Question

A wire of length $4$ m carrying a current of $1$ A is bent to form a circular loop. The magnetic moment of the loop (in A m$^2$) is

• A. $\frac{4}{\pi^2}$
• B. $\frac{2}{\pi^2}$
• C. $\frac{2}{\pi}$
• D. $\frac{4}{\pi}$
• E. $4\pi$

Hint:

For circular loops: - First find radius using circumference - Then compute area and magnetic moment

Answer 1

The Correct Option is D

Concept: Magnetic moment of a current loop: \[ m = IA \] For a circle: \[ A = \pi r^2 \] Circumference: \[ 2\pi r = \text{length} \]

Step 1: Find radius.
\[ 2\pi r = 4 \Rightarrow r = \frac{2}{\pi} \]

Step 2: Find area.
\[ A = \pi \left(\frac{2}{\pi}\right)^2 = \pi \cdot \frac{4}{\pi^2} = \frac{4}{\pi} \]

Step 3: Calculate magnetic moment.
\[ m = IA = 1 \times \frac{4}{\pi} = \frac{4}{\pi} \]