Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Velocity of propagation in lossy media

  1. Sep 5, 2006 #1
    regarding plane waves theory and their properties, for lossy media (conductors) in different books appear a formula that represent alfa y beta constants in the followig way:

    alfa = beta = root square( pi*frequency*mu*sigma) valid for good
    conductors (high loss material)

    I have checked this formula in different books and it works well, and
    it's used further to calculate skin effect as well

    My question arises from one conclusion derived from the formula, that I
    found in just a specific book (David Cheng's Fundamentals of
    engineering electromagnetics).
    In that book the author says:
    velocity of propagation = omega / beta
    For copper (good conductor):
    sigma = 5.8 * 10 exp 7
    mu = 4 *pi *10 exp -7
    and therefore v = 720 m/sec. @ f = 3 Mhz.

    so the velocity of propagation is << c

    I am confused with the final result, because I've checked the formula, and the math in the example is right, but I know that in a copper transmission line, the velocity of propagation is about 2/3 c = 200,000 km/sec.
    The formula appears in different books, but the specific example just
    appears in Cheng's book
    I think the application for the example is valid in a different situation,
    but I can't figure out which
     
  2. jcsd
  3. Sep 5, 2006 #2

    marcusl

    User Avatar
    Science Advisor
    Gold Member

    I think beta here is what other books refer to as the wavenumber
    k=2*pi/lambda
    Since omega=2*pi*f, the formula is actually the familiar one
    c=lambda*f
     
  4. Sep 5, 2006 #3
    in lossy media, beta is the phase constant, and alfa is the attenuation constant.
    the complex propagation constant gamma is defined = alfa + j * beta
    in this case the wavenumber k is complex as well, and it is related to gamma by
    gamma = j *k

    for lossless media, alfa = 0 and there are no losses at all, just phase change (beta) and in that special case (alfa = 0), we get:
    gamma = j*beta = j*k
    so beta =k
     
  5. Sep 6, 2006 #4

    Meir Achuz

    User Avatar
    Science Advisor
    Homework Helper
    Gold Member

    Copper is not a "lossy" conductor".
    In a lossy conductor the wave goes (almost) nowhere slowly.
    That is why it is called skin depth.
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?