Question

A wire, carrying a current i, is kept in the X-Y plane along the curve y - Asin((2π/λ)x). 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 = λ.

Answer 1

Here the displacement vector vectot (dI) = λ

So magnetic for i → t vectot (dI) x vector B = i × λB

Answer 2

\(\vec {dl} \rightarrow \lambda\\\vec F = i(\vec {dl}\times\vec B)\\=i\vec {dl}Bsin90° \\\vec F=idlb\\\vec F= i\lambda B \)