Question

A bar magnet of length l and magnetic dipole moment M is bent in the form of an arc as shown in the figure.

The new magnetic dipole moment will be

• A. $\text{M}$
• B. $\frac{3}{\pi }\text{M}$
• C. $\frac{2}{\pi }\text{M}$
• D. $\frac{\text{M}}{2}$

Answer 1

The correct option is B

$\frac{3}{\pi }\text{M}$

For straight magnet,

$\text{M}=q_{\text{m}}\times l$

For bent magnet,

$l^{{}^{\prime }}=2\text{r sin}{30}^{\circ }=2\text{r}\times \frac{1}{2}=\text{r}$

But, $\frac{1}{\text{r}}=\frac{\pi }{6}$

$\Rightarrow \text{r}=\frac{3}{\pi }$

$\therefore {\text{M}}^{{}^{\prime }}=q_{\text{m}}\times \frac{3}{\pi }=\frac{3}{\pi }\text{M}$