On 14 Mar, 12:40, "Tom Donaly" wrote:
John E. Davis wrote:
On Wed, 14 Mar 2007 09:09:27 -0800, Tom Donaly
wrote:
Different texts have Maxwell's equations in different order. What text
did you get this from? Becker has it (in Gaussian CGS units) as
div D = 4\pi\rho (where the backslash indicates multiplication, and D
and rho have the usual meanings. You can add the 't' if you want to, but
it's unnecessary. Also, since you're dealing in 3 dimensions, why not
indicate them as in E(x,y,z), or E(x,y,z,t) (if the time means something
to you)?

I tend to write equations in LaTeX form as most people I exchange
emails with mathematical equations use that for formatting mathematics.
Here, \pi represents the greek letter pi, and \rho is the greek letter
rho. I used x to represent a spatial 3-vector. I could have written
it as (x,y,z) but I did not think this shorthand would cause any
confusion given the context.

The difference between E and D is not important here. If you use D,
then \rho must be interpreted as the so-called "free" charge density.
However, the fundamental field is E, and if you use it the \rho must
be interpreted as the _full_ charge density. The relationship between
E and D can be very complex and may well depend upon the strength of
the applied field E. For simple materials a linear relationship is
usually assumed, e.g., D = \epsilon E, where \epsilon is the
dielectric constant of the medium. Also even here in this linear
relationship, \epsilon need not be a scalar (a number). It could be a
tensor (a 3x3 matrix), in which case D and E would not have the same
direction.

--John

Thanks for explaining that, John. I am unfamiliar with the conventions
of LaTex, obviously (I get my information from books that are generally
older than I am, and I'm not young). I don't have any problem with
Gauss' law being used in a non-static context. It applies, regardless.
That's as far as I go in agreeing with Art, though, since I can't
understand the rest of his theory, at all (but might if I could turn
off the left side of my brain - maybe).
73,
Tom Donaly, KA6RUH- Hide quoted text -

- Show quoted text -

Tom
I was rereading this thread as to why people have a hard time in
understanding Gauss's law
with respect to conservative fields and a transition to a non
conservative field where with the addition of time one can consider
what is outside the enclosed surface. Since you pursued the
mathematical side of the subject to a minor conclusion ( you stated
you didn't understand what I was proposing) with John E Davis of
M.I.T. I wish to share with you some notes on the Internet by David J
Raymond called "a radically modern aproach"
which to me is the best I have seen on Radiation in it's entirety.
Obviously there is a lot written that as hams it is not essential
reading for hams but what it does do is explain in a very clear way
the mechanics of radiation with specific applications with respect to
the transition from conservative fields ala Gaussian law of statics to
non conservative fields where at the cessation of time one can
reconcile what is outside the enclosed surface with that which is
inside the surface where what is inside the enclosure is in
equilibrium and the enclosing surface is frictionless. As can
obviously seen a Yagi inside the enclosed border cannot be considered
since at the cessation of time interaction between elements is still
taking place after the cessation of time. The notes are so well
written that one not conversant
with upper math can still follow the implications of the discussion at
hand and thus can be considered as recommended reading for all hams
interested in antennas as a subject. It also gives a very clear
mathematical progression from Gaussian law to the subject of non
conservative fields can be formed with the activation of curl during a
moment in time.
It is this progression that leads designers to design around cluster
arrays that are in equilibrium regardless of orientation ie without
continuing coupling effects after the cessation of time and is very
well chronicalled in the above stated notes.
Best regards
Art