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Conductivity vs. Permittivity

  1. Apr 20, 2010 #1
    Hi,

    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_external is equal to σ(ω)*E(ω) but in foregoing solution I used J_internal which 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?
     
  2. jcsd
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