First slide

The bar magnet

Question

A steel wire of length l has a magnetic moment M It is then bent into a semicircular arc. The new magnetic moment is

Moderate

A

$\frac{M}{π}$
B

$\frac{2 M}{π}$
C

$\frac{3 M}{π}$
D

$\frac{4 M}{π}$

Solution

Poles strength,
$m = \frac{magnetic moment}{seperation between poles} = \frac{M}{l}$
when the wire is bent, the pole strength remains the same. In semi-circular arc, the separation between poles is 2r, where r is the radius of semi-circle. Given $π$ r = I New magnetic moment, M' = m.2r = m(2l/ $π$ )
$∴ M^{'} = (\frac{M}{l}) \times (\frac{2 l}{π}) = \frac{2 M}{π}$

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