# Electric field due to current carrying wire

1. Sep 7, 2013

### Aziza

What is the electric field due to a current carrying wire? In a Griffiths EM problem, he treats the E field outside a current-carrying wire as if it were due to a static charge distribution. Is this a valid approximation? Upon google-searching i get very vague/contradicting answers, so any help is appreciated!

2. Sep 8, 2013

### GregoryGr

Outside the wire, I think there should be no E field, seeing that the net charge is 0 (?).

3. Sep 8, 2013

### Astrum

That's only if the wire has enough positive charges to make it a charge neutral wire.

To the OP: Are you referring to the magnetic field due to a current, or the electric field from a non-neutral wire? As far as I remember, there were no examples in Griffiths where he talked about E-Field outside of a current-carrying wire.

In electrostatics, you often will encounter something like "a wire with charge density $\lambda$.

4. Sep 8, 2013

### UltrafastPED

Yes, Griffiths looks at the charge distribution in a current carrying wire as static: this is because the electrons even though the electrons have quite large velocities (easily calculated via kinetic theory), the motion is essentially random except for the drift velocity due to the impressed field of the battery or generator.

As a result the field is essentially zero outside the wire for DC currents; for AC the situation changes dramatically as the AC frequency increases from a few Hz to kHz to MHz to GHz - though Griffiths text does not get into transmission line theory in any depth.

5. Sep 8, 2013

### vanhees71

This is a misconception pretty common. It comes from the fact that many textbooks do not discuss the electric field around the current conducting wire. There is a detailed treatment of a current conducting coax cable in

A. Sommerfeld, Lectures on Theoretical Physics, Vol. III (Electrodynamics), Academic Press (1952)

You find this also on my German FAQ page (including a relativistic treatment too).

What's not discussed there, is the surface charge on the wire, but that's implicit in the jump of the radial component of the electric field:

http://theory.gsi.de/~vanhees/faq/coax/coax.html

The toroidal conductor is treated in

PHYSICAL REVIEW E 68, 046611 (2003)
Electric potential for a resistive toroidal conductor carrying a steady azimuthal current
J. A. Hernandes and A. K. T. Assis
DOI: 10.1103/PhysRevE.68.046611

6. Sep 9, 2013

### mikeph

I don't speak German, could someone outline why the E-field would be nonzero? Surely the AC surface charge won't have any effect, take any Gauss' law cylindrical volume and however the charge is distributed radially within the cable, it'll still be zero net charge within the volume unless your cable is itself charged (i.e. someone added some extra electrons so that they outnumber the Cu protons).