Magnetic Force & Lorentz Force

Charged particles in magnetic fields

The Lorentz force on a moving charge in a magnetic field is always perpendicular to both the velocity and the field (F = qv×B). Since the force is perpendicular to velocity, it does no work — kinetic energy is constant, only direction changes. This produces circular motion in the plane perpendicular to B. If the particle has a velocity component along B, the path becomes a helix. The radius r = mv/(|q|B) is called the cyclotron radius.