Lorentz force

When a charged particle moves through a magnetic field, it experiences a sideways push perpendicular to both its direction of motion and the field direction itself. This push is the Lorentz force, and it is the fundamental mechanism behind electric motors, particle accelerators, and magnetic focusing systems. The force does not exist when the particle is stationary, nor when it moves parallel to the field lines, but arises only when velocity and field have a component perpendicular to each other.

The magnitude of this force is proportional to three things: the charge of the particle (q, measured in coulombs), the strength of the magnetic field (B, in tesla), and the component of velocity perpendicular to that field (v sin θ). The resulting formula, F = qvB sin θ, is one of the most direct relationships in electromagnetics. An electron moving at 1 million meters per second through a 1 tesla field experiences a force of about 1.6 × 10^-13 newtons, tiny in absolute terms but decisive for the electron's trajectory over even short distances.

Where this matters in practice

In a DC electric motor, current flows through coils in a magnetic field, and the Lorentz force on each current-carrying segment of wire produces torque. In a vacuum tube or cathode ray oscilloscope, magnetic deflection coils use this force to steer electron beams onto screens with micron-level precision. Particle physics accelerators rely on it to bend proton or electron beams along circular or curved paths without a physical track. Hall effect sensors exploit it to measure magnetic field strength by detecting the sideways accumulation of charge carriers in a current-carrying conductor placed in a field.

The force can cause unwanted effects too. In high-current conductors exposed to stray magnetic fields, the Lorentz force can create mechanical stress on the wire or cause it to move; large power transformers and transmission cables must be braced to withstand these forces during faults. Cosmic ray particles moving through Earth's magnetic field are deflected by this same mechanism, creating the auroras near the poles.

The term honors Dutch physicist Hendrik Lorentz, who formalized the relationship in the 1890s. The force is often called the Lorentz force law when stated as part of the full description of how electric and magnetic fields interact with charges and currents, though in modern physics the Lorentz force emerges naturally from the geometry of spacetime under relativity, making it more fundamental than the Maxwell equations from which it was historically derived.