Verified Solution • 2025–26 Session moderate

QPages 230-234: Q57: HC Verma: Concepts of Physics - Volume 2 Magnetic Field Pages 230-234: Q57 Solution: A circular loop carrying a current is made of a wire of length…

⚠️ Common Exam Traps & Conceptual Pitfalls

Students often incorrectly assume a square loop has a larger area than a circular loop for the same perimeter, or they miscalculate the area of the circle as $L^2/4$ instead of $L^2/(4\pi)$. Remember that for a fixed perimeter, the circle encloses the maximum area, so the circular loop will always experience a larger torque ($\tau = iAB\sin\theta$) than the square loop.

A circular loop carrying a current ii is made of a wire of length LL. A uniform magnetic field BB exists parallel to the plane of the loop. a) Find the torque on the loop. b) If the same length of the wire is used to form a square loop, what would be the torque? Which is larger?

Step-by-Step Verified Solution

**Answer:** (a) τ=BiL24π\tau = \frac{B i L^2}{4\pi} (b) Square loop has larger torque. **Step-BY-Step Explanation:** (a) For a circular loop of length L, A=L2/(4π)A = L^2/(4\pi). τ=iAB=BiL24π\tau = i A B = \frac{B i L^2}{4\pi}. (b) For a square loop of length L, A=L2/16A = L^2/16. τ=iAB=BiL216\tau = i A B = \frac{B i L^2}{16}. The circular loop has larger torque.

All Questions in this Chapter

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