Plane waves

Plane waves are a specific type of electromagnetic wave solution to Maxwell’s equations in which the electric and magnetic field vectors oscillate sinusoidally in planes perpendicular to the direction of wave propagation.

In a plane wave, the electric field (E) and magnetic field (B) are constant in magnitude and direction over any plane perpendicular to the direction of propagation. The electric and magnetic fields are mutually perpendicular and also perpendicular to the wave’s direction of travel.

A plane wave can be represented mathematically as:

E(r, t) = E₀ * sin(k • r – ωt + φ₁)

B(r, t) = B₀ * sin(k • r – ωt + φ₂)


  • E₀ and B₀ are the amplitudes of the electric and magnetic fields, respectively.
  • k is the wave vector (pointing in the direction of wave propagation).
  • r is the position vector.
  • ω is the angular frequency of the wave.
  • t is time.
  • φ₁ and φ₂ are phase constants for the electric and magnetic fields, respectively.

Plane waves are an idealized concept that simplifies the analysis of electromagnetic waves in many situations. They are often used as an approximation in scenarios where the wave source is far away from the observation point, and the curvature of the wavefront can be neglected. Examples of such situations include radio wave propagation in free space, light from distant stars, or analysis of antennas and waveguides.

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