
12.17. Maxwell Equations (Electromagnetic Field Equations) 1109
The second and third equations in (1) imply the continuity equation
ρ
t
+ div j = 0,
which expresses the charge conservation law.
According to experimental data, the vector fields E, H, D, B, and j are not indepen-
dent and should be supplemented with the material equations (constitutive relations) of the
medium. For isotropic linear media, these equations are
D = εE, B = µH, j = λE, (2)
where ε and µ are the dielectric permittivity and the magnetic permeability of the medium
and λ is the conductance of the medium. For a perfect dielectric, i.e., for a medium that
does not conduct current