Re: [Phys-l] defn of capacitance

[John Denker <jsd@av8n.com>]

On 02/06/2008 02:44 PM, Carl Mungan wrote:

> My initial stab at a definition was the following: ....
>  Q is the absolute value of the average difference in charges of 
> the two plates (ie. half of the difference in charges on the two 
> plates).

You're not going to be very happy with that definition.
For starters, the "absolute value" is going to mess
things up.  For capacitors, V versus Q is linear. 
Absolute value is not linear.

.....

> Please fix my definition of C for the case of two isolated conductors 
> in vacuum carrying charges which are not necessarily equal and 
> opposite.

It turns out that capacitance is, in general, a _matrix_.

In some situations it reduces to a 1x1 matrix, so it looks
like a scalar ... but this ain't one of those situations.

The relevant equation is
    Qi = Cij Vj

This equation and the underlying physics is discussed at
  http://www.av8n.com/physics/laplace.html#q_of_v