Source-free Maxwell equations in a linear medium

For

D = ϵ E

and

B = μ H

with no free charge or current,

\nabla \cdot D = 0, \nabla \cdot B = 0, \nabla \times E = - \partial_{t} B, \nabla \times H = \partial_{t} D .

Table of contents
- Plane electromagnetic wave in a linear medium Source-free Maxwell equations in a linear medium
  - Transversality of an electromagnetic plane wave Plane electromagnetic wave in a linear medium

Plane electromagnetic wave in a linear medium

A plane wave in a homogeneous linear medium satisfies

ω^{2} = \frac{∣ k ∣ ^{2}}{ϵ μ}, v = \frac{1}{ϵ μ}, B_{0} = \frac{1}{ω} k \times E_{0} .

Transversality of an electromagnetic plane wave

The source-free divergence equations imply

k \cdot E_{0} = k \cdot B_{0} = 0

, so both fields are transverse to the wavevector.

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