Re: non-potential voltage

["Eugene P. Mosca" <mosca@NADN.NAVY.MIL>]

John Denker wrote:

<< Kirchhoff's laws are tantamount to making two simplifying
approximations:
   a) A capacitor is a two-terminal black box, and there are no
significant
capacitances outside of capacitors;
   b) An inductor is a two-terminal black box, and there are no
significant
inductances outside of inductors.

As soon as you make those approximations, you are _assuming_ that at
every  point (excluding inaccessible points inside the black boxes), the

electric field has no significant curl. >>

Good point.  I agree Kirchhoff's laws ignore stray capacitances and
inductances.  Textbooks and teachers should emphatically state these
limitations on Kirchhoff's laws, and often this is not done.  It seems
to me that treating inductors and capacitors as black boxes is not an
assumption required to establish Kirchhoff's laws.

In my earlier message I stated:

> Emf is
> determined only by the rotational part whereas potential difference is
> determined only by the irrotational part.

And John asked:

<< I've never heard that distinction made before -- and it seems
unhelpful.  Can you cite a reference and/or argue why such a distinction
is
useful? >>

I am not sure I understand the question.  As I remember Romer's paper on
this topic, he avoids discussing the potential in regions where both
kinds of electric fields coexist.  It seems to me this is constraint is
not helpful and not necessary.  I would like to cite a reference on why
it is useful to use the potential field in regions, but my paper on this
topic was rejected (by Romer).  It is useful because it avoids treating
circuit elements as black boxes.

I said:

>                  V = E - Ir = -LdI/dt - Ir.

where V is the potential difference across the inductor.

And John commented.

<< I've never before seen an expression of that form -- and it seems
unhelpful.  Can you cite a reference and/or argue why distinguishing E
(EMF) from V (voltage) is useful? >>

I am surprised you have not seen this form before.  Using Kirchhoff's
rules for an inductor is common to express the potential drop across an
inductor as LdI/dt + Ir.

Gene Mosca