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 ............

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?

$A$ uniform but time-varying magnetic field $B(t)$ exists in a circular 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 $r$ $(r > a)$ from the centre of the circular region is:

$A$ uniform magnetic field $B$ exists in a cylindrical region of radius $10\,cm$ as shown in the figure. $A$ uniform wire of length $80\,cm$ and resistance $4.0\,\Omega$ is bent into a square frame and is placed with one side along a diameter of the cylindrical region. If the magnetic field increases at a constant rate of $0.010\,T/s$,find the current induced in the frame.

$A$ uniform magnetic field of induction $B$ is confined to a cylindrical region of radius $R$. The magnetic field is increasing at a constant rate of $\frac{dB}{dt} \ (T/s)$. An electron is placed at the point $P$ on the periphery of the field. The acceleration experienced by the electron is:

$A$ magnetic field at a distance $r$ from the $z$-axis is given by $\vec{B} = B_0 r t \hat{k}$,where $B_0$ is a constant and $t$ is time. The magnitude of the induced electric field at a distance $r$ from the $z$-axis is: