Question

Two similar wires of equal lengths are bent in the form of a square and a circular loop. They are suspended in a uniform magnetic field and same current is passed through them. Torque experienced by}

• A. circular loop is greater.
• B. square loop is greater.
• C. both loops is same.
• D. both will be zero.

Hint:

Circle has the maximum area for a fixed perimeter. Torque $\propto$ Area.

Answer 1

The Correct Option is A

Step 1: Torque Formula
$\tau = NIAB \sin \theta \implies \tau \propto \text{Area } (A)$.
Step 2: Area Comparison
For a fixed perimeter (length $L$): - Square Area: $(L/4)^2 = L^2/16 \approx 0.0625 L^2$. - Circle Area: $\pi (L/2\pi)^2 = L^2/4\pi \approx 0.0795 L^2$.
Step 3: Conclusion
For a given perimeter, the circle encloses the maximum area. Thus, the circular loop experiences greater torque.
Final Answer: (A)