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Re: Toward the equilibrium



The model described does not assert any superluminal effects. 1E-19 sec
is a time constant in the exponential decay of a quantity (charge density
at a spatial point). For completeness, I outline the derivation below.
Note the similarity with the decay of a charged capacitor through a
resistor - would a small time constant for an RC circuit imply
superluminal effects?

[ j ] = sigma * [ E ] where [ ] denotes a vector
Div [ j ] = sigma * Div [ E ] , for a region of spatially uniform
conductivity (sigma).

Use the continuity equation for the LHS: Div [ j ] = - d(rho)/dt ;
Use Maxwell's Div [E ] = rho/epsilon for the RHS ==>

d(rho)/dt = - rho*sigma/epsilon ; the LHS is a partial derivative - rho
is a function of space and time.

The solution of this DE is:

rho(t) = rho_0 * exp(-sigma*t/epsilon)

This can be found in Scott, Corson & Lorrain, Jefimenko, etc. Ask if you
need specifics.

Bob

Bob Sciamanda (W3NLV)
Physics, Edinboro Univ of PA (em)
trebor@velocity.net
http://www.velocity.net/~trebor

----- Original Message -----
From: "brian whatcott" <inet@INTELLISYS.NET>
To: <PHYS-L@lists.nau.edu>
Sent: Friday, January 05, 2001 08:00 AM
Subject: Re: Toward the equilibrium


At 11:15 1/4/01 -0500, Bob wrote:
/snip/
The model which I described envisions an unbalanced charge present in
the
interior of a uniform conductor at t=0, and predicts an exponential
decay
of the charge at that point - with a time constant of
epsilon/conductivity.

The derivation is not complex and is in almost any Junior E/M text.

Bob

Bob Sciamanda (W3NLV)


I had better pursue this one - the concept is important to
intending engineers.

If the initials following Bob's signature represent his amateur
radio interest, then I expect he will have no dificulty in describing
the time progression of a shock excited end fed dipole of 1 meter
length,
and say 5 mm diameter.
For non enthusiasts, I am describing a high Q structure that
resonates
near 150 MHz for numerous cycles after a shock impulse on one end.

Military sites that need more bandwidth capability from a dipole
antenna
replace the slender wire first with lower length/diameter conductors,
or if
necessary with two cones, base to base. The Q is reduced, and the
bandwidth
increased.
The conductive sphere is a limiting case of this design variation.
You expect resonant frequency lowering, very low Q and wide
bandwidth.

The side to side electrical field effects are certainly in the
nanoseconds
timescale so if Bob cares to cite an elementary E/M text which appears
to
show superluminal effects on the timescale he mentions, I expect I will
be able to point out the appropriate interpretation.

Sincerely



brian whatcott <inet@intellisys.net> Altus OK
Eureka!