A wire of length 4 m carrying current I A is bent in the form of a circle. Its magnetic moment will be:
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → \( \displaystyle\frac{4I}{\pi} \)
The magnetic moment of a current loop is \( m = IA \). The whole length of the wire forms the circumference of the circle, so its radius follows from \( l = 2\pi r \).
\( \displaystyle r = \frac{l}{2\pi} = \frac{4}{2\pi}\,\mathrm{m} = \frac{2}{\pi}\,\mathrm{m} \)
\( \displaystyle A = \pi r^{2} = \pi\times\frac{4}{\pi^{2}}\,\mathrm{m^{2}} = \frac{4}{\pi}\,\mathrm{m^{2}} \)
\( \displaystyle m = IA = \frac{4I}{\pi} \)