Di ff erential Fo rms of Electrodynamic Laws With the aid of Gauss' and Stokes' theorems we may transform the laws of electrodynamics
given in integral form in Section 1.6 to the equivalent differential forms below.
∇ × E = −∂B∂t
∇ ×H = J + ∂D∂t
∇ · D = ρ
∇ · B = 0
(1.16)
These equations, together with the definitions
D = ²0E + P (1.17)
and
B = μ0(H+M) (1.18)
are regarded as the basic laws of electrodynamics in the presence of media. Note that
they are quite general in that they do not assume linearity or spatial uniformity of those
media.
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