Preamble

Once the amplitude of a wave is defined, the electric and magnetic energies in the waves are calculated in terms of this amplitude. However, the total energy in the waves cannot be identified in any simple way in general. The damping of waves is used to identify the total energy by relating the damping to the dissipative part of the response tensor in two ways. One way involves calculating the work done by the dissipative process and equating this to the energy lost by the waves. The other way involves including damping in terms of an imaginary part of the frequency (§11.4). The equivalence of the two ways of treating damping provides an explicit expression for the total energy in the waves. A semiclassical description of a distribution of waves is useful for both formal and practical purposes; the semiclassical description is based on regarding the waves as a collection of wave quanta.

The Electric and Magnetic Energies in Waves

In any physical theory, energy is defined in terms of its mechanical equivalent. In §15.2 this is achieved by calculating the work done by an arbitrary dissipative process and equating it to the energy lost by the waves. An important preliminary step is to define the amplitude of the waves and to calculate the electric energy in waves in Fourier space by using the fact that the electric energy density in coordinate space is given by ½ε0∣E∣2. The magnetic energy in waves is calculated in an analogous way.