# Electric field due to current carrying wire

• Aziza
In summary, the conversation discusses the electric field due to a current-carrying wire, specifically in the context of a Griffiths EM problem. The question arises if treating the field outside the wire as a static charge distribution is a valid approximation. Some sources give vague or contradictory answers, but it is clarified that for DC currents, the field outside the wire is essentially zero. However, for AC currents, the situation changes as the frequency increases. The conversation also mentions resources that discuss the electric field around current conducting wires, such as a treatment in a book by Sommerfeld and a paper by Hernandes and Assis. There is also a reference to a German FAQ page that discusses the toroidal conductor and the effects of surface charge on the wire

#### 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!

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

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

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##.

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.

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

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).

## 1. What is an electric field?

An electric field is a region of space around a charged object where another charged object experiences a force. It is a fundamental concept in physics that helps us understand the behavior of electrically charged particles.

## 2. How is an electric field created by a current carrying wire?

An electric field is created by a current carrying wire due to the movement of charged particles (electrons) within the wire. As the electrons move, they create a flow of electric charge, which produces an electric field in the surrounding space.

## 3. What factors affect the strength of the electric field around a current carrying wire?

The strength of the electric field around a current carrying wire depends on the amount of current flowing through the wire, the distance from the wire, and the medium in which the wire is placed (air, water, etc.). The strength of the electric field also decreases with distance from the wire.

## 4. How is the direction of the electric field around a current carrying wire determined?

The direction of the electric field around a current carrying wire is determined by the direction of the current flow. The electric field lines point in the direction that a positive test charge would move if placed in the field. For a wire with a current flowing to the right, the electric field lines would point clockwise around the wire.

## 5. Can the electric field around a current carrying wire be manipulated?

Yes, the electric field around a current carrying wire can be manipulated by changing the distance from the wire or by altering the amount of current flowing through the wire. This can be useful in various applications, such as in the design of electrical circuits or in electromagnets.