# Boundary condition between conductor and free-space

1. May 1, 2014

### yykcw

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?

2. May 1, 2014

### maajdl

There must be some electric charge on the wire, and some electric field outside the wire.

3. May 1, 2014

### yykcw

But isn't that those E-field outside is perpendicular to the wire?
I don't understand why tangential E-field will exist outside.

4. May 1, 2014

### sophiecentaur

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.

5. May 1, 2014

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:

6. May 1, 2014

### the_emi_guy

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.