6. Use Maxwell's equations (see Section 4.1.1) to show that if the charge density field e and the current density field J are zero, the electric vector field E satisfies the "wave equation" c?V²E = 0. This is the fundamental equation that describes the propagation of electromagnetic waves, such as light.
6. Use Maxwell's equations (see Section 4.1.1) to show that if the charge density field e and the current density field J are zero, the electric vector field E satisfies the "wave equation" c?V²E = 0. This is the fundamental equation that describes the propagation of electromagnetic waves, such as light.
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Transcribed Image Text:6. Use Maxwell's equations (see Section 4.1.1) to show that if the charge density field e and the current density
field J are zero, the electric vector field E satisfies the "wave equation"
c?V²E = 0.
This is the fundamental equation that describes the propagation of electromagnetic waves, such as light.
Transcribed Image Text:An electromagnetic field is composed of an electric field E(t, x, y, z) and a magnetic field
H(t, x, y, z), which are time-dependent vector fields on R°. With appropriate choice of units,
Maxwell's equations read
ƏE
= cV x H – 47J
at
(4.7)
ƏH
-cV x E
(4.8)
V.E = 4TE
(4.9)
V.H= 0,
(4.10)
where e is the charge density and j is the current vector. The constant c has the dimensions
of velocity, and is in fact the speed of light in a vacuum. Mathematically these equations
form a system of linear partial differential equations in 6 unknowns, namely the components
of E and H.
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