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Find an expression for the attenuation from the eqn given

  1. Nov 6, 2016 #1
    • Poster has been reminded to use the Homework Help Template to organize their HH threads
    Having a big issue working through this problem and was wondering if somebody, much smarter than I, could give me a few pointers. Anyway here's the problem:

    Given that k2=εμω2-iωμσ

    By writing the wave number as k=kr-iki.
    Show that ki, which determines attenuation, can be expressed by:
    ki=ω(εμ/2)1/2[(1+(σ22ε2))1/2)-1]1/2

    I've started by equating real and imaginary parts however I find an impasse where I have a quartic equation.

    I'd been incredibly grateful for any answers, thank you in advance!

    Just as a quick note, I followed the following process but reached an impasse (may be completely off base here):
    k2=εμω2-iωμσ
    Substitute k=kr-iki. into the equation which gives;
    kr2-2ikrki-ki2=εμω2-iωμσ
    Then split into two equations by equating real and imaginary parts;
    (1) kr2-ki2=εμω2
    (2) εμω2=ωμσ/2ki
    Now (2) into (1) gives;
    (ωμσ/2ki)2-ki2=εμω2
    Then rearranging gives;
    ki4+εμω2ki22μ2σ2/4

    [EDIT: Realised i'd been a bit of an idiot and missed what should have been quite obvious, thank you for pointing it out!]
     
    Last edited: Nov 6, 2016
  2. jcsd
  3. Nov 6, 2016 #2

    Dr Transport

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    Gold Member

    it is a quadratic... set [itex] k_{i} = \alpha [/itex] and us the quadratic equation for [itex] \alpha [/itex] and take the square root.....
     
  4. Nov 6, 2016 #3
    Actually really disappointed i myself for not seeing that.... Thank you for that, really made this a lot easier.
     
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