situations described by the following figures.

$A$ rectangular coil of $20$ turns and area of cross section $25 \text{ cm}^2$ has a resistance of $100 \Omega$. If a magnetic field which is perpendicular to the plane of the coil changes at a rate of $100 \text{ T/s}$, the current in the coil is . . . . . . . (in $\text{ A}$)

$A$ 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:

$A$ coil with $10$ turns and a resistance of $20\,\Omega$ is connected in series with a ballistic galvanometer ($B$.$G$.) of resistance $30\,\Omega$. The coil is placed with its plane perpendicular to the direction of a uniform magnetic field of induction $10^{-2}\,T$. If it is now turned through an angle of $60^{\circ}$ about an axis in its plane, find the charge induced in the coil $..............\times 10^{-5} \, C$ (Area of the coil $= 10^{-2}\,m^2$).