Introduction to Mathematical Physics/Electromagnetism/Electromagnetic interaction

Electromagnetic forces

Postulates of electromagnetism have to be completed by another postulate that deals with interactions: Template:IMP/postulat This result can be generalized to continuous media using Poynting vector.\index{Poynting vector}

Electromagnetic energy, Poynting vector

Previous postulate using forces can be replaced by a "dual" postulate that uses energies: Template:IMP/postulat Using Green's theorem, $𝒫$ can be written as: Template:IMP/eq which yields, using Maxwell equations to: Template:IMP/eq Two last postulates are closely related. In fact we will show now that they basically say the same thing (even if Poynting vector form can be seen a bit more general).

Consider a point charge $q$ in a field $E$. Let us move this charge of $dr$. Previous postulated states that to this displacement corresponds a variation of internal energy: Template:IMP/eq where $dD$ is the variation of $D$ induced by the charge displacement. Template:IMP/thm Template:IMP/pf