## Propagation of Electromagnetic Waves in a Conducting Medium

In a conducting medium, such that the conductivity Maxwell's equations become and By neglecting resonant or other effects we may use the linear approximations and where and are independent of time.

Maxwell's equations become and Taking the curl of the last of these gives We have now the wave equation in a conducting medium: Similarly The last two equations are called the telegraph equations and incorporate damping terms and so electromagnetic waves travelling in a conducting medium experience attenuation proportianal too the conductance.

By assuming and are of complex exponential form the last two of Maxwells equations above become and The first telegraph equation then becomes which has the form of the Helmhotz equation with We may use the identity to demonstrate the that the equations for conducting and non conducting media are the same if the dielectric constant is replaced by a complex dielectric constant Since we have replaced by a complex equivalent, we must obtain a complex equivalent for the refractive index. This is done by writing where k is a constant called the extinction coefficient.

We replace the propagation constant k by Assuming that is parallel to the – axis, then This wave is attenuated by the factor  