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Find the magnetic moment of a thin round loop with current if the radius of the loop is equal to $R$ and the magnetic induction at its centre is equal to $B$ .

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$\frac{4 {πBR}^{3}}{μ_{0}}$

$\frac{{πBR}^{3}}{2 μ_{0}}$

$\frac{2 {πBR}^{3}}{μ_{0}}$

$\frac{{πBR}^{3}}{4 μ_{0}}$

answer is B.

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Detailed Solution

We know that,

$B = \frac{μ_{0} i}{2 R} . ∴ M = i \times {πR}^{2} = \frac{2 {πR}^{3} B}{μ_{0}}$

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