Question

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 in Fig. 25.21.

The magnitude of the induced electric field at point P at a distance r from the centre of the circular region

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

Answer 1

The correct option is B

decreases as $\frac{1}{r}$

A time varying magnetic field produces an electric field. The magnitude of the electric field at a distance r from the centre of a circular region of radius a where a time varying field B exists is given by
$E=\frac{a^2}{2r}\frac{dB}{dt}$
At $r=a,E=\left(\frac{a}{2}\right)\frac{dB}{dt},$ which the value of E at the edge of the circular region. For r > a, E decreases as $\frac{1}{r}$.