Electromagnetic Waves in Conducting medium Let us assume that medium is linear, homogeneous and isotropic and is characterized by permittivity , permeability , and conductivity , but not any charge or any current other than that determined by Omh’s law. Then Thus, Maxwell’s equations: and

Taking curl of 3rd equation: Using 4th equation: From equation 1st:

Similarly we can find: These last two equations are wave equations governing electromagnetic waves in a homogeneous isotropic conducting medium. Let us assume that the fields vary as then solution of above equation may be expressed as: Substituting this value of E in the above equation, we get:

k is complex quantity here and can be written as: or After comparing:

and By adding eq (1) and (2):

By subtracting eq (1) and (2): Now, in terms of  and , the field vector E take the form: So, field amplitude are spatially attenuated (diminishes) due to the presence of the term so  is a measure of attenuation and is known as absorption coefficient.

Now, for good conductors: and then, the medium may be classified as a conductor. and then, because: If; and then, the medium may be classified as a dielectric,

Skin depth or penetration depth Wave in conducting medium gets attenuated. The distance it takes to reduce the amplitude by a factor of 1/e is called the skin depth. The term 1/ measures the depth at which electromagnetic waves entering a conductor is damped to 1/e =0.369. d = 1/ [= for good conductors] It is a measure of how far the wave penetrates into the conductor.

Retarded Potential Electromagnetic radiation (time varying electric fields especially) are produced by time varying electric charges. Since influence of charge (i.e. field) travels with a certain velocity so at a point, the effect of charge (i.e. potential at that point) is experienced after a certain time only. These kind of potentials are known as retarded potentials.

Suppose we have a varying charge (charge density (t)) and lets find the potential due to this charge at point P. A charge segment dV is at: The position vector of P is: Hence the position of P with respect to dV is:

Potential at P at time t, is due to charge segment dV at the time: Hence the potential at P due to whole charge: Just to understand this form for V