Home / Topics / Magnetism & Induction
Lorentz force law
Intermediate
Combined electric and magnetic force.
F = q(E + v×B)F = q(E + v×B) gives the complete electromagnetic force on a charge. It governs particle accelerators, mass spectrometers and plasmas.
An electron in crossed fields drifts at E/B.
Magnetic part does no work.
In more detail
The Lorentz force law gives the total force on a charge from electric and magnetic fields, F = q(E + v × B). It is the central equation for charged particle motion.
Real-world uses
- Particle accelerators and detectors are designed using the Lorentz force.
- Plasma physics relies on the Lorentz force to describe charged fluids.
- Physicists use the Lorentz force law to calculate the total force on a charged particle in combined electric and magnetic fields.
Open the interactive lesson, with simulation and quiz →
Frequently asked questions
Why does the magnetic part use a cross product?
Because the magnetic force is perpendicular to both velocity and field.
Does the magnetic part do work?
No, only the electric part changes energy.
Which part of the force depends on velocity?
The magnetic part, qv cross B, is the only part that depends on the velocity of the particle.
Related topics in Magnetism & Induction
Hall effect and sensors · Magnetic energy density · Magnetic pressure · Magnetic shielding