Re: Kirchhoff's laws and conservation laws

[John Denker <jsd@AV8N.COM>]

Quoting Dan Crowe <dcrowe@SOTC.ORG>:

> I have always seen Kirchhoff's voltage law derived from
> conservation of energy, not flux.  The potential energy
> of a charge is well defined at each point in the circuit.
> As the charge circulates around the circuit, it must
> return to the same potential energy.  Is there a flaw
> in the derivation from conservation of energy?

Well, since the law of conservation is always valid, and
K's loop law is not always valid, the correspondence
cannot be completely simple.

It is unsafe to start the analysis with "the potential
energy of the electron" since the energy of the electron
might not be a potential.  Non-potential voltages *can*
exist.  Kirchhoff's "laws" describe the case where they
don't happen to exist, which is why I write the word
"laws" in scare quotes.

If you want to know that the voltage is a potential, then
you need to know something about the flux.

Bottom line:  I think I'm pretty safe thinking in terms
of flux.  The equation
  voltage = flux dot
is a Maxwell equation.  Hard to go wrong with that.

(Here "dot" means time derivative.)

Once you are sure of the voltage, any statements about
voltage can be translated into statements about energy.