The magnetic field at the centre of a current carrying circular coil of an area ' $A$ ' is ' $B$ '. The…
The magnetic field at the centre of a current carrying circular coil of an area ' $A$ ' is ' $B$ '. The magnetic moment of the coils is
[ $\mu 0=$ permeability of free space.]
$\frac{2 B A^{3 / 2}}{\mu_0 \pi^{1 / 2}}$
$\frac{B A^2}{\mu_0 \pi}$
$\frac{\mu_0 \pi^{1 / 2}}{B A^{3 / 2}}$
$\frac{B A^{3 / 2}}{\mu_0 \pi}$
Solution
The correct option is (A)
$\frac{2 B A^{3 / 2}}{\mu_0 \sqrt{\pi}}$
Let $r$ be the radius of the circular loop.
$\therefore A=\pi r^2$ or $r=\sqrt{\frac{A}{\pi}}$
Magnetic field at the centre of the loop is
$\begin{aligned} & B=\frac{\mu_0 I}{2 r}=\frac{\mu_0 I}{2 \sqrt{\frac{A}{\pi}}} \\ & I=\frac{2 B}{\mu_0} \sqrt{\frac{A}{\pi}}\end{aligned}$
The magnetic moment of the loop is
$M=I A=\left(\frac{2 B}{\mu_0} \sqrt{\frac{A}{\pi}}\right) A=\frac{2 B A^{3 / 2}}{\mu_0 \sqrt{\pi}}$