A uniform but time-varying magnetic field $B\left(t\right)$ exists in a cylindrical region of radius $a$ and is directed into the plane of the paper, as shown. The magnitude of the induced electric field at point $P$ at a distance $r$ from the centre of the circular region

A conducting rod $PQ$ of length $L=1.0 \mathrm{m}$ is moving with a uniform speed $v=2 \mathrm{m}/\mathrm{s}$ in a uniform magnetic field $B=4.0 \mathrm{T}$ directed into the paper. A capacitor of capacity $C=10 \mu \mathrm{F}$ is connected as shown in figure. Then,

A conducting rod $AC$ of length $4l$ is rotated about a point $O$ in a uniform magnetic field $B$ directed into the paper. $AO=l$ and $OC=3l$. Then,

The network shown in the figure is a part of a complete circuit. If at a certain instant the current $i$ is $5 \mathrm{A}$ and decreasing at the rate of ${10}^3 \mathrm{A} {\mathrm{s}}^{-1}$ then, $V_{\mathrm{B}}-V_{\mathrm{A}}$ is

Some magnetic flux is changed from a coil of resistance $10 \mathrm{\Omega }$. As a result an induced current is developed in it, which varies with time as shown in figure. The magnitude of change in flux through the coil in $\mathrm{Wb}$ is

The current $i$ in an induction coil varies with time $t$ according to the graph shown

in figure. Which of the following graphs shows the induced $emf\left(E\right)$ in the coil with time?

Switch $S$ of the circuit shown in figure is closed at $t=0$. If $e$ denotes the induced $\mathrm{emf}$ in $L$ and $i$, the current flowing through the circuit at time $t$, which of the following graphs is correct?