Verified Solution • 2025–26 Session moderate

QPages 230-234: Q15: HC Verma: Concepts of Physics - Volume 2 Magnetic Field Pages 230-234: Q15 Solution: A current loop of arbitrary shape lies in a uniform magnetic…

⚠️ Common Exam Traps & Conceptual Pitfalls

Students often treat the line integral $oint d\vec l$ as a scalar length or assume it can be non‑zero, forgetting that it is a vector sum of infinitesimal displacements which always vanishes for a closed path; thus $\vec F=i\oint d\vec l\times\vec B = i(\oint d\vec l)\times\vec B=0$ only when the field is uniform and the loop is closed.

A current loop of arbitrary shape lies in a uniform magnetic field

B

. Show that the net magnetic force acting on the loop is zero.

Step-by-Step Verified Solution

**Answer:** Net force is zero. **Step-by-Step Explanation:** For a closed loop in a uniform magnetic field, the net force is

\vec{F} = \oint i d\vec{l} \times \vec{B} = i (\oint d\vec{l}) \times \vec{B} = 0

because the vector sum of all line elements around a closed loop is zero.

All Questions in this Chapter

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