Question

A magnet of magnetic moment $M$ and length $2l$ is bent at its mid point such that the angle of bending is ${60}^{\circ }$. The new magnet moment is-

• A. $M$
• B. $2M$
• C. $\frac{M}{2}$
• D. $\frac{M}{\sqrt{2}}$

Answer 1

The correct option is C $\frac{M}{2}$



The resultant magnetic moment is,

$M_{res}=\sqrt{M_1^2+M_2^2+2M_1{M}_2\cos \theta }$

Here, $M_1=M_2=\frac{M}{2};\theta ={120}^{\circ }$

$\Rightarrow M_{res}=\sqrt{{\left(\frac{M}{2}\right)}^2+{\left(\frac{M}{2}\right)}^2+2\left(\frac{M}{2}\right)\left(\frac{M}{2}\right)\cos {120}^{\circ }}$

$=\sqrt{2{\left(\frac{M}{2}\right)}^2-2\times \frac{1}{2}\times {\left(\frac{M}{2}\right)}^2}$

$\therefore M_{res}=\sqrt{{\left(\frac{M}{2}\right)}^2}=\frac{M}{2}$

<!--td {border: 1px solid #ccc;}br {mso-data-placement:same-cell;}--> Hence, $\left(C\right)$ is the correct answer.