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:

$A$ conducting loop is kept perpendicularly in an increasing magnetic field,as shown in the figure. The direction of the induced current in the loop will be:

The adjoining figure shows two different arrangements in which two square wire frames are placed in a uniform constantly decreasing magnetic field $B.$ The direction of induced current in the case $II$ is

The magnetic flux linked with a coil,in webers,is given by the equation $\phi = 3t^2 + 4t + 9$. The magnitude of the induced $e.m.f.$ at $t = 2 \ s$ will be $...... \ V$.

$A$ 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 $= 10^{-2}\,m^2$).

$A$ bar magnet is allowed to fall vertically through a copper coil placed in a horizontal plane. The magnet falls with a net acceleration: