The electric field and the electric displacement are related through the polarization vector as:

(9–6)

where is the permittivity of vacuum. For linear materials (typically diamagnetic or paramagnetic), the polarization vector can be written as

(9–7)

where is the electric susceptibility, which can be a function of the electric field .

A similar relationship is used to relate the magnetic induction to the magnetic field , and the magnetization vector .

(9–8)

where is the permeability of vacuum. For linear materials, the magnetization vector can written as

(9–9)

where is the magnetic susceptibility.

Finally, for the current density can be written as

(9–10)

where is the electrical conductivity.