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Concept of complex permitivity |
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Let us consider a medium with finite conductivity, we have the conductivity of the medium is non-zero and finite. |
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The medium has conduction as well as displacement currents |
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Conduction current density is |
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where
 is the conductivity of the medium. |
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Displacement current density for a sinosidal electrical field is
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The total current density is |
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The ampere's law therefore gives |
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Rewriting the equation, we get |
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the quantity in the curly brackets is the dielectric constant of a medium which has finite conductivity |
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NOTE |
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The dielectic constant of a medium which has conductivity is therefore a complex quantity. |
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