Power & energy relations for macroscopic dipolar continua

Maxwell´s equations in macroscopic dipolar continua can be used to derive Poynting´s theorem as equation with D = ϵ0E + P, B = µ0(H + M) (2) where ϵ0 and µ0 are the free-space permittivity and permeability. The unit normal n̂ to the closed surface S points out of its volume V so that the left-hand side (and thus the right-hand side) of (1) is equal to the instantaneous electromagnetic power flow entering the volume V. Integrating (1) from time t0 when the macroscopic fields are zero to the present time t gives an electromagnetic energy density W(r,t) on the right-hand side of (1) equal to equation.