Lorentz force

The Lorentz force is expressed as **F** = q(**E** + **v** × **B**), where q is the particle's electric charge, **E** is the electric field, **v** is the particle's velocity, and **B** is the magnetic field. The cross product with **B** means the magnetic component of the force is always perpendicular to the particle's direction of motion.

The force is named after Dutch physicist Hendrik Lorentz, who formulated the expression in the late 19th century as part of his electron theory. Lorentz shared the 1902 Nobel Prize in Physics with his student Pieter Zeeman for their investigations of the influence of magnetism on radiation.

Because the magnetic force component is always perpendicular to the particle's velocity vector, it changes the particle's direction of motion but not its speed or kinetic energy. This causes charged particles in a uniform magnetic field to follow circular or helical paths, which is the principle behind devices like cyclotrons and mass spectrometers.

The Lorentz force is the operating principle behind electric motors, loudspeakers, mass spectrometers, and particle accelerators such as the Large Hadron Collider at CERN. It is also fundamental to magnetohydrodynamics and to the magnetic confinement of plasma in fusion reactors like tokamaks.