# Microscopic electric fields in a conductor

issacnewton
Hello

I have just read first five chapters from Feynman's "Lectures on Physics Vol. 2"
on electromagnetism and couldn't find satisfactory answer to my question, so I am posting this question.

Its claimed that electric field inside a "perfect conductor" (something with unlimited supply of free electrons) is zero. Even in the presence of an externally applied E, the field
inside is zero. But we have atoms inside the conductor and electrons go around the nucleus
because of the electric field of the protons. So there is an electric field at a microscopic level.
So what do physics authors mean when they say that E= 0 inside a conductor ?

Thanks

Staff Emeritus
The electric field from the external source to the metal is zero, save for the skin depth.

Zz.

issacnewton
Zapprer

Yes, and even the excess charge appears only on the surface. But what about the
microscopic electric fields as I said. How can we make statements that "Electric field
is zero inside the conductor " ?There is some missing info here I guess

thanks

Staff Emeritus
Zapprer

Yes, and even the excess charge appears only on the surface. But what about the
microscopic electric fields as I said. How can we make statements that "Electric field
is zero inside the conductor " ?There is some missing info here I guess

thanks

You are misreading the CONTEXT of the statement!

Besides, ON AVERAGE (be it time or spatial), the NET E-field IS zero inside such a conductor if you consider the bulk property. That is what classical E&M does!

Zz.

issacnewton
ON AVERAGE, the fields may be zero in the metal crystal , but the fields can never be zero inside an atom. Right ? I understand that in the inter atomic space, fields probably average to zero ( time variations and spatial variations ) but we will need to have a field inside an atom.

Can you refer me to the mathematical treatment at the graduate level for this ? May be J.D.Jackson or Landau ... The mathematical proof (may be from Maxwell's equations)
that gives the average field to be zero

issacnewton
I found some interesting discussion on the microscopic fields in J.D. Jackson 3 ed
( Section 6.6- Derivations of the equations of macroscopic electromagnetism )
Jackson also gives further references for the development of macroscopic equations .
(page no . 282, 283)

A thought provoking discussion of the derivation of the macroscopic equations of electromagnetism, as well as of the thermodynamics of electric and magnetic systems, is given by Robinson

The derivation of the macroscopic Maxwell equations from a statistical-mechanical point of view has long been the subject of research for a school of Dutch physicists.Their
conclusions are contained in two comprehensive books,
de Groot
de Groot and Suttorp

The books are

Robinson F.N.H, Macroscopic Electromagnetism, Pergamon Press, Oxford (1973)

DeGroot S.R. , The Maxwell Equations , Studies in Statistical Mechanics, Vol IV ,North Holland, Amsterdam (1972)

DeGroot S.R. and L.G. Suttorp ,Foundations of electrodynamics, North Holland, Amsterdam (1972)