Editing Lorentz force (section)

== Significance of the Lorentz force ==

While the modern Maxwell's equations describe how electrically charged particles and currents or moving charged particles give rise to electric and magnetic fields, the Lorentz force law completes that picture by describing the force acting on a moving point charge {{mvar|q}} in the presence of electromagnetic fields.{{sfn|Jackson|1998|pp=2-3}}{{sfn|Griffiths|2023|p=340}} The Lorentz force law describes the effect of {{math|'''E'''}} and {{math|'''B'''}} upon a point charge, but such electromagnetic forces are not the entire picture. Charged particles are possibly coupled to other forces, notably gravity and nuclear forces. Thus, Maxwell's equations do not stand separate from other physical laws, but are coupled to them via the charge and current densities. The response of a point charge to the Lorentz law is one aspect; the generation of {{math|'''E'''}} and {{math|'''B'''}} by currents and charges is another.

In real materials the Lorentz force is inadequate to describe the collective behavior of charged particles, both in principle and as a matter of computation. The charged particles in a material medium not only respond to the {{math|'''E'''}} and {{math|'''B'''}} fields but also generate these fields. Complex transport equations must be solved to determine the time and spatial response of charges, for example, the [[Boltzmann equation]] or the [[Fokker–Planck equation]] or the [[Navier–Stokes equations]]. For example, see [[magnetohydrodynamics]], [[fluid dynamics]], [[electrohydrodynamics]], [[superconductivity]], [[stellar evolution]]. An entire physical apparatus for dealing with these matters has developed. See for example, [[Green–Kubo relations]] and [[Green's function (many-body theory)]].