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At these frequencies, electromagnetic waves are no longer reflected as in a mirror. Losses can also occur due to the materials with complex permittivity or permeability. As can be seen from Eq. 57), the complex propagation constant, γ , is purely imaginary for the lossless case when µ and ε are real and σ = 0. On the other hand, γ becomes complex and the material is lossy when µ or ε are complex. This is usually due to some molecular, atomic, or electronic resonance that causes the material to absorb power such as the heating of food in a microwave oven.

Directed out of the plane of the paper. 6: A plane wave in an arbitrary direction. components in the −a X and +a Z directions. The wave nature is exhibited by the imaginary ′ term in the exponential as e − jβz . Though all these details are correct, it is often more useful to represent the fields in the x−y−z coordinates instead of the primed coordinates. It is clear that z′ has both x and z components; their relative amplitudes depending upon the angle θ . 25) a simple coordinate transformation.

The resistive part, 1/σ δ, is often called wave resistance or resistance/square and has units of ohms. The H field lags the E field by π /4 due to the inductive component of the wave impedance. book Mobk081 August 13, 2007 22:30 ELECTROMAGNETIC WAVES 51 The mathematics clearly indicates a high attenuation of the wave as it propagates into the good conductor, but what is the physical explanation of this effect? The time-varying electric field establishes a current, aligned with the electric field, which in turn establishes a perpendicular magnetic field that has a phase delay of π /2.

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A Kinematical Interpretation of Electromagnetism (1919)(en)(8s) by Page L.

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