Question

The figure shows a non-conducting ring of radius $R$ carrying a charge $q$. In a circular region of radius $r$, a uniform magnetic field $\overrightarrow{B}$ perpendicular to the plane of the ring varies at a constant rate $\frac{dB}{dt}=\beta$. The torque acting on the ring is :

• A. $\frac{1}{2}q{r}^2\beta$
• B. $\frac{1}{2}q{R}^2\beta$
• C. $q{r}^2\beta$
• D. zero

Answer 1

The correct option is A $\frac{1}{2}q{r}^2\beta$

$El=\frac{d\varphi }{dt}=S\cdot \frac{dB}{dt}$

$E\left(2\pi R\right)=\left(\pi r^2\right)\left(\beta \right)$

$\therefore$ $E=\frac{r^2}{2R}\beta$

$F=qE$

and $\tau =FR=qER$

$=\frac{1}{2}q{r}^2\beta$