Question

A bar magnet of length 'l' and magnetic dipole moment' is bent in the form of semicircle. The new magnetic dipole moment will be:

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

Answer 1

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

Given: original length of magnet=$l$

seperation between poles of magnet,$L=l$

and now it is bent in form of semicircle

To find: New magnetic moment,$M^{\prime }=?$

Solution:

original pole strength,$m=\frac{M}{L}==>m=\frac{M}{l}$ $.....\left(1\right)$

& now wire is bent in semicircle, so seperation between pole

change from $l$ $to$ $2r$

So, $L=2r$ $......\left(2\right)$

new length of magnet $=\pi \ast r$

also, new length$=$original length

so, $\pi \ast r=l$

$r=\frac{l}{\pi }$ $....\left(3\right)$

new magnetic moment, $M^{\prime }=m\ast L$

using eq$\left(2\right)$,we get

$M^{\prime }=m\ast 2r$

using eq$\left(1\right)$ and eq$\left(3\right)$, we get

$M^{\prime }=\frac{M}{l}\ast \frac{2l}{\pi }$

$M^{\prime }=\frac{2M}{\pi }$

hence,

The correct opt: C