12.2 Magnetism and Moving Charges

The magnetic force on a moving charge is given by the vector equation

Its magnitude is

where ${\theta}$ is the angle between velocity and magnetic field. The right-hand rule gives the direction for a positive charge, and the force reverses for a negative charge. Since the force is perpendicular to both $mathbf{v}$ and ${\mathbf{B}}$, a uniform magnetic field often produces circular motion when the velocity is perpendicular to the field.

If the motion is purely perpendicular, then the magnetic force serves as the centripetal force:

which gives

and

Notice that the period does not depend on speed. This is one of the most elegant results in the unit and is the reason charged particles of fixed q/m cycle predictably in magnetic devices.