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 [2025]

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Solution

Q.
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 [2025]

1 2 : 1

2 4 : 1

3 1 : 4

4 1 : 2

Ans.
(3)

Magnetic moment, $M = I A$

$∴$ $\frac{M_{1}}{M_{2}} = \frac{I \times π r_{1}^{2}}{I \times π r_{2}^{2}} = \frac{r_{1}^{2}}{r_{2}^{2}} or \frac{M_{1}}{M_{2}} = {(\frac{1}{2})}^{2} = \frac{1}{4}$

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