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# MAXWELL'S EQUATIONS

 Name or Description SI Gaussian Faraday's law dB V x E = dt 1 dB V x E = c dt Ampere's law dD V x H = + J dt 1 dD 4tt V x H = + J c dt c Poisson equation V • D = p V D = 4trp [Absence of magnetic monopoles] V • B = 0 V • B = 0 Lorentz force on q (E + v x B) / 1 \ q ( E + -v X B J charge q V c J Constitutive D = fE D = fE relations B = /vH B = /vH

In a plasma, p ~ po = 4tt X 10 7 H m 1 (Gaussian units: p ~ 1). The permittivity satisfies e ~ eo = 8.8542 x 10~12 Fm_1 (Gaussian: e ~ 1) provided that all charge is regarded as free. Using the drift approximation vj_ = Ex B/ B2 to calculate polarization charge density gives rise to a dielec­tric constant K = e/e0 = 1 + 36tt X 10gp/B2 (SI) = 1 + 4ttpc2/B2 (Gaussian), where p is the mass density.

The electromagnetic energy in volume V is given by

W = - I dV(H B + E D)

— I dV(tt • B + E • D)

8tt

(SI)

(Gaussian),

Poynting's theorem is

dW

~dT

+

N • dS = -

dVJ • E.

where S is the closed surface bounding V and the Poynting vector (energy flux across S) is given by N = E x H (SI) or N = cE x H/4tt (Gaussian).

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