Answer to Question #100848 in Electricity and Magnetism for abdod

Question

Can a charged particle q move through a uniform magnetic field B without experiencing any force F ? Explain.

Answer 1

A charged particle moving in a magnetic field may experience Lorentz's force, which depends on particle's velocity, charge, the field magnitude, and the orientation of the field with regard to the velocity:

$$F_L=qvB\text{ sin}\theta.$$

That is why any charged particle where the angle $\theta$ between $B$ and $v$ is not $0^\circ$, experiences some force. Also, we can place an electric field to "compensate" the influence of the magnetic field and it will seem that the particle will move in a straight line, but actually it will experience two opposite but equal forces.

So without an electric field if $v$ is parallel to $B$, i.e. the particle moves along the field lines, the force is zero.