Question

A bar magnet of magnetic moment M is bent to form a semicircle. What is the magnetic moment of
the bent magnet ?

Answer 1

The magnetic moment of the bent magnet=$\frac{2M}{\pi}$

Explanation:

Let l be the distance between two poles of bar magnet.

Magnetic moment of bar magnet=M

We know that

Magnetic moment=$ml$

Where

l=Distance between two poles

m=Magnetic strength of any one pole

$m=\frac{M}{l}$

Let r be the radius of semi-circle.

Distance between two poles=l

$\pi r=l$

Where $\pi r$=Circumference of semi- circle

$r=\frac{l}{\pi}$

Distance between two poles when the bar magnet is convert into bent magnet=2r=$2\times \frac{l}{\pi}=\frac{2l}{\pi}$

The new magnetic moment of bent magnet=$m\times \frac{2l}{\pi}$

The new magnetic moment of bent magnet=$\frac{M}{l}\times \frac{2l}{\pi}=\frac{2M}{\pi}$

Hence, the magnetic moment of the bent magnet=$\frac{2M}{\pi}$

#Learns more:

A bar magnet of length l and magnetic dipolemoment M is bent in the form of an arc as shown in figure. The new magnetic dipole

moment will be :-

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