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BadPhysicistAtWork
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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+(σ2/ω2ε2))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+εμω2ki2=ω2μ2σ2/4
[EDIT: Realised i'd been a bit of an idiot and missed what should have been quite obvious, thank you for pointing it out!]
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+(σ2/ω2ε2))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+εμω2ki2=ω2μ2σ2/4
[EDIT: Realised i'd been a bit of an idiot and missed what should have been quite obvious, thank you for pointing it out!]
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