The magnetic flux linked with a coil is given by the equation $\phi$ (in webers) = $8t^2 + 3t + 5$. The induced $e.m.f.$ in the coil at the $4^{th}$ second will be.......$units$.

The direction of induced e.m.f. during electromagnetic induction is given by

Consider a magnet surrounded by a wire loop with an on/off switch $S$ as shown in the figure. If the switch is thrown from the off position (open circuit) to the on position (closed circuit), will a current flow in the circuit? Explain.

$A$ 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.)

$A$ coil of area $100 \, cm^2$ has $500$ turns. $A$ magnetic field of $0.1 \, Wb/m^2$ is perpendicular to the coil. The field is reduced to zero in $0.1 \, s$. The induced $e.m.f.$ in the coil is $...... \, V$.

$A$ long solenoid with $15$ turns per $cm$ has a small loop of area $2.0 \; cm^{2}$ placed inside the solenoid normal to its axis. If the current carried by the solenoid changes steadily from $2.0 \; A$ to $4.0 \; A$ in $0.1 \; s$, what is the induced $emf$ in the loop while the current is changing?