Question

A long straight wire AB carries a current I. A particle (mass m and charge q) moves with a velocity `vec"v"`, parallel to the wire, at a distance d from it as shown in the figure. Obtain the expression for the force experienced by the particle and mention its directions.

 

Answer 1

Magnetic field induction at P due to current I in long straight wire AB is

`B = mu_0/(4pi) (2I)/d`

It acts perpendicular to the plane of the paper inward, represented by `hatn`.

Lorentz force acting on the particle at P can be given by

`vecF = q(vecv xx vecB) = e(vecv xx (mu_0. 2I)/(4pid)hatn)`

or `vecF = (mu_0Iev)/(2pid)(hatv xx hatn)`

∴ `F = (mu_0Iev)/(2pid)`

Acting in the plane of paper away from the wire.