Question

A bar magnet of length '$l$' and magnetic dipole moment 'M' is bent in the form of an arc as shown in figure. The new magnetic dipole moment will be

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

Answer 1

Answer: (C)

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

Answer 2

Let magnetic pole strength be m then
M$= m \ell$

In new situation
$M' = (m) \left(2r \,\,sin \frac{60^\circ}{2}\right) where\, \, r \left( \frac{\pi}{3}\right) = \ell$
$M' = 2m \left(\frac {2 \ell}{\pi}\right) \left(\frac{1}{2}\right) = \frac{3m\ell}{\pi} = \frac {3M}{\pi}$