The figure shows a circular area of radius $R$ where a uniform magnetic field $\vec B$ is directed into the plane of the paper and is increasing in magnitude at a constant rate. In this case,which of the following graphs,drawn schematically,correctly shows the variation of the induced electric field $E(r)$ with distance $r$ from the center?

$A$ magnetic field $\vec{B} = B_0 \sin(\omega t) \hat{k}$ covers a large region where a wire $AB$ slides smoothly over two parallel conductors separated by a distance $d$ as shown in the figure. The wires are in the $xy$-plane. The wire $AB$ (of length $d$) has resistance $R$ and the parallel wires have negligible resistance. If $AB$ is moving with velocity $v$,what is the current in the circuit? What is the force needed to keep the wire moving at constant velocity?

Two concentric circular coils,$C_{1}$ and $C_{2}$,are placed in the $XY$ plane. $C_{1}$ has $500$ turns and a radius of $1\; cm$. $C_{2}$ has $200$ turns and a radius of $20\; cm$. $C_{2}$ carries a time-dependent current $I(t) = (5t^{2} - 2t + 3)\; A$,where $t$ is in $s$. The $emf$ induced in $C_{1}$ (in $mV$) at the instant $t = 1\; s$ is $\frac{4}{x}$. The value of $x$ is:

Flux $\phi$ (in weber) in a closed circuit of resistance $10 \, \Omega$ varies with time $t$ (in $s$) according to the equation $\phi = 6t^2 - 5t + 1$. What is the magnitude of the induced current at $t = 0.25 \, s$ (in $, A$)?

The figure shows a circular region of radius $R$ in which a uniform magnetic field $B$ exists. The magnetic field is increasing at a rate $\frac{d B}{d t}$. The magnitude of the induced electric field at a distance $r$ from the centre for $r < R$ is ............

$A$ uniform magnetic field $B$ exists in a direction perpendicular to the plane of a square loop made of a metal wire. The wire has a diameter of $4 \, mm$ and a total length of $30 \, cm$. The magnetic field changes with time at a steady rate $dB/dt = 0.032 \, T s^{-1}$. The induced current in the loop is close to $.... A$ (Resistivity of the metal wire is $1.23 \times 10^{-8} \, \Omega m$).