Write the equation for the induced charge.

The magnetic flux passing perpendicular to the plane of the coil and directed into the paper is varying according to the relation $\phi = 3t^2 + 2t + 3$,where $\phi$ is in milliwebers $(mWb)$ and $t$ is in seconds $(s)$. The magnitude of the $emf$ induced in the loop when $t = 2 \ s$ is ...... $mV$.

$A$ and $B$ are two metallic rings placed at opposite sides of an infinitely long straight conducting wire as shown. If current in the wire is slowly decreased,the direction of induced current will be

In the above diagram,a strong bar magnet is moving towards solenoid-$2$ from solenoid-$1$. The direction of induced current in solenoid-$1$ and that in solenoid-$2$,respectively,are through the directions:

$A$ highly conducting ring of radius $R$ is perpendicular to and concentric with the axis of a long solenoid as shown in the figure. The ring has a narrow gap of width $d$ in its circumference. The solenoid has a cross-sectional area $A$ and a uniform internal magnetic field of magnitude $B_0$. Starting at $t = 0$,the solenoid current is steadily increased such that the field magnitude at any time $t$ is given by $B(t) = B_0 + \alpha t$,where $\alpha > 0$. Assuming that no charge can flow across the gap,the end of the ring which has an excess of positive charge and the magnitude of the induced e.m.f. in the ring are respectively:

$A$ coil of resistance $250 \Omega$ is placed in a magnetic field. If the magnetic flux $(\phi)$ linked with the coil varies with time $t$ $(s)$ as $\phi = 50t^2 + 7$,the current in the coil at $t = 4 \ s$ is: (in $A$)