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  4. The magnetic moment of a current (I) carrying circular coil of radius (r) and number of turns (n) varies as

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Q. The magnetic moment of a current $(I)$ carrying circular coil of radius $(r)$ and number of turns $(n)$ varies as

AIIMSAIIMS 2004Moving Charges and Magnetism

Solution:

The magnetic moment is a measure of the strength of a magnetic source. The equation for magnetic moment in the current carrying loop, carrying current $I$ and of area vector $A$ for which the magnitude is given by
$M=I A$
where $I$ is current $A$, is area $\left(=\pi r^{2}\right)$
$\therefore M=I \pi r^{2} $
$\Rightarrow M \propto r^{2}$