Presentation on theme: "Electromagnetic Waves in Conducting medium"— Presentation transcript:
1 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. ThenThus, Maxwell’s equations:and
2 Taking curl of 3rd equation: Using 4th equation:From equation 1st:
3 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:
4 k is complex quantity here and can be written as: orAfter comparing:
6 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 termso is a measure of attenuation and is known as absorption coefficient.
7 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,
8 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.
9 Retarded PotentialElectromagnetic 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.
10 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:
11 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