文档介绍：ic Interactions1
1
c 1999
Chapter 1
Maxwell’s Equations and
ic Fields
Introduction
Maxwell’s Equations (1865)
The governing equations of ism
ρ
∇.E = ∇.B = 0
0
(Coulomb’s Law)
()
∂B 1 ∂E
∇∧ E = −∇∧ B = µ j +
∂t 0 c2 ∂t
(Faraday’s Law) (Ampere’s Law)
E electric field, describes the force felt by a (stationary) charge q: F = qE
B ic field, describes the force felt by a current
. a moving charge (velocity v): F = qv ∧ B
Thus the Lorentz Force (on charge q) is
F = q (E + v ∧ B) ()
3 R 3
ρ electric charge density (Coulombs/m ). Total charge Q = V ρd x
j electric current density (Coulombs/s/m2)
Current crossing area element dA is j . dA Coulomb/s = Amps.
Historical Note
Much scientific controversy in 2nd half of 19th century concerned question of whether E,
B were ‘real’ physical quantities of science or else mere mathematical conveniences for ex-
pressing the forces that charges exert on one another. English science (Faraday, Maxwell)
5
dA j
Charge-density
ρ
dA
Volume V
Figure : Charge density is local charge per unit volume. Current density is current per
unit area.
emphasized the fields; German mostly the act-at-a-distance. Since ∼ 1900 this question has
been regarded as settled in favor of the fields. And modern physics, if anything, tends to
regard the field as more fundamental than the particle.
Auxiliary Fields and ic Media
ic texts often discuss two additional “auxiliary”fields D the “electric displace-
ment” and H the “ic intensity” which account for dielectric and ic properties
of materials. These fields are not fundamental and introduce plication and
possible confusion for most of our topics. Therefore we will avoid them as much as possible.
For the vacuum, 0E = D and B = µ0H.
Units
Historically there were two (or more!) different systems of units, one defining the quantity
of charge in terms of the force betwee