Presentation on theme: "Electromagnetic Waves in Conducting medium Let us assume that medium is linear, homogeneous and isotropic and is characterized by permittivity, permeability,"— Presentation transcript:
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 Omhs law. Then Thus, Maxwells equations: and
Taking curl of 3 rd equation: Using 4 th equation: From equation 1 st :
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 asthen 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:
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. By subtracting eq (1) and (2):
Now, for good conductors: and then, If; and then, the medium may be classified as a dielectric, and then, the medium may be classified as a conductor. because:
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.
A charge segment dV is at: The position vector of P is: Hence the position of P with respect to dV is: Suppose we have a varying charge (charge density (t)) and lets find the potential due to this charge at point P.
Hence the potential at P due to whole charge: Potential at P at time t, is due to charge segment dV at the time: Just to understand this form for V