The Lorentz force

A magnetic field only pushes on charge that is already moving, and it pushes in a very specific direction: perpendicular to both the velocity and the field itself. The magnitude is F = qvB sin θ, largest when velocity and field are perpendicular and zero when they are parallel — a charge moving straight along the field lines feels nothing at all, and a charge sitting still feels nothing regardless of how strong the field is, since v = 0 makes the force zero outright.

That perpendicularity has a consequence worth sitting with: a force always at right angles to the motion can never do work, because work requires a component of force along the direction of travel and there is none here. A charged particle circling in a magnetic field moves at constant speed forever, however long it circles — the magnetic force bends the path without ever changing how fast the particle is going. This is exactly analogous to uniform circular motion under gravity or tension: the centripetal force turns the direction of velocity without touching its magnitude.

Because the force continuously redirects the velocity while never changing its size, the natural path is a circle, with the magnetic force supplying exactly the centripetal force needed: qvB = mv²/r. If the particle also has a velocity component along the field, that component is unaffected — nothing perpendicular to it acts on it — so the full motion is a circle superimposed on steady motion along the field, a helix. This is the physics behind mass spectrometers, cyclotrons, and the auroras: charged particles from the solar wind spiral along Earth's magnetic field lines toward the poles rather than travelling straight through space.