Two circular loops of radii r and 2r have current I and I/2 flowing through them clockwise and anticlockwise sense respectively. If their equivalent magnetic moments are M₁ and M₂ respectively, state the relation between M₁ and M₂.

Solution

Given, two circular loops of radii r and 2r respectively.
Current on two loops are I (clock-wise) and I/2 (anti-clockwise) respectively.

Now, Magnetic moment is given as M=IA

Therefore,

$M_{1} = I ({πr}^{2})$ and,

$M_{2} = \frac{I}{2} [π (2 r)^{2}]$

$∴$ $\frac{M_{1}}{M_{2}} = \frac{{Iπr}^{2}}{Iπ 2 r^{2}} = \frac{1}{2}$

i.e., $M_{1} = \frac{1}{2} M_{2}$