$A$ coil having $100$ turns and an area of $1 \times 10^{-3} \ m^2$ is placed in a magnetic field of $1 \ Wb/m^2$. If the magnetic field is reversed,what is the total charge that flows through the circuit,given that the resistance of the circuit is $10 \ \Omega$?

It is desired to measure the magnitude of the magnetic field between the poles of a powerful loudspeaker magnet. $A$ small flat search coil of area $2 \; cm^{2}$ with $25$ closely wound turns is positioned normal to the field direction and then quickly snatched out of the field region. (Equivalently,one can give it a quick $90^{\circ}$ turn to bring its plane parallel to the field direction). The total charge flown in the coil (measured by a ballistic galvanometer connected to the coil) is $7.5 \; mC$. The combined resistance of the coil and the galvanometer is $0.50 \; \Omega$. Estimate the field strength of the magnet.

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 $I$ is

The magnetic flux $\phi$ through a coil varies with time $t$ as shown in the diagram. Which graph best represents the variation of the induced electromotive force (e.m.f.) $E$ in the coil with time $t$?

$A$ coil of resistance $400\,\Omega$ is placed in a magnetic field. If the magnetic flux $\phi$ (in $Wb$) linked with the coil varies with time $t$ (in $s$) as $\phi = 50t^2 + 4$,the current in the coil at $t = 2\,s$ is $..........\,A$.

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 $...... \ V$.