Verified Solution • 2025–26 Session moderate

QPages 230-234: Q27: HC Verma: Concepts of Physics - Volume 2 Magnetic Field Pages 230-234: Q27 Solution: The magnetic field existing in a region is given by . A square…

⚠️ Common Exam Traps & Conceptual Pitfalls

Students often assume the magnetic forces on opposite sides of a closed loop cancel, as they do in a uniform field, and therefore claim zero net force. In a field that varies with $x$, the force magnitude on each side depends on the local $B(x)$, so the forces are parallel and unequal; one must integrate $i,mathrm{d}\vec l\times\vec B(x)$ for each segment rather than treating $B$ as constant.

The magnetic field existing in a region is given by

\vec{B} = B_0 1 + \frac{x}{l}) \hat{k}

. A square loop of edge

l

and carrying a current

i

, is placed with its edges parallel to the

x - y

axes. Find the magnitude of the net magnetic force experienced by the loop.

Step-by-Step Verified Solution

**Answer:**

F = i l^2 B_0/2

. **Step-by-Step Explanation:** The magnetic field varies with x. The net force is the integral of

i B(x) dl

over the loop. The result is

F = i l^2 B_0/2

.

All Questions in this Chapter

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