A loop carrying current I lies in the x-y plane as shown in the figure. The unit vector is coming out of the plane of the paper. The magnetic moment of the current loop is

Engineering

Physics

Magnet and Magnetic Dipole

Question

A loop carrying current I lies in the x-y plane as shown in the figure. The unit vector $\hat{k}$ is coming out of the plane of the paper. The magnetic moment of the current loop is

$(2 π + 1) a^{2} I \hat{k}$

$(\frac{π}{2} + 1) a^{2} I \hat{k}$

$a^{2} I \hat{k}$

$- (\frac{π}{2} + 1) a^{2} I \hat{k}$

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$M = (a^{2} + \frac{π {(\frac{a}{2})}^{2}}{2} \times 4) I = a^{2} (1 + \frac{π}{2}) \times I$