(B) Let $l$ be the length of the wire.When the wire is bent into a circular loop of radius $r$,the circumference is equal to the length of the wire:$l

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(B) Let $l$ be the length of the wire.When the wire is bent into a circular loop of radius $r$,the circumference is equal to the length of the wire:$l = 2 \pi r \Rightarrow r = \frac{l}{2 \pi}$The magnetic dipole moment $M$ of a current loop is given by:$M = i A$Substituting the area $A = \pi r^2$:$M = i \cdot \pi r^2 = i \pi \left( \frac{l}{2 \pi} \right)^2$$M = i \pi \cdot \frac{l^2}{4 \pi^2} = \frac{i l^2}{4 \pi}$Rearranging for $l$:$l^2 = \frac{4 \pi M}{i}$$l = \sqrt{\frac{4 \pi M}{i}}$

Class 12 Physics Moving Charges and Magnetism Magnetic Moment of Current Carrying Coil

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

AP EAMCET 2020 All AP EAMCET

A
$4 \pi i M$
B
$\sqrt{\frac{4 \pi M}{i}}$
C
$\sqrt{\frac{4 \pi i}{M}}$
D
$\frac{M \pi}{4 i}$

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Moving Charges and Magnetism

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Magnetic Moment of Current Carrying Coil

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

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