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    5

MAXWELL'S EQUATIONS

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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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