Answer to Question #126931 in Electricity and Magnetism for sarv

Question

A circular coil is carrying current in clockwise direction. A charged particle is crossing the circular coil exactly along the axis of the circular coil. Will the velocity of charged particle change?

Answer 1

When interacting with the magnetic field, the charged particle can change its velocity because of the Lorentz force:

$$\mathbf{F} = q\mathbf{v}\times \mathbf{B}$$

where $\mathbf{v}$ is the velocity of the particle and $\mathbf{B}$ is the magnetic field induction. The $\times$ denotes the cross-product.

In a circular coil the magnetic field is directed along the axis. Thus, the magnetic field induction and velocity of the particle are collinear. This means that their cross-product is equal to 0 and the velocity will not change.

Answer. The velocity will not change.