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(C) The magnetic moment $(M)$ of a circular coil is given by $M = I \cdot A$,where $I$ is the current and $A$ is the area of the coil.For a circular c

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$M \propto L^2$

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(C) The magnetic moment $(M)$ of a circular coil is given by $M = I \cdot A$,where $I$ is the current and $A$ is the area of the coil.For a circular coil of radius $r$,the length of the wire $L$ is equal to the circumference,so $L = 2\pi r$,which implies $r = \frac{L}{2\pi}$.The area of the coil is $A = \pi r^2 = \pi \left(\frac{L}{2\pi}\right)^2 = \frac{L^2}{4\pi}$.Substituting this into the magnetic moment formula: $M = I \cdot \left(\frac{L^2}{4\pi}\right)$.Since $I$ and $4\pi$ are constants,we have $M \propto L^2$.

The relation between magnetic moment $(M)$ of a current-carrying circular coil and the length $(L)$ of the wire used is:

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