Maxwell's equations & Conductors

Click For Summary

Discussion Overview

The discussion revolves around the behavior of electric fields within conductors, particularly in relation to Maxwell's equations and the implications of conductivity. Participants explore theoretical aspects, idealizations, and specific scenarios involving conductors, including the distinction between solid and hollow regions within conductive materials.

Discussion Character

  • Exploratory
  • Technical explanation
  • Conceptual clarification
  • Debate/contested

Main Points Raised

  • Some participants question whether the absence of an electric field inside a conductor is purely experimental or can be derived from Maxwell's equations.
  • One participant suggests that if there is an electric field in a region with mobile charge carriers, it would lead to a current, implying that the electric field must be canceled or that charge carriers would be depleted over time.
  • Another participant notes that the zero electric field is an idealization applicable to perfect conductors, while in ordinary metals, a small electric field can exist according to Ohm's Law.
  • There is a discussion about the meaning of "inside" a conductor, particularly in the context of hollow versus solid regions, with participants clarifying their interpretations.
  • Some participants assert that, for perfect conductors, the electric field in the solid region would always be zero, while acknowledging that this is an idealization.

Areas of Agreement / Disagreement

Participants express differing views on the implications of electric fields in conductors, particularly regarding the definitions of "inside" and the conditions under which electric fields may exist. There is no consensus on the derivation of the absence of electric fields from Maxwell's equations, and the discussion remains unresolved regarding the nuances of these concepts.

Contextual Notes

Participants highlight the limitations of idealizations in classical physics, particularly in the context of perfect versus ordinary conductors. The discussion also reflects on the dependence of conclusions on specific definitions and assumptions regarding the regions within conductors.

Swapnil
Messages
459
Reaction score
6
Is the fact that there could be no E-field inside a conductor purely experimental? I don't see any way to apply Maxwell's equations to prove this fact.
 
Physics news on Phys.org
If there is an E field in a region with mobile charge carriers then there will be a current. So after all currents have died away, either the E field must be canceled or the medium will have run out of charge carriers. Does that help?
 
Zero E field is an idealization that holds for perfect conductivity where exactly enough charges can move to the surface to screen out an ambient field. This is actually seen in superconductors, although related phenomena like the Meissner effect require quantum mechanics to explain. For ordinary metals of finite conductivity, a small DC field can exist inside according to Ohm's Law
[tex]\vec{J}=\sigma\vec{E}[/tex]

Time varying fields, on the other hand, are screened by circulating eddy currents, and penetrate a small distance characterized by the skin depth. This is covered under discussions of wave propagation in conducting media, in upper class E&M books like Schwartz or Reitz and Milford. Here's a link that contains the derivations in sections 6.19-6.20
"www.sp.phy.cam.ac.uk/teaching/em/waves.pdf"[/URL]
 
Last edited by a moderator:
Dick said:
If there is an E field in a region with mobile charge carriers then there will be a current. So after all currents have died away, either the E field must be canceled or the medium will have run out of charge carriers. Does that help?
Yeah, this makes sense. Eventhough in order to prove that there is no E-field inside the conductor we are assuming that there is no current inside the conductor, the assumption of there being no current is more pleasing.

BTW, whenever we say "inside" a conductor (in the context of there being no E-field), do we always refer to the region where the conductor is solid?
 
If you mean inside a void in a conductor - sure, E can be non-zero in there.
 
Dick said:
If you mean inside a void in a conductor - sure, E can be non-zero in there.
No, I meant to say that in general when we say "There is no E-field inside a conductor," what does "inside" actually mean?

For example, consider spherical conductor shell. It hass two regions -- the region between the inner and outer surface of the conductor which is solid and the region between the center of the conductor and the inner surface which hollow. Which region would you call the "inside" of the conductor?
 
Last edited:
I would call 'inside the conductor' inside of the conducting shell.
 
Dick said:
I would call 'inside the conductor' inside of the conducting shell.

I am not sure which region you are referring to... the hollow region or the solid region?
 
  • #10
The solid region - where the mobile charges are.
 
  • #11
So, in general, the E-field in the solid region of a conductor would always be zero (for perfect conductors of course), right?
 
  • #12
Swapnil said:
So, in general, the E-field in the solid region of a conductor would always be zero (for perfect conductors of course), right?

Anyone? ...
 
  • #13
Swapnil said:
So, in general, the E-field in the solid region of a conductor would always be zero (for perfect conductors of course), right?

Yes, it would always be zero. Just keep in mind that this, like much of classical physics, is an idealization.
 

Similar threads

Graduate How to define ##\nabla \cdot D ## at the interface between dielectrics
  • · Replies 4 ·
Replies
4
Views
2K
Undergrad Can the Last Maxwell's Equation Explain Polarization of a Wire's Insulator?
  • · Replies 3 ·
Replies
3
Views
2K
Graduate Voltage and current waves in a transmission line
  • · Replies 4 ·
Replies
4
Views
3K
Undergrad Are Maxwell's equations linearly dependent?
  • · Replies 13 ·
Replies
13
Views
2K
Graduate Relationship between magnetic potential and current density in Maxwell
  • · Replies 2 ·
Replies
2
Views
2K
Graduate A question about current density in finite element analysis
  • · Replies 2 ·
Replies
2
Views
2K
Undergrad Do electron density waves accompany EM waves in coaxial cables?
  • · Replies 5 ·
Replies
5
Views
1K
High School Electric Fields inside Conductors & Gauss' Law
  • · Replies 7 ·
Replies
7
Views
1K
Undergrad Magnetic field inside a capacitor
  • · Replies 16 ·
Replies
16
Views
3K
Graduate Maxwell equation at the surface of a conductor - paradox?
  • · Replies 23 ·
Replies
23
Views
3K