Saturday, January 16, 2010

Electromagnetic Wave Equation or Helmholtz Equation

We will consider a linear, isotropic, homogeneous medium. Moreover, the net free charge in the source free region is zero (ρv = 0) and that any currents in the region are conduction currents (JE). These types of regions are quite general ones and include the practical cases of free space (σ = 0) as well as most conductors and dielectrics. Maxwell’s equations for this region:
Electromagnetic Wave Equation
Taking curl of (3) and substituting (1) and (4) we have

Taking Curl

Similarly, by taking curl of (4) and substituting (2) and (3) we have
Taking Curl
The equations in (5) are called electromagnetic wave equations or Helmholtz equations. Equations (5a) and (5c) are given in time domain and equations (5b) and (5 d) are in terms of the phasor form. The wave equations in E and in H have exactly the same form.

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