First slide

The bar magnet

Question

A magnetised wire of magnetic moment M and length I is bent in the form of a semi-cycle of radius r. The new magnetic moment is

Easy

A

M
B

$\frac{2 M}{π}$
C

$\frac{M}{π}$
D

none of the above

Solution

Magnetic moment M = ml
When the magnet is bent in the form of a semicircle of radius r, the distance between poles becomes 2 r. The new magnetic moment is
$\begin{array}{l} M^{'} = m (2 r) \\ ∴ \frac{M^{'}}{M} = \frac{m (2 r)}{ml} = \frac{2 r}{l} \\ But l = πr \\ ∴ \frac{M^{'}}{M} = \frac{2}{π} . \end{array}$

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