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Maxwell Equations in Conductors

  1. May 5, 2014 #1
    1. The problem statement, all variables and given/known data

    34f1v94.png

    Part (a): Show wave equation for E can be reduced to that.
    Part (b): Show impendance of material is:
    Part (c): Find skin depth.

    2. Relevant equations



    3. The attempt at a solution

    I've got parts (a) and (b) solved, part (c) I've worked it out, but I'm not sure how to use the information of senstivity of ##1 \mu V m^{-1} ##.

    The characteristic timescale during transient state where charges flow in a conductor is ##\tau = \frac{\epsilon_0 \epsilon_r}{\sigma}##.

    For a low frequency regime, ##\tau << \frac{1}{\omega}##.

    Substituting, ##\frac{\epsilon_r \epsilon_0}{\sigma} << \frac{1}{\omega}## and finally ##f << \frac{\sigma}{2\pi \epsilon_r \epsilon_0} = 0.01 Hz##.

    Now to find skin depth, d:

    [tex]d = \sqrt{\frac{2}{\mu_0 \mu_r \sigma \omega}}[/tex]

    Using ##E = \frac{\sigma}{\epsilon_0 \epsilon_r}##,

    [tex]d = \sqrt{\frac{2}{\mu_0 \mu_r \epsilon_0 \epsilon_r E \omega}} = 2.67 x 10^4 m[/tex]

    What's the point of giving the sensitivity of the receiver?
     
  2. jcsd
  3. May 9, 2014 #2
    Maybe the sensitivity is simply there to say that after passing through a maximum depth ##x_max##, the amplitude of the attenuated wave must be at least ##1\mu Vm^{-1}##?

    [tex]E = E_0 exp(-\frac{x}{d})[/tex]

    Let ##E = 10^{-6}##:

    This gives a value of ##x_{max} = 4.92 \times 10^5 m##.
     
    Last edited: May 9, 2014
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