Verified Solution • 2025–26 Session moderate

QPages 230-234: Q25: HC Verma: Concepts of Physics - Volume 2 Magnetic Field Pages 230-234: Q25 Solution: The figure shows a circular wire loop of radius and carrying a…

⚠️ Common Exam Traps & Conceptual Pitfalls

Students often write $d\mathbf F = iB\,dl$ as a scalar, forgetting the vector cross product $d\mathbf F=i\,\mathbf{dl}\times\mathbf B$; because $\mathbf{dl}$ is tangent and $\mathbf B$ is perpendicular, the force is radial, not along the wire. Ignoring this direction makes them sum the forces as if they add linearly around the loop, yielding a non‑zero net force instead of the correct zero net force and the correct compression $F=iBa$ for each half‑loop.

The figure shows a circular wire loop of radius

a

and carrying a current

i

, which is placed in a perpendicular magnetic field

B

. a) Consider a small part

dl

of the wire. Find the force on this part of the wire exerted by the magnetic field. b) Find the force of compression in the wire.

Step-by-Step Verified Solution

**Answer:** (a)

dF = i B dl

(b)

F = i B a

. **Step-by-Step Explanation:** (a) The force on a small element

dl

is

dF = i dl B

. (b) The force of compression is the net force on half the loop:

F = i B (2a) = 2 i B a

.

All Questions in this Chapter

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