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**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

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**Taking curl of 3rd equation:**

Using 4th equation: From equation 1st:

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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:

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**k is complex quantity here and can be written as:**

or After comparing:

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

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**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.

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**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,

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**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.

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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.

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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:

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**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

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1 Electromagnetic waves Hecht, Chapter 2 Monday October 21, 2002.

1 Electromagnetic waves Hecht, Chapter 2 Monday October 21, 2002.

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