256 Chapt. 34 Maxwell’s Equations, Electromagnetic Radiation and Special Relativity
system behaves, one must solve the equations for electromagnetic Felds. The particular solutions
are determined by the laws together with particular
which for timevarying
systems include
in time which are often initial conditions.
a) formulae
b) middle conditions
c) equations
d) boundary conditions
e) laws
034 qmult 00200 1 1 1 easy memory: EMR wave equation
6. In the absence of charge, Maxwell was able to manipulate the Maxwell’s equations such that
they yielded for one dimension in vacuum in scalar form the equations
∂
2
E
∂x
2
=
μ
0
ε
0
∂
2
E
∂t
2
and
∂
2
B
∂x
2
=
μ
0
ε
0
∂
2
B
∂t
2
.
Despite appearances, the EFelds and BFelds satisfying these equations are coupled and one
has in fact that
B
E
=
√
μ
0
ε
0
,
Maxwell’s recognized his equations as examples of the standard
∂
2
f
∂x
2
=
1
v
2
∂
2
f
∂t
2
,
where
v
was the phase speed of propagation. He thus identiFed
v
=
1
√
μ
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 Fall '06
 Buchler
 Physics, Special Relativity, Light, Radiation, Speed of light, wave equation, James Clark Maxwell

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