Larmor formula

The Larmor formula gives the total electromagnetic power radiated by a nonrelativistic point charge as a function of its acceleration. It scales with the square of the charge and acceleration.

Electromagnetic radiation: Energy carried through space by coupled electric and magnetic fields. The formula quantifies the radiated energy per unit time.
Coulomb: The SI unit of electric charge. The radiated power depends on the square of charge, measured in coulombs.
James Clerk Maxwell: Scottish physicist whose equations unified electricity, magnetism, and light. Maxwell's field theory provides the foundation for calculating radiation from moving charges.
Synchrotron radiation: Electromagnetic radiation emitted by relativistic charged particles moving in curved paths. Its classical power law generalizes the acceleration dependence in this formula.
Quantum electrodynamics: The quantum field theory of electromagnetic interactions between charged particles and photons. It replaces the classical continuous-radiation picture when quantum effects matter.
Poynting vector: A vector describing the direction and rate of electromagnetic energy flow per unit area. Integrating its outward flux gives the radiated power in the formula.
Acceleration: The rate at which velocity changes with time. It is the motion variable whose squared magnitude sets the emitted power.
Joseph Larmor: Irish physicist who developed early theories of electromagnetic radiation from accelerated charges. The formula bears his name for his work deriving the emitted power.
Bremsstrahlung: Radiation emitted when a charged particle is accelerated or decelerated, often by a nucleus. The formula estimates its power when the particle remains nonrelativistic.
Liénard formula: The relativistic expression for power radiated by an accelerated point charge. It removes this formula's nonrelativistic speed restriction.

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Thomson scatteringRelated: The incident wave accelerates the charge, whose radiation constitutes the scattered field.