Question

A conducting ring of mass 2 kg and radius 0.5m is placed on a smooth horizontal plane. The ring carries a current $i=4A$. A horizontal magnetic field $B=10T$ is switched on at $t=0$ as shown in figure. The initial angular acceleration is :

• A. $40\pi rad/s^2$
• B. $20\pi rad/s^2$
• C. $5\pi rad/s^2$
• D. $15\pi rad/s^2$

Answer 1

The correct option is B $20\pi rad/s^2$

Torque on the ring is,
$\overrightarrow{\tau }=\overrightarrow{M}\times \overrightarrow{B}$
$\overrightarrow{\tau }=MBSin\theta$

$=i\pi r^{2}BSin90$
$=4\times \pi \times 0.25\times 10\times 1$
$=10\pi Nm$
$\overrightarrow{\tau }=I\alpha$
$10\pi =M{r}^2\alpha$
$\alpha =\frac{10\pi }{2\times 0.25}$$=20\pi rad/s^2$