Question

Two 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. square loop is greater.
• B. both the loops is same but not zero.
• C. both the loops is zero.
• D. circular loop is maximum.

Hint:

For a fixed perimeter, a circle always encloses a larger area than any polygon.

Answer 1

The Correct Option is D

Step 1: Concept
Torque $\tau = NIA \sin \theta$. For a given length $L$ and current $I$, torque is proportional to the area $A$ enclosed by the loop.

Step 2: Analysis
- For a square: Side $s = L/4$. Area $A_s = (L/4)^2 = L^2/16 \approx 0.0625 L^2$. - For a circle: Circumference $2\pi r = L \implies r = L/2\pi$. Area $A_c = \pi(L/2\pi)^2 = L^2/4\pi \approx 0.0796 L^2$.

Step 3: Comparison
Since $A_c > A_s$, the circular loop encloses the maximum area for a fixed perimeter.

Step 4: Conclusion
Hence, the circular loop experiences the maximum torque. Final Answer: (D)