First slide

Magnetism

Question

When a thin bar magnet of magnetic moment M is bent in the form of S shape with the arms of equal length as shown in figure, then its new magnetic moment is

Moderate

A

$\frac{M}{\sqrt{2}}$
B

$\frac{M}{\sqrt{3}}$
C

$\frac{M}{2}$
D

$\frac{M}{\sqrt{5}}$

Solution

If the magnet is bent in the above shape magnetic length changes but pole strength remains constant .
$I n i t i a l l y, M = m l F i n a l l y, M^{1} = m (A F)$
From $Δ A F E, A F^{2} = (A E)^{2} + (F E)^{2}$
$\Rightarrow (A F)^{2} = {(\frac{2 l}{5})}^{2} + {(\frac{l}{5})}^{2}$
$\Rightarrow (A F)^{2} = \frac{4 l^{2}}{25} + \frac{l^{2}}{25} = \frac{5 l^{2}}{25} = \frac{l^{2}}{5}$
$\Rightarrow A F = \frac{l}{\sqrt{5}}$
Hence,
$M^{1} = m (A F) = \frac{m l}{\sqrt{5}} = \frac{M}{\sqrt{5}} (M = m l)$

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