A wire of length (L) meters, carrying a current (I) ampere is bent in the form of a circle. The magnitude of its magnetic moment, in SI units, is
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → \( \displaystyle\frac{IL^2}{4\pi} \)
The magnetic moment of a current loop is \( m = IA \), where \( A \) is the area enclosed by the loop.
The whole wire forms the circumference of the circle:
\( \displaystyle 2\pi r = L \;\Rightarrow\; r = \frac{L}{2\pi} \)
\( \displaystyle A = \pi r^{2} = \pi\left(\frac{L}{2\pi}\right)^{2} = \frac{L^{2}}{4\pi} \)
\( \displaystyle m = IA = \frac{IL^{2}}{4\pi} \)