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free space as a transmission medium

Discussion in 'Electronic Design' started by Jamie Morken, Nov 2, 2005.

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  1. Jamie Morken

    Jamie Morken Guest

    Hi,

    I was reading through the ARRL uhf/microwave experimenter's manual
    and came across this formula for the propagation velocity in a
    transmission medium:

    v = 1/sqrt(LC)

    and substituting the values for L and C for free space:

    v = 1/sqrt(ue) where u and e are permeability and permittivity

    u= 4*pie*10^7 (H/m)
    e= (1/36)*pie*10^9 (F/m)

    So does the value of pie determine the speed of light in free space
    or am I reading this wrong? Also I have read that the characteristic
    impedance of free space is 120*pie from this formula:

    Z = sqrt(u/e)

    This info is in chapter 5 pages 6 and 7.

    cheers,
    Jamie
     
  2. Tim Shoppa

    Tim Shoppa Guest

    So does the value of pie determine the speed of light
    Pi comes up in a lot of places. (I almost said areas...)
    Well, if 120 had a different value that wasn't 120, then would the
    impedance of free space be different than 377 ohms because of that too?

    I once had a physics professor who said that not only would he be
    working in units where hbar == h/(2*pi) was equal to one, he was also
    going to be using units where h, 2, and pi were all individually equal
    to one :).

    Tim.
     
  3. I read in sci.electronics.design that Jamie Morken <>
    You are not reading it wrong. But pi is not the only dish on the menu.
    Apart from pi there are the numerical values 4 x 10^-7 and 36 x 10^9.
    No-one knows why these numbers are what they are (apart from depending
    on the units of measurement we use), and that bugs current physicists a
    LOT!

    It's possible to devise a system of units in which both numbers are 1,
    but you wouldn't like it.(;-)
    Yes, it is 377 ohms.
     
  4. Jamie Morken

    Jamie Morken Guest

    Not sure what you mean, how can you set them to 1?

    cheers,
    Jamie
     
  5. Hmm. c = 1.8*10^12 furlongs per fortnight. Looks OK to me.
     
  6. I read in sci.electronics.design that Jamie Morken <>
    Choose your units of length, mass, time and electric charge to make them
    1. But don't try it with pi!
     
  7. Tim Williams

    Tim Williams Guest

    I wish my stomach could fit fourty million pies, but I usually eat only a
    third pi at a time instead.

    (Note that 1 pie = 2pi radians.)

    Tim
     
  8. Tim Wescott

    Tim Wescott Guest

    The 4 * pi * 10^-7 was either chosen arbitrarily, or there were other
    arbitrary choices made elsewhere in the SI system of measurements that
    resulted in that value being what it is.

    To set them to one you say "u_o = 1" and "e_o = 1". Then you deduce
    that C = 1 must be true. Now you arbitrarily pick either a time or a
    length measure, and the other one is fixed. With your measures of
    length and time in hand you know all you need to know for you measures
    of inductance and capacitance, and therefore charge, electromotive
    force, and current. I suspect that you'll have force in there too,
    which means that mass won't be far behind. Keep going, and pretty soon
    you'll have your own system of measurements to rival the SI system; then
    you'll just have to find names for them -- I'd like to reserve "Wescott"
    for inductance, in honor of all of the folks who think I'm loopy.
     
  9. No, they are both determined by the Fundamental Nature of Reality. :)

    [I presume that when you say, 'pie', you're talking about 'pi', the
    ratio of the circumference of a circle to its diameter? - thanks!]
     
  10. I read in sci.electronics.design that Tim Williams
    But the ratio of circumference to diameter of a large member of the
    gourd family is pumpkin pi.
     
  11. Fred Bartoli

    Fred Bartoli Guest

    Also note that 1 pea = 4 pi steradians
     
  12. Jamie Morken

    Jamie Morken Guest

    Yes, I meant pi really :)

    Thanks all for the humorous and inductive/loopy answers.

    cheers,
    Jamie
     
  13. Ben Bradley

    Ben Bradley Guest

    Can we talk about geography now? I'm getting Hungary.
     
  14. Jamie Morken

    Jamie Morken Guest

    Ok so after you deduce C = 1 is true, then you pick a time or a length
    measure..? So velocity=distance/time and I set distance to 1meter, then
    time is equal to 1second.. so we need to redefine how long one second is
    and/or how long 1meter is so that it matches up with the actual speed of
    light? I guess that this is what you and John are talking about, or am
    I missing something more obvious? I occasionally have a thick skull so
    this would be no surprise :)

    cheers,
    Jamie



    -- I'd like to reserve "Wescott"
     
  15. Greetings, Jamie.
    The confusion comes from the fact that e0 =~ 8.85419 * 10^12 [F/m],
    which is very close to (1/36) * pi * 10^10 [not (1/36) * pi * 10^9] (an
    error of roughly 1.4 %). The same is true for the impedance of free
    space. It is simply VERY close to 120 * pi, but not quite right on.

    Mario Chenier
     
  16. I read in sci.electronics.design that Jamie Morken <>
    No, abandon 'second' and 'metre' and give the new units new names, such
    as 'Jamie' and 'Morken'. (;-)
     
  17. John Fields

    John Fields Guest

     
  18. If you want to alter pi you need to alter the geometry of space.

    --
    Dirk

    The Consensus:-
    The political party for the new millenium
    http://www.theconsensus.org
     
  19. I read in sci.electronics.design that Dirk Bruere at Neopax
    Yes, and the energy demands are horrendous. So don't try it at home!
     
  20. Well, horrendous using known methods.
    I suspect there may be easier ways that making black holes.

    --
    Dirk

    The Consensus:-
    The political party for the new millenium
    http://www.theconsensus.org
     
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