Verified Solution • 2025–26 Session moderate

QPages 230-234: Q18: HC Verma: Concepts of Physics - Volume 2 Magnetic Field Pages 230-234: Q18 Solution: A wire, carrying a current , is kept in the plane along the…

⚠️ Common Exam Traps & Conceptual Pitfalls

Students often replace $\int\!dl$ with the curve’s arc length, assuming $F=iB\times$(arc length). In reality $d\mathbf F=i\,\mathbf{dl}\times\mathbf B$, so only the component of $\mathbf{dl}$ perpendicular to $\mathbf B$ contributes; the net force equals $iB$ times the projection of the wire onto the $x$‑axis, not its total curved length.

A wire, carrying a current

i

, is kept in the

x - y

plane along the curve

y = A \sin2\pi x / \lambda)

. A magnetic field

B

exists in the

z

direction. Find the magnitude of the magnetic force on the portion of the wire between

x = 0

and

x = \lambda

.

Step-by-Step Verified Solution

**Answer:**

F = i B \lambda

. **Step-by-Step Explanation:** The wire follows the curve

y = A \sin(2\pi x/\lambda)

from

x = 0

to

x = \lambda

. The net displacement in the y-direction is zero. The effective length is

\lambda

along the x-axis.

F = i B \lambda

.

All Questions in this Chapter

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