First slide

Magnetic Dipole moment

Question

A current carrying wire is bent in the form of a circular ring and its magnetic dipole moment is found to be M. Now the same wire is bent in the form of a circular ring having two turns. Then new magnetic moment will be

Moderate

A

M/2
B

M/4
C

2 M
D

4 M

Solution

$M = π r^{2} i a n d r = \frac{l}{2 π} \Rightarrow M = \frac{π l^{2} i}{4 π^{2}} = \frac{l^{2} i}{4 π}$
In the second case, $2 π r^{1} \times 2 = l \Rightarrow r^{1} = \frac{l}{4 π}$
$∴ M^{1} = 2 \times π {(r^{1})}^{2} . i = 2 \times π {(\frac{l}{4 π})}^{2} . i = \frac{l^{2} i}{8 π}$
$∴ M^{1} = \frac{M}{2}$

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