Re: paradox?


"Timo A. Nieminen" <timo@xxxxxxxxxxxxxxxxx> wrote in message
news:Pine.WNT.4.64.0703130437000.392@xxxxxxxxxxxx
On Sun, 11 Mar 2007, Jon Slaughter wrote:

The point is that one uses
this concept in everyday life when the conductors are not very large but
when conceptually enlargin the conductors then one runs into a problem.

What problem? Two things happen at the same time because a magic
restraining force is assumed to turn off instantly, everywhere. It's no
more of a problem than both ends of a dropped pole hitting the ground at
the same time. Neither communicates information from A to B or carries
energy or momentum instantly from A to B. What problem?

[cut]
My only conclusion is that I would have to use Maxwell's equations that
take
into accoung special theory of relativity. I haven't every seen those
equations before but I have seen them mentioned many times.

You're reading Stratton and you haven't seen those equations? IIRC,
they're in the first chapter; they're usually called the Maxwell
equations.


No, They are not maxwell's equations WITH SPECIAL THEORY OF RELATIVITY TAKEN
INTO ACCOUNT. They are just plain old maxwell's equations

http://en.wikipedia.org/wiki/Formulation_of_Maxwell%27s_equations_in_special_relativity

Now I suppose I was wrong in thinking that the equations ment something
different as it seems they are just formalized in the language of special
theory of relativity. I thought one had to modify the equations but I guess
I was wrong.

It isn't that hard. Assume an Ohmic linear isotropic homogeneous
conductor. Thus, div(E) = A rho. Thus, div(J) = B rho. From conservation
of charge, dJ/dt = C rho, and exponential decay. Also from conservation of
charge, it has to go somewhere, namely the outside of the conductor.

If you don't like that result, what are you going to change? Conservation
of charge? The Maxwell equations? You could stomp on assumptions of
Ohmicity and linearity, since they're just convenient engineering
approximations, but why bother - what's the problem in the first place?


yes, you get the answer from the solution of the the equation of continuity
and the divergence of the E field(and a few other conditions). I gave the
result already.

NOW! Stratton says:

"This surface charge makes its appearance at the exact instant that the
interior charge begins to decay, for the total charge is constant."

This is obvious if the charge cannot leave the conductor. Stick an charge in
the center of the conductor and it will decay exponentially. But where does
it end up? Where does the charge go infintesimally later? It ends up on the
surface(where else can it go?) It must do this instantaneously because all
the charge in the conductor decays. (so if the charge "moved" to some other
point in the conductor it wouldn't decay at that new point but increase).

Now since its instantaneous one just has to take a large sphere that larger
than the magnitude of the speed of light and then this charge will go faster
than the speed of light. Ok, not the same charge but the E-field(or
something) must cause this to happen. It might not be a paradox but it
seems strange.

Ofcourse I've stated all that stuff in my first post. My issue was to know
if it was a "defect" in maxwell's equations or if it was something else.
(after all, maxwell's equations are not perfect as nothing is) Ofcourse
maybe the assumptions are the issue. Maybe there is no real world conductor
that satisfies those assumptions perfectly. Maybe it has to do with quantum
mechanics, etc... I do not know and that is why I asked... but so far I
have just been given the runaround.


.

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