🚀 go-pugleaf

  James McLean (jgm@LASSP.CORNELL.EDU) wrote:

> * the capacitance of parallel plates equation C=e*A/d requires the
>   idealization that fringe fields are ~= 0

This is a good example of an idealization (approximation) which does not
bother me because a plate capacitor can in principle be constructed with
a fringe effect as small as practically desirable. (Actually, the plates
do not have to be parallel, as in the case of a Leyden jar. Commercial C are
often "parallel foils of metals separated by dielectric material" rolled
into a cylinder.) The parallel plate case was chosen for the simplicity of
derivation. It is not at all hard to show that Q1/Q2=(e1*r1)/(e2*r2) is
valid for spherical and cylindrical capacitors, or for any two irregular
chunks of metal separated by a uniform dielectric material. But why should
we be distracted by mathematical nuances?

>  Saying what happens with 2 capacitors in series using the "equal charges
>  theory" requires the idealization that e1*r1=e2*r2, which is often
>  justified by assuming r1 & r2 to be infinite.

e1*r1=e2*r2 is not an idealization, it is a possible coincidence because r1
and r2 are ALWAYS FINITE. Suppose that e1=e2 and that r2=10*r1. Then we say
that e2*r2=10*e1*r1. Multiply r1 and r2 by 100, you still have e2*r2=10*e1*r1.
The situation does not change when r1 and r2 are very large. In the context
of our problem capacitors do not become "more ideal" when their leakage
resistance become larger. Yes, I see, you are saying this below.
>
>   I certainly agree with you that in the last case the "idealization" is
>   rather too restrictive to be useful for evaluating real-world circuits
>   directly.
>   First off, there can easily be confusion because even though having
>   r1=r2=infinity is sufficient, having r1 & r2 very large (~= infinity)
>   is not sufficient to satisfy the idealization.  (As you point out.)
>   So justification for the idealization can be misleading.
>   Second, there's no particular reason to expect a real-world system to
>   satisfy e1*r1=e2*r2.  So the idealization itself isn't very useful.
>   So in all this I agree that for the purpose of evaluating real-world
>   circuits, the "equal charges theory" is not directly applicable.

>   But an awful lot of what you do with electrostatics applied to real world
>   circuits is modeling real components as combinations of ideal components.

I strongly agree with the last sentence. I will try to address some nuances
in a separate message, hopefully after we hear from other people who may
supply fresh data.


                 Ludwik Kowalski    kowalski@apollo.montclair.edu
Ym g# X