The Magnetic Force on a Moving Charge

A magnetic field only pushes on charge that is already moving, and it never pushes along the direction of motion. That's what the cross product in F = qv x B is telling you: the force is perpendicular to both v and B at every instant. Because the force is always sideways to the velocity, it never has a component along the direction of travel, so it can change where the charge is headed but never how fast it's going.

To get the direction, point your right-hand fingers along v, then curl them toward B, and your thumb gives the direction of v x B. If the charge is negative, flip the result. Magnitude is F = qvB sin(theta), where theta is the angle between v and B; this is maximum when v and B are perpendicular (sin 90 = 1) and zero when v is parallel or antiparallel to B (sin 0 = 0), since there is no sideways direction left to push toward.

This force is the engine behind everything else in the unit: because it's always perpendicular to velocity, a charge moving perpendicular to a uniform field is pushed into circular motion, which is where the next topic on circular orbits in magnetic fields picks up. It also sets up the contrast with electric force, which can speed a charge up or slow it down because it acts along the field direction instead.