Electricity The Maxwell equations are the fundamental equations of electromagnetism. These local equations relate the electric field E and the magnetic field B to their sources: the charge density ρ, the conduction current density j (εo and μo being respectively the permittivity and the permeability of a vacuum, related by μo * εo * c2 = 1):
. div E = ρ / εo
. rot E = -dB/dt (the Maxwell-Faraday relation)
. div B = 0.
. rot B =μo * j + μo * εo * dE/dt (Maxwell-Ampere relation)
The derivatives are partial, the physical quantities involved being dependent on space and time, except under special conditions which can lead to simplifications.