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5.Magnetism and Matter
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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
$M$
B
$\frac{3}{\pi }M$
C
$\;\frac{2}{\pi }M$
D
$\frac{M}{2}$
(AIPMT-2013)
Solution
Let $m$ be strength of each pole of bar magnet of length $l .$ Then
$M=m \times l………(i)$
When the bar magnet is bent in the form of an arc as shown in figure Then
$l=\frac{\pi}{3} \times r=\frac{\pi r}{3}$
or $\quad r=\frac{3 l}{\pi}$
New magnetic dipole moment $M^{\prime} =m \times 2 r \sin 30^{\circ} $
$=m \times 2 \times \frac{3 l}{\pi} \times \frac{1}{2}=\frac{3 m l}{\pi}=\frac{3 M}{\pi}$ (Using $(i)$)
Standard 12
Physics
