A 2 amp current is flowing through two different small circular copper coils having radii ratio $1:2

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A 2 amp current is flowing through two different small circular copper coils having radii ratio $1:2$. The ratio of their respective magnetic moments will be

Accepted Answer

Magnetic moment of current carrying circular loop $= IA$

$$M = IA $$$M \propto A\ \lbrack I -$ Same $\rbrack$

$$\frac{M_{1}}{M_{2}} = \frac{A_{1}}{A_{2}} = \frac{\pi r_{1}^{2}}{\pi r_{2}^{2}} = \left( \frac{1}{2} \right)^{2} = \frac{1}{4}$$

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