Boundary condition between conductor and free-space

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Discussion Overview

The discussion revolves around the boundary conditions between an imperfect conductor and free space, particularly focusing on the behavior of electric fields inside and outside the conductor when current flows. The scope includes theoretical considerations of electric fields, boundary conditions, and the nature of current density in conductors.

Discussion Character

  • Debate/contested
  • Technical explanation

Main Points Raised

  • Some participants assert that an electric field is established inside an imperfect conductor along the direction of current flow, raising questions about the continuity of the tangential electric field at the boundary.
  • One participant proposes that there must be an electric charge on the wire, implying the existence of an electric field outside the wire.
  • Another participant questions the nature of the electric field outside the wire, suggesting it is perpendicular to the wire and expressing confusion about the existence of a tangential electric field outside.
  • A participant reiterates the initial concern about the boundary condition and suggests that there will indeed be an electric field outside the wire, proposing a relationship based on voltage drop and distance.
  • One participant discusses the current density in conductors, noting that the electric field is parallel to the current density and suggesting that outside the conductor, the field is oriented perpendicular to the conductor tangent, with no tangential field existing.
  • A hypothetical scenario is presented involving a high resistance wire and a high voltage source, suggesting that a tangential electric field would exist in this case, prompting consideration of scaling down to lower resistances and voltages.

Areas of Agreement / Disagreement

Participants express differing views on the existence and orientation of electric fields both inside and outside the conductor, indicating that multiple competing perspectives remain unresolved.

Contextual Notes

There are limitations regarding assumptions about the nature of the electric field in different materials and the specific conditions under which these fields are analyzed, which remain unresolved in the discussion.

yykcw
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For an imperfect conductor, when there is current, an electric field is set up inside the wire along the direction of the current flow, and is parallel to the wire.
If this is true, then what I don't understand is
boundary condition tells me the tangential E-field is always continuous, if there is no E-field outside the wire, how come there will be E-field inside the wire?
 
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There must be some electric charge on the wire, and some electric field outside the wire.
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But isn't that those E-field outside is perpendicular to the wire?
I don't understand why tangential E-field will exist outside.
 
yykcw said:
For an imperfect conductor, when there is current, an electric field is set up inside the wire along the direction of the current flow, and is parallel to the wire.
If this is true, then what I don't understand is
boundary condition tells me the tangential E-field is always continuous, if there is no E-field outside the wire, how come there will be E-field inside the wire?

I think this is your problem. Imo, there will be an E field outside the wire which, for a straight wire, between two large flat plates (the easiest example I can think of), will bt ΔV/x where ∇V is the voltage drop (imperfect wire) and x is the length.
 
The current density-J- in conductor includes only “free current density” since the polarization current is negligible then E=ρJ .That means in a conductor the electric field [intensity] E is parallel with current density –directed along the conductor.
Outside-in a dielectric as air or insulation-it is no free current then the field is oriented perpendicular to the conductor tangent. However, no tangent field exists- in my opinion-only an equipotential line follows the conductor outside surface.:shy:
 
Perhaps consider an extreme case...very high resistance wire (say 1Meg ohm) laying straight with high voltage source driving the ends against each other (say 1Meg V). You may agree that there will be a tangential E-field in the direction of the wire right?

Now just scale things down to uohms and volts.
 

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