Electromagnetic Waves and Changes in Energy Density(example) #gravitationalenergy #chargedparticles

Protons and electrons vibrate, emitting electromagnetic waves. The electromagnetic energy density u(x,y,z,t) varies over space and time. With its total derivative, the below equation can be derived :

du / dt = ∇u ㆍv - ∇ㆍS

The physical meaning of each term in this equation is as follows:
ⓐ du / dt : Represents how the energy density changes over time within a given volume V. [J m-3 s-1]
ⓑ ∇u ㆍv : Describes how the energy density within the volume changes due to motion v . [N m-3 m s-1]
ⓒ - ∇ㆍS : According to Gauss's divergence theorem, it represents the amount of energy that escapes through the closed surface. [W m-2 m-1]

If there is no net change in total energy, the terms on the right-hand side of the equation must sum to zero. Additionally, if the permeability 'μ' and permittivity 'ε' change due to motion, electromagnetic radiation will occur to satisfy the equation.