Question

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

• A. $\frac{dB}{dt}\frac{r}{2}$
• B. Zero
• C. $\frac{dB}{dt}$
• D. $\frac{dB}{dt}\frac{R^2}{2r}$

Answer 1

Answer: (A)

Rate of increase of $B=\frac{dB}{dt}$
$E_n\times 2\pi r=-\frac{d\varphi }{dt}$
or $E\times 2\pi r=-A\frac{dB}{dt}$
$E\times 2\pi r=-\pi r^2\frac{dB}{dt}$
$\therefore E=\frac{-r}{2}\frac{dB}{dt}$