$A$ 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?

To induce an $e.m.f.$ in a coil, the linking magnetic flux

$A$ conducting circular coil is placed in a uniform magnetic field with the magnetic field initially directed perpendicular to the plane of the coil. In step $A$,the coil is rotated from its initial position by $60^{\circ}$ about its diameter in time $t$. In step $B$,the coil is further rotated about the same axis in the same sense by another $120^{\circ}$ in time $2t$. The ratio of the emf induced in the coil in step $A$ to that in step $B$ is:

$A$ copper ring having a cut such as not to form a complete loop is held horizontally and a bar magnet is dropped through the ring with its length along the axis of the ring as shown in figure. The acceleration of the falling magnet is ($g=$ acceleration due to gravity)

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 $...... \ V$.

$A$ square wire loop of $10.0 \, cm$ side lies at right angles to a uniform magnetic field of $20 \, T$. $A$ $10 \, V$ light bulb is in series with the loop as shown in the figure. The magnetic field is decreasing steadily to zero over a time interval $\Delta t$. The bulb will shine with full brightness if $\Delta t$ is equal to.......$ms$.