Question

Find the resultant magnetic moment when $\theta ={240}^o$.

• A. $M/4\pi$
• B. $2M/\pi$
• C. $3M/\pi$
• D. $3\sqrt{3}M/4\pi$

Answer 1

The correct option is D $3\sqrt{3}M/4\pi$

Let pole strength of wire is m and length = l

then $M=mL$

Length $AB=2\ast cos{30}^{\circ }$

an $L=2\pi r\ast \frac{{240}^{\circ }}{{360}^{\circ }}$

$L=\frac{4\pi r}{3}$

$\therefore$ magnetic moment

$M^{\prime }=m\left(AB\right)$

$=m\ast 2\ast r\ast \frac{\sqrt{3}}{2}$

$=m\sqrt{3}r$

$=m\sqrt{3}\ast \frac{3L}{4\pi }$

$=\frac{3\sqrt{3}}{4\pi }\left(mL\right)$

$=\frac{3\sqrt{3}}{4\pi }M$