One of the most disorienting points on first reading is this: the Lorentz force is always perpendicular to the velocity, so it does no work. Yet electric motors work, magnets lift objects and accelerators spend energy bending beams. Where’s the trick?
The trick is that the magnetic force, by itself, does not exchange kinetic energy with the particle, but redirects its motion. In the devices we use there is almost always a source of electrical energy (a battery, the mains) that indirectly provides the work. When a DC motor turns, energy enters as electrical power at the brushes and leaves as mechanical work, while the magnetic field acts only as a mediator between the two forms. When a magnet lifts a nail, the work is done by the forces that magnetised the nail (ultimately the atomic currents coupled to internal electric fields).
This distinction between “force that redirects” and “force that does work” is one of the subtlest in all of classical physics. A cousin of it is found in the constraint force that keeps a car on a curve (also perpendicular to the velocity, also doing zero work) or in the tension of the string in a conical pendulum. The general moral is that energy does not rise and fall according to the forces at play, but according to the scalar products between forces and displacements.
Worth remembering
A force perpendicular to the velocity changes the direction of motion but not the magnitude of the velocity, and hence not the kinetic energy. It is worth keeping this in mind in the energy balances of circuits with motors and in induction generators.
Collegamenti
Argomenti: Magnetismo Concetti: Forza di Lorentz · Lavoro di una forza
Esercizi collegati: Worked exercise — charge in an outward field · Cyclotron frequency of a proton · Ranking the Lorentz force (four angles)