# free space as a transmission medium

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

1. ### Jamie MorkenGuest

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)

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 ShoppaGuest

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. ### John WoodgateGuest

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 MorkenGuest

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

cheers,
Jamie

5. ### Paul Hovnanian P.E.Guest

Hmm. c = 1.8*10^12 furlongs per fortnight. Looks OK to me.

6. ### John WoodgateGuest

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 WilliamsGuest

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 WescottGuest

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. ### Rich The PhilosopherGuest

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. ### John WoodgateGuest

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 BartoliGuest

Also note that 1 pea = 4 pi steradians

12. ### Jamie MorkenGuest

Yes, I meant pi really

Thanks all for the humorous and inductive/loopy answers.

cheers,
Jamie

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

14. ### Jamie MorkenGuest

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. ### Mario ChenierGuest

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. ### John WoodgateGuest

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'. (;-)

18. ### Dirk Bruere at NeopaxGuest

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. ### John WoodgateGuest

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. ### Dirk Bruere at NeopaxGuest

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