Question

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

• A. is zero
• B. decreases as 1/r
• C. increases as r
• D. decrease as 1/r${}^2$

Answer 1

Answer: (B)

decreases as 1/r

The induced electric field is given by:

$\oint \overrightarrow{E}.d\overrightarrow{l}=-\int \frac{d\overrightarrow{B}}{dt}.d\overrightarrow{A}$

$⟹\left|E\right|\left(2\pi r\right)=\frac{dB}{dt}.\pi a^2$

$⟹\left|E\right|\propto \frac{1}{r}$