Poynting's theorem

Poynting's theorem is the local conservation law for electromagnetic energy: changes in field energy equal energy flowing through space minus work done by fields on charges.

Electromagnetic energy density: The energy stored per unit volume in electric and magnetic fields. Its time change is one of the two local energy changes in the theorem.
Electric field: A vector field that exerts electric forces on charged particles. Its energy density and interaction with current both appear in the theorem.
James Clerk Maxwell: Scottish physicist whose electromagnetic theory unified electricity, magnetism, and light. His field equations provide the basis from which the energy balance is derived.
Electromagnetic radiation pressure: Pressure exerted when electromagnetic radiation transfers momentum to a surface or material. Energy flux in the theorem is related to radiation’s ability to deliver momentum and pressure.
Poynting vector: The vector quantity describing the direction and rate of electromagnetic energy flow per unit area. The theorem uses this flux, but the vector alone does not state the full energy balance.
Lorentz force: The force on a charged particle due to electric and magnetic fields. The theorem’s matter-work term is the field force dotted with charge-current density.
Magnetic field: A vector field produced by moving charges and changing electric fields, acting on moving charges. Its energy storage and coupling to the electric field enter the conservation law.
John Henry Poynting: English physicist who formulated the electromagnetic energy-flux theorem in 1884. He identified a vector expression for the flow of electromagnetic energy.
Waveguide: A structure that confines and directs electromagnetic waves along a path. Integrating the energy balance across a waveguide reveals transmitted power and losses.
Electromagnetic momentum: Momentum carried by electromagnetic fields and transferred through their interactions with matter. Its conservation law parallels Poynting’s energy balance but tracks momentum rather than energy.

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