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Module 4 : Uniform Plane Wave
Lecture 28 : Uniform Plane Wave in a Conducting Media
Objectives
In this course you will learn the following
Dielectric medium with finite conductivity.
Concept of complex dielectric constant.
What is a conductor and dielectric?
Wave equation for a dielectric medium for a finite conductivity.
The complex propagation constant for a medium with finite conductivity.
Loss Tangent.
Module 4 : Uniform Plane Wave
Lecture 28 : Uniform Plane Wave in a Conducting Media
Concept of complex permitivity
Let us consider a medium with finite conductivity, we have the conductivity of the medium is non-zero and finite.
The medium has conduction as well as displacement currents
Conduction current density is
where
is the conductivity of the medium.
Displacement current density for a sinosidal electrical field is
The total current density is
The ampere's law therefore gives
Rewriting the equation, we get
the quantity in the curly brackets is the dielectric constant of a medium which has finite conductivity
NOTE
The dielectic constant of a medium which has conductivity is therefore a complex quantity.
Module 4 : Uniform Plane Wave
Lecture 28 : Uniform Plane Wave in a Conducting Media
What is a Conductor and Dielectric?
The ratio of the conduction and displacement current densities for a given electric field decides whether the medium is a
conductor or a dielectirc
This means the absolute value of conductivity is not very meaningful in calling a medium good conductor.
Any medium with finite conductivity behaves like a conductor as we reduce the frequency and behaves more like a
dielectric if we increase the frequency.
Generally, we call copper( which has a conductivity
conductor upto frequency of
) a good conductor because it behaves like a
Hz.
Whereas, a medium like sea water which has a conductivity of
100KHz.
can behave like a conductor only below
Module 4 : Uniform Plane Wave
Lecture 28 : Uniform Plane Wave in a Conducting Media
Propogation constant of a uniform plane wave in conducting medium
The wave equation for the conducting medium is
The propogation constant of the uniform plane wave in this medium is
Separation of real and imaginary parts gives attenuation constant
And the Phase Constant
Loss-Tangent
Loss-Tangent is the tangent of the phase of complex dielectirc constant of the medium
Loss tangent is a measure of loss in a good dielectric. For ideal lossless dielectric, the loss tangent is zero and for a good
dielectric the loss tangent is
Module 4 : Uniform Plane Wave
Lecture 28 : Uniform Plane Wave in a Conducting Media
Recap
In this course you have learnt the following
Dielectric medium with finite conductivity.
Concept of complex dielectric constant.
What is a conductor and dielectric?
Wave equation for a dielectric medium for a finite conductivity.
The complex propagation constant for a medium with finite conductivity.
Loss Tangent.