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I am trying to drive this famous equation: ε_r(ω) = 1 + iσ(ω)/(ε_0*ω)

First the regular solution:

J=∂P/∂t→In Fourier domain→J=iωP(ω)=iω{D(ω)-ε_0*E(ω)}; then replace J with σ(ω)*E(ω) and rearrange to reach the result

What makes me puzzle is we know that J_externalis equal to σ(ω)*E(ω) but in foregoing solution I used J_internalwhich is is equal to ∂P/∂t

Here are definitions for all types of currents:

- J_total = -ε_0*∂E/∂t
- J_external = -∂D/∂t
- J_internal = ∂P/∂t

and

J_total = J_external + J_internal.

If the above definitions are correct then I can not drive ε_r(ω) = 1 + iσ(ω)/(ε_0*ω)

Any idea?

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# Conductivity vs. Permittivity

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