(B) The magnetic field at the center of a circular loop of radius $R$ carrying current $i$ is given by $B = \frac{{\mu _0 i}}{{2R}}$.From this,we can

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(B) The magnetic field at the center of a circular loop of radius $R$ carrying current $i$ is given by $B = \frac{{\mu _0 i}}{{2R}}$.From this,we can express the current $i$ as $i = \frac{{2RB}}{{\mu _0}}$.The magnetic moment $M$ of a current loop is given by $M = i \times A$,where $A$ is the area of the loop.For a circular loop,$A = \pi R^2$.Substituting the expression for $i$ and $A$ into the formula for $M$:$M = \left( \frac{{2RB}}{{\mu _0}} \right) \times (\pi R^2) = \frac{{2\pi B R^3}}{{\mu _0}}$.

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

Medium

Due to the flow of current in a circular loop of radius $R$,the magnetic induction produced at the centre of the loop is $B$. The magnetic moment of the loop is (where ${\mu _0}$ is the permeability constant).

A
$B{R^3}/2\pi {\mu _0}$
B
$2\pi B{R^3}/{\mu _0}$
C
$B{R^2}/2\pi {\mu _0}$
D
$2\pi B{R^2}/{\mu _0}$

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Moving Charges and Magnetism

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Magnetic Moment of Current Carrying Coil

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Due to the flow of current in a circular loop of radius $R$,the magnetic induction produced at the centre of the loop is $B$. The magnetic moment of the loop is (where ${\mu _0}$ is the permeability constant).

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