The magnetic field at the centre of a current carrying circular coil of area ' $\mathrm{A}$ ' is '…

The magnetic field at the centre of a current carrying circular coil of area ' $\mathrm{A}$ ' is ' $\mathrm{B}$ '. The magnetic moment of the coil is ( $\mu_0=$ permeability of free space)
  1. $\frac{2 \mathrm{BA}^{3 / 2}}{\mu_0 \sqrt{\pi}}$
  2. $\frac{\mathrm{BA}^{3 / 2}}{\mu_0 \pi}$
  3. $\frac{\mu_0 \sqrt{\pi}}{2 \mathrm{BA}^2}$
  4. $\frac{2 \mathrm{BA}^2}{\mu_0 \sqrt{\pi}}$

Solution

$\begin{aligned} & A=\pi R^2 \\ & \Rightarrow R=\sqrt{\frac{A}{\pi}} \\ & B=\frac{\mu_0 I}{2 R} \end{aligned}$ Magnetic Moment, $\begin{aligned} & M=I A=\frac{2 A B R}{\mu_0} \\ & =\frac{2 \mathrm{BA}^{3 / 2}}{\mu_0 \sqrt{\pi}} \end{aligned}$ /

Asked in: MHT CET 2021 (20 Sep Shift 1)

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