[geocentrism] Re: SI units.

  • From: Martin Selbrede <mselbrede@xxxxxxxxxxxxx>
  • To: geocentrism@xxxxxxxxxxxxx
  • Date: Sun, 25 Feb 2007 23:37:03 -0600

Let's be careful here: the "four times pi" factor in the following _expression_, ,  is based on the number of steradians in a sphere: the E field is integrated over an entire sphere. This accounts for the presence of the "four times pi" factor in the denominator or numerator of other equations governing electromagnetism.

Moreover, you could derive this from the electrical permittivity with equal ease, given the algebraic relationship of the magnetic permeability and electrical permittivity of free space to the speed of light in a vacuum.

Finally, it should be noted that in the SI system, the Ampere is a fundamental unit and not a derived unit (which makes the Coulomb a derived unit, namely, an Ampere-Second). Most of us would find it more logical to define the Coulomb in terms of a integral number of charge carriers (e.g., electrons) and make the Ampere a derived unit defined from that quantity of charge carriers passing through a fixed region within one second of time, but the SI Committee, well.... What can I say?   

Martin




On Feb 25, 2007, at 4:47 PM, philip madsen wrote:

I know that some of you might consider me irrational when it comes to modern physics in general, and its math in particular. I got particularly angry with the new SI units system..  and I hear often here and elsewhere, where math is use to fake reality.
 
To some extent here is supporting proof of my case.

Since 1948, the SI Ampere has been defined by choosing μ0 to be H/m. Similarly, since 1983 the SI metre has been defined by choosing the speed of light c to be 299792458 m/s. Consequently

Z0 = μ0c = 119.9169832πΩ ?

exactly, or

Z0 = 376.73031346177...Ω

approximately. This situation may change if the the Ampere is redefined in 2011.

[edit] 120π-approximation

It is very common in textbooks and learned papers to substitute the approximate value 120π for Z0. This is equivalent to taking the speed of light to be 3 \times 10^8 m/s. For example, Cheng 1998 states that the radiation resistance of a Hertzian dipole is

R_{r} = 80 \pi^{2} \left( \frac{l}{\lambda}\right)^{2} [not exact]

This practice may be recognized from the resulting discrepancy in the units of the given formula. Consideration of the units, or more formally dimensional analysis, may be used to restore the formula to a more exact form - in this case to

R_{r} = \frac{2 \pi}{3} Z_{0} \left( \frac{l}{\lambda}\right)^{2}
Ampere is the unit of electric current. It can be precisely defined from Faradays laws, and in particular from the amount of silver deposited on an electrode during electrolysis.
Perhaps they will go back to that in 2011.. Fat chance.
 
 
 
Philip.


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