$A$ coil having effective area $A$ is held with its plane normal to a magnetic field of induction $B$. The magnetic induction is quickly reduced by $25 \%$ of its initial value in $2 \ s$. The e.m.f. induced across the coil will be:

In a coil of resistance $8 \, \Omega$,the magnetic flux due to an external magnetic field varies with time as $\phi = \frac{2}{3}(9 - t^2)$. The value of total heat produced in the coil,till the flux becomes zero,will be $.... \, J$.

$A$ circular loop of wire of radius $14 \ cm$ is placed in a magnetic field directed perpendicular to the plane of the loop. If the field decreases at a steady rate of $0.05 \ Ts^{-1}$ in some interval,then the magnitude of the emf induced in the loop is (in $mV$)

$A$ rectangular loop of wire $ABCD$ is kept close to an infinitely long wire carrying a current $I(t) = I_0(1 - t/T)$ for $0 \le t \le T$ and $I(t) = 0$ for $t > T$ as shown in the figure. Find the total charge passing through a given point in the loop in time $T$. The resistance of the loop is $R$.

$A$ square wire loop of side $10.0 \, cm$ is placed in a uniform perpendicular magnetic field of $20 \, T.$ The magnetic field decreases to zero in time interval $\Delta t.$ The bulb will glow with full brightness if the value of $\Delta t$ is.....$ms.$ (Assume the bulb requires $10 \, V$ to glow with full brightness.)

If the flux associated with a coil of $60$ turns varies at the rate of $1 \text{ Wb/hour}$,the induced emf is . . . . . . .