[SI-LIST] FEM/BEM/MoM

Gary, 

Ok that makes sense, 1/4 Joules of Energy being dessipated as 
heat, as to the Paradox that Geoff is talking about, I think 
he is trying to illustrate the fact that a circuit analysis 
alone doesn't give one the full picture of what physically is 
going on in the circuit. As from a purely circuit analysis 
prespective you find that the Initial energy is 1/2 Joule, 
and after the switch is closed you find it to be 1/4 Juoles. 

Intutively, or from experimentally you could probably figure 
out that there is some energy being desipated as heat. 

However if one views the circuit from from a more "physical" 
or "geometric" perspective one can explictly account for the 
energy, thus satisfying the conservation of energy laws.


Thanks, 

A. Rafiq

---------------------------------
The quarter-Joule turns into heat when the switch is 
vaporized into a
cloud of smoke. 
Whats the paradox?

Gary L. Pratt, P.E.
Product Manager
High-Speed Design Kits
Mentor Graphics
(503) 685-1177
gary_pratt@xxxxxxxxxx


Geoff, 

Could you ellaborate on this a little more, as I am afraid i 
can't quite see what happened to the 1/4 Joule of energy. 
Perhaps if you could do a quick back of the envelope 
calculation as an example. 

-----------------

Just a little diversion to show the error in a schematic:
An old example often quoted is the problem of connecting two 
one farad
capacitors together by a switch; one is at 1V potential, the 
other zero.
The initial energy is 1/2 CV**2 =3D 0.5 joule.  After closing 
the switch th=
ere
is charge distribution, and energy =3D 1/8 +1/8 =3D 0.25 
joule.  Where did =
the
missing 0.25 joule go?  If you did an electrical degree, 
you'd see the
paradox.  If you studied high frequencies, you'd know the 
answer.  (I did a
Physics degree, then built RF circuits, so for me a capacitor 
is not a
capacitor.)

The answer is
1) it's not physically possible to put two capacitors 
together at one point
2) therefore they are separated by a distance
3) therefore on closing the switch, the discharge current 
travels a distance
4) the conductors have finite conductivity
5) therefore there is a varying electromagnetic field and 
energy is
dissipated and radiated
6) please don't talk about too much about inductance because 
it's only an
approximation.
-------------------
--------------------------------------- 
Abdulrahman Rafiq
Department of Physics
University of California
Riverside, Ca. 92521
Email: arafi001@xxxxxxx
URL: www.geocities.com/arafiq786
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-----------------------------------

--------------------------------------- 
Abdulrahman Rafiq
Department of Physics
University of California
Riverside, Ca. 92521
Email: arafi001@xxxxxxx
URL: www.geocities.com/arafiq786
-------------------------------------- 
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