Re: Confused by a derivation.

["John S. Denker" <jsd@MONMOUTH.COM>]

"RAUBER, JOEL" wrote:
...
> How do you prove the E field is zero inside an ideal conducting material?

For electrodynamics, I don't.
For electrostatics, see below.

> I do it with Gauss' Law (and the electro-static equilibrium assumption).

I do it with no Gauss's Law at all:
Proof by contradiction;  hypothesize field in equilibrium.
  Conductor ==> mobile charges in interior.
  Field applied to mobile charge ==> not equilibrium.

> This tells me that in some fashion Gauss' Law is sufficient for deducing
> zero field in the conductor and hence the rest of the arguement.

Not quite.

You need at least:
 -- definition of conductor
    (You can't prove anything about conductors without
     invoking the definition of conductor!)
 -- definition of "static" as in "electrostatic"
 -- Coulomb force law.
    (It doesn't help to know the fields if you
     don't know how charges respond thereto.)
 -- Gauss's law, or some other way to work out the fields.