Question

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

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

Answer 1

Answer: (A)

Rate of increase of $B=\frac{d B}{d t}$
$E_{n} \times 2 \pi r=-\frac{d \phi}{d t}$
or $E \times 2 \pi r=-A \frac{d B}{d t}$
$E \times 2 \pi r=-\pi r^{2} \frac{d B}{d t}$
$\therefore E=\frac{-r}{2} \frac{d B}{d t}$