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 $...... \ V$.

As shown in the figure,a magnet is moved with a fast speed towards a coil at rest. Due to this,the induced electromotive force,induced current,and induced charge in the coil are $E$,$I$,and $Q$ respectively. If the speed of the magnet is doubled,which of the following statements is incorrect?

$A$ magnetic field $4 \times 10^{-2} \, T$ acts at right angles to a coil of area $100 \, cm^2$ with $50$ turns. The average e.m.f. induced in the coil is $0.1 \, V$, when it is removed from the field in time '$t$'. The value of '$t$' is

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

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.

Lenz's law applies to