First slide

Magnetic Dipole moment

Question

A wire of length I metre carrying a current i ampere is bent in the form of a circle. The magnitude of magnetic moment is

Easy

A

${iL}^{2} / 4 π$
B

${iL}^{2} / 2 π$
C

$iL / 4 π$
D

${πiL}^{2}$

Solution

The magnetic moment is given by
$p_{m} = iA = i ({πr}^{2})$
Given that $2 πr = L or r = (L / 2 π)$
$∴ p_{m} = iπ (L / 2 π)^{2} = {iL}^{2} / 4 π$

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