On Mar 11, 12:38 am, Richard Clark wrote:
On Sun, 11 Mar 2007 06:00:27 +0000 (UTC), (John E.


Davis) wrote:
On Sat, 10 Mar 2007 23:21:35 GMT, Dave
wrote:


I will make one last effort to to set the record straight. In volume
II of the Feynman Lectures on Physics, the title of chapter 15,
section 6 is "What is true for statics is false for dynamics". The
5th paragraph of that section states "Gauss' law, [eq omitted]
remains...". Also in that section, he has a table (Table 15-1) that
contains two columns:

FALSE IN GENERAL | TRUE ALWAYS
(true only for statics) |
------------------------------------------------------
Coulomb's Law | Gauss' law
[...] | [...]

At the bottom of that Table is a footnote explaining the bold arrow of
your Gauss' law. It reads:
"The equations marked by an arrow (-») are Maxwell's equations."

The table equation, and the one you reference in the text are both
Maxwell's.

Then in chapter 18, section 1 paragraph 3 you will find the statement:

"In dynamic as well as static fields, Gauss' law is always valid".

That chapter, too, clearly defines the same equation you are making an
appeal to as "Maxwell's equations." Observe Table 18-1 "Classical
Physics"

It is explicitly derived from the treatment as equation 4.1 - also
denoted Maxwell's equations.

"All charges are permanently fixed in space, or if they do move,
they move as a steady flow in the circuit ( so rho and j are
constant in time). In these circumstances, all of the terms in
the Maxwell equations which are time derivatives of the field are
zero."

Equations 4.6 and 4.8, the cross and dot products resolve to zero.

If you crank up the clock, Feynman concludes
"Only when there are sufficiently rapid changes, so that the time
derivatives in Maxwell's equations become significant, will E and
B depend on each other."

We will, of course, recognize this EB relationship as the field of
radiation and further recognize there is no field of radiation without
a significant time factor.

The grad operator, an inverted, enbolded del, is discussed by Feynman
in Chapter 2-4 is a significant element of these equations. The grad
operator obeys the same convention as the derivative notation.

Feynman's instruction clearly shows that Maxwell's treatment (actually
Heaviside's work before him) is a generalization of Gauss to include
time (sorry Art, he got there two centuries ago) and hence describes
Gauss equations as special (zero-time) instances of the generality.

73's
Richard Clark, KB7QHC



I'm easily impressed, but none the less I'm still impressed.

Derek.