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  4. 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 :-

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Q. A bar magnet of length ' $\ell$ ' and magnetic dipole moment '$M$' is bent in the form of an arc as shown in figure. The new magnetic dipole moment will be :-Physics Question Image

Moving Charges and Magnetism

Solution:

$\frac{2 \pi r }{4}= L $
$\Rightarrow r =\frac{2 L }{\pi}$
$d =\sqrt{2} r =\frac{2 \sqrt{2 L }}{ \pi }$
$M _{\text {new }}=( M .d )$
$= mL \left\{\frac{2 \sqrt{2}}{\pi}\right\}=\frac{2 \sqrt{2} M }{\pi}$

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