Re: How many volts ?

[John Mallinckrodt <ajmallinckro@CSUPomona.Edu>]

On Tue, 25 Mar 1997 SCIAMANDA@edinboro.edu wrote:

> John,
>     This seems to be a special case of the matrix equation relating 
> the potentials and charges on a system of N separated conductors:
>
> |V| = P*|Q|
>
> where |V| is the column vector of N potentials, Q is the column 
> vector of charges, and P is the matrix of "coefficients of potential".
> The P_i,j are functions only of the geometry.  In your case N=2.
>
> The relation can obviously be turned into:
>
> |Q| = C*|V| , where the C_i,j are the "coefficients of capacitance".
>
> These relations have gone out of fashion in most recent textbooks
> (only the "capacitor" of two equally and oppositely charged 
> conductors is typically now treated). An exception is 
> "Electromagnetic Fields", Roald K. WAngsness
> (Also, one of the earlier editions of Corson & Lorrain).

Just so Bob.  Another gap in my own training. I went to the library this
afternoon and found references to the coefficients of capacitance in
O'Hanian's Classical Electrodynamics (1988) and also in a couple of short
notes in AJP by Uehara (V54, 184, 1986) and Lorenzo and Carrascal (V56,
565, 1988).  Ludwig might also be interested in a paper entitled "The
circular disk parallel plate capacitor" by Carlson and Illman which
appeared just a couple of years ago (V62, 1099, 1994). 

Clearly my formulation is just a different way of talking about the
coefficients of capacitance in the restricted case of two conductors.  (I
still kind of like the idea of "common mode capacitance"  in the simple
case of two conductors, though.  Oh well.) 

John
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