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(C) The magnetic moment $M$ of a circular loop is given by the formula $M = I A$,where $I$ is the current and $A$ is the area of the loop.For a circul

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$\left[\frac{4 M \pi}{I}\right]^{\frac{1}{2}}$

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(C) The magnetic moment $M$ of a circular loop is given by the formula $M = I A$,where $I$ is the current and $A$ is the area of the loop.For a circular loop of radius $R$,the area is $A = \pi R^2$.Thus,$M = I (\pi R^2)$.The length of the wire $L$ forms the circumference of the loop,so $L = 2 \pi R$,which implies $R = \frac{L}{2 \pi}$.Substituting the value of $R$ into the magnetic moment equation:$M = I \pi \left( \frac{L}{2 \pi} \right)^2$$M = I \pi \left( \frac{L^2}{4 \pi^2} \right)$$M = \frac{I L^2}{4 \pi}$Rearranging to solve for $L$:$L^2 = \frac{4 M \pi}{I}$$L = \sqrt{\frac{4 M \pi}{I}}$ or $\left[ \frac{4 M \pi}{I} \right]^{\frac{1}{2}}$.

$A$ straight wire carrying a current $I$ is turned into a circular loop. If the magnitude of the magnetic moment associated with it is $M$,then the length of the wire will be

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