December 2014
Intermediate to advanced
418 pages
16h 17m
English
Content preview from Electricity and Magnetism
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Chapter 48
Wavelike Solutions of Maxwell’s Vacuum Equations
In the previous chapter, two of Maxwell’s Equations, viz., Faraday’s and Amp`ere’s Laws,
were applied to the plane-wave Ansatz, and two coupled linear first-order partial differential
equations with constant coefficients were obtained.
Vacuum Faraday
∂E
∂x
= −
∂B
∂t
Vacuum Amp
`
ere
∂B
∂x
= −µ
0
ǫ
0
∂E
∂t
The standard trick, fruitfully employed to uncouple such sets of equations, is to
DIFFERENTIATE Take the partial derivative [with respect to x, say] of one equation.
COMMUTE Interchange the order of action of the distinct partial derivatives.
[For consistency, the functions must have continuous second-order
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