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Two wires of length l₁ and l₂ carries equal currents. Two circular loops are made by these wires. If the ratio of their magnetic moment is 9 : 4 respectively then length ratio of wires is

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9 : 4

4 : 9

$\sqrt{3} : \sqrt{2}$

3 : 2

answer is D.

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Detailed Solution

$\begin{array}{l} M = {Iπr}^{2} \\ But l = 2 πr \\ \Rightarrow M = I (\frac{l^{2}}{4 π}) \\ \Rightarrow \frac{9}{4} = {(\frac{l_{1}}{l_{2}})}^{2} \end{array}$

$\Rightarrow \frac{l_{1}}{l_{2}} = \frac{3}{2}$

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