Magnetic field at the centre of a circular loop of area A is B. The magnetic moment of the loop is

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Question

Magnetic field at the centre of a circular loop of area A is B. The magnetic moment of the loop is

\(\frac{{B{A^2}}}{{{\mu _0}\pi }}\)
\(\frac{{BA\sqrt A }}{{{\mu _0}}}\)
\(\frac{{BA\sqrt A }}{{{\mu _0}\pi }}\)
\(\frac{{2BA\sqrt A }}{{{\mu _0}\sqrt \pi }}\)

Answer 1

Concept:

Magnetic field: The region around the current-carrying wire or around a magnet in which the magnetic force on other current-carrying wire or magnets can be experienced is called the magnetic field.

The magnetic field (B) at the center of a circular coil is given by:

\(B = \;\frac{{{μ _0}\;N\;I}}{{\;2\;r}}\)

Where μ0 is the permeability of free space, N is the number of turns, I is current and r is the radius.

Calculation:

Let r be the radius of the circular loop.

∴ A = πr²

Or \(r = \sqrt {\frac{A}{\pi }} \)

The magnetic field at the center of the loop is

\(B = \frac{{{\mu _0}I}}{{2r}} = \frac{{{\mu _0}I}}{{2\sqrt {\frac{A}{\pi }} }}\)

\(I = \frac{{2B}}{{{\mu _0}}}\sqrt {\frac{A}{\pi }} \)

The magnetic moment of the loop is

\(M = IA = \frac{{2B}}{{{\mu _0}}}\sqrt {\frac{A}{\pi }} A\)

\( = \frac{{2BA\sqrt A }}{{{\mu _0}\sqrt \pi }}\)

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Magnetic field at the centre of a circular loop of area A is B. The magnetic moment of the loop is

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