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 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.

In the diagram shown,a time-varying non-uniform magnetic field passes through a circular region of radius $R$. The magnetic field is directed outwards and it is a function of radial distance $r$ and time $t$ according to the relation $B = B_0rt$. What is the induced electric field strength at a radial distance $R/2$ from the center?

$A$ circular loop of radius $20 \text{ cm}$ and resistance $2 \text{ } \Omega$ is placed in a time-varying magnetic field $\vec{B} = (2t^2 + 2t + 3) \text{ T}$. The plane of the loop is perpendicular to the magnetic field. The induced current in the loop at $t = 3 \text{ s}$ is $\frac{\alpha}{50} \text{ A}$. The value of $\alpha$ is . . . . . . .

$A$ magnetic field is changing at the rate of $4 \, T/s$ in a circular region of $5 \, cm$ radius. The value of the induced electric field at a point $P$,which is $10 \, cm$ away from the center $O$ of the region,is ..... $V/m$.

Which conclusion can we obtain from the fact that an $emf$ is induced in a stationary conductor placed in a time-varying magnetic field? Discuss the characteristics of the induced electric field.