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: Understanding the Question:
Torque depends on the area of the loop. We must compare areas of different shapes with the same perimeter.

Step 2: Key Formula or Approach:
Maximum torque \( \tau_{\text{max}} = I A B \).

Step 3: Detailed Explanation:
Let the length of the wire be \( L \).
1. Square loop: Side \( a = L/4 \). Area \( A_{\text{sq}} = (L/4)^2 = L^2/16 \approx 0.0625 L^2 \).
2. Circular loop: Radius \( r = L/(2\pi) \). Area \( A_{\text{circ}} = \pi r^2 = \pi \left( \frac{L^2}{4\pi^2} \right) = \frac{L^2}{4\pi} \approx 0.0796 L^2 \).
Since \( A_{\text{circ}} > A_{\text{sq}} \), the torque for the circular loop is greater.

Step 4: Final Answer:
The circular loop experiences the maximum torque.