the Lorentz force
/ LOR-ents /
The Lorentz force is the total electric-plus-magnetic push felt by a charged particle as it moves through fields. It is the rule that governs how electrons steer inside an old television tube, how particle accelerators bend beams, and how the aurora glows as charged particles spiral in the Earth's field. It answers, given the electric and magnetic fields at a point, what force does a moving charge actually feel?
For a particle of charge q moving with velocity v through an electric field E and a magnetic field B, the Lorentz force is F = q E + q v B sin(theta), where theta is the angle between v and B; more precisely the magnetic part is the vector cross product q(v cross B). The electric part q E acts on the charge whether it moves or not and points along E. The magnetic part q v B sin(theta) acts only when the charge is moving, and it is always perpendicular to both v and B, given by the right-hand rule. Because that magnetic force is sideways to the motion, it changes the particle's direction but never its speed.
A key honest point: the magnetic force does no work. Since it always points at right angles to the velocity, it cannot speed a particle up or slow it down; it can only turn it. All the energy change of a charged particle comes from the electric part. This is why a charge in a pure magnetic field travels in a circle at constant speed rather than spiraling faster and faster.
An electron shot into a uniform magnetic field, moving perpendicular to B, feels a constant sideways force. That force is always turned across its path, so the electron curves into a circle at unchanging speed.
Perpendicular to v at every instant, the magnetic force curves the path without changing the speed.
The magnetic force is zero when the charge moves exactly along B (theta = 0), and largest when it moves perpendicular to B (theta = 90 degrees). A stationary charge feels only the electric part q E.