The magnetic flux through a loop of resistance $10 \Omega$ varies according to the relation $\phi = 6t^2 + 7t + 1$,where $\phi$ is in milliweber and time is in seconds. At time $t = 1 \ s$,the induced e.m.f. is:

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 $.... \, J$.

The total charge induced in a conducting loop when it is moved in a uniform magnetic field depends on

The north pole of a long horizontal bar magnet is being brought towards a closed circuit consisting of a coil. The direction of the induced current produced in it is

$A$ long solenoid has $20$ turns per cm. $A$ small loop of area $\frac{4}{\pi} \text{ cm}^2$ is placed inside the solenoid normal to its axis. If the current carried by the solenoid changes steadily from $1.0 \text{ A}$ to $3.0 \text{ A}$ in $0.2 \text{ s}$,what is the magnitude of the induced emf in the loop while the current is changing (in $\mu \text{V}$)?

The figure shows a bar magnet and a metallic coil. Consider four situations:
$(I)$ Moving the magnet away from the coil.
$(II)$ Moving the coil towards the magnet.
$(III)$ Rotating the coil about the vertical diameter.
$(IV)$ Rotating the coil about its axis.
An emf in the coil will be generated for the following situations.