Maxwell's Equations for linear, isotropic, non-dispersive media

by electromagnetics.info


In linear, isotropic non-dispersive materials (that is materials having field-independent, direction-independent and frequency-independent electric and magnetic properties) the Maxwell's equations for general media can be simplified. In these cases we can relate B to H and D to E as follows:

B = mH ,

D = eE ,
where m is the magnetic permeability in henrys per metre and e is the electric permittivity in farads per metre. Electric losses that convert the current to heat energy can be accounted for by the relation

J = sE  .
where s is the electric conductivity in siemens per metre.

We can rewrite the Maxwell's equations as follows:

H
t
 = - 1
m
 Ñ×E
(1)

E
t
 = - 1
e
 Ñ×H- s
e
 E
(2)

Ñ. H = 0
(3)

Ñ. E = r
e
(4)

where the bold characters represent vector quantities:

E: the electric field vector in volts per metre,

H: the magnetic field vector in amperes per metre,

and we have used the notation of vector calculus The scalar quantity r is the volume charge density in coulombs per cubic metre.

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