# Does a conductor E field include a tangential component?

• I

## Main Question or Discussion Point

Background: an ordinary wire supports an external radial electric field proportional to voltage, and an internal axial field equal to current times resistance per unit length. The present question is whether the internal axial field has an external counterpart. The original question that generated this inquiry was:

How does the electric field (therefore the electric force) in a wire remain parallel to the wire even if it is randomly curved (current still flows)?

In a discussion of this, the second question led to the first one. A Poynting vector interpretation of an external tangential component of the E field would indicate power flowing from the conductor into space, even for zero frequency (DC). This seems implausible, hence the question.

• Delta2

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Dale
Mentor
The surface of the wire has charges. The presence of the surface charges causes a discontinuity in the E field, allowing parallel E-fields inside and radial E-fields outside. See:

http://depa.fquim.unam.mx/amyd/archivero/El_flujo_de_energia_de_una_bateria_a_otros_elementos_de_un_circuito_20867.pdf for a quantitative discussion and:

https://www.tu-braunschweig.de/Medien-DB/ifdn-physik/ajp000782.pdf for a qualitative discussion.

A Poynting vector interpretation of an external tangential component of the E field would indicate power flowing from the conductor into space, even for zero frequency (DC). This seems implausible, hence the question.
You have made a mistake in your Poynting vector analysis. The power flows from space in to the conductor. See the first paper above.

• Delta2
Delta2
Homework Helper
Gold Member
The surface of the wire has charges. The presence of the surface charges causes a discontinuity in the E field, allowing parallel E-fields inside and radial E-fields outside. See:

http://depa.fquim.unam.mx/amyd/archivero/El_flujo_de_energia_de_una_bateria_a_otros_elementos_de_un_circuito_20867.pdf for a quantitative discussion and:

https://www.tu-braunschweig.de/Medien-DB/ifdn-physik/ajp000782.pdf for a qualitative discussion.

You have made a mistake in your Poynting vector analysis. The power flows from space in to the conductor. See the first paper above.
In the 2nd paper, Figures 7 and 9, shows clearly that the electric field is not perfectly normal to the surface of the conductors in a DC circuit. So there is a tangential component that survives outside of the conductor.

So the "DC situation" is different from the "pure electrostatic situation" in which the electric field in the surface of a conductor is always in the direction normal to the surface.

The 2nd paper is very good, a reference point for all the questions regarding the surface charges in DC and low frequency AC circuits.

Dale
Mentor
In the 2nd paper, Figures 7 and 9, shows clearly that the electric field is not perfectly normal to the surface of the conductors in a DC circuit. So there is a tangential component that survives outside of the conductor.
Yes, it is also shown in Figure 4 in the first paper. That non-normality of the E-field is also what makes the Poynting vector point slightly inwards towards the conductor in Figure 5 of the first paper.

So the "DC situation" is different from the "pure electrostatic situation" in which the electric field in the surface of a conductor is always in the direction normal to the surface.
Yes, definitely!

• Delta2
Baluncore
2019 Award
I find it difficult to discuss the electric and magnetic fields in the vicinity of a conductor without identifying the assumptions made with regard to symmetry and the boundary conditions that are implied by the presence of the return circuit.

Between two plane conductors, forming a return circuit, the flock or field of poynting vectors would gradually diverge, with a proportion entering the conductor surfaces as resistive losses progressively occur and the voltage difference between the plates falls towards the terminal load.

But the simplest model for discussion might be a circular section conductor over a flat ground plane or mirror. That will also model a two wire parallel transmission line, which makes an idealised two wire real circuit.

Dale
Mentor
I find it difficult to discuss the electric and magnetic fields in the vicinity of a conductor without identifying the assumptions made with regard to symmetry and the boundary conditions that are implied by the presence of the return circuit.
The first paper above used a coaxial cable type of geometry for the return path. The second paper simply used standard wires.

Baluncore
2019 Award
I believe the OP question was not satisfactorily answered earlier because the return circuit was not being considered. That changed when you linked to those two excellent papers, and the OP problem became tractable.

How does the electric field (therefore the electric force) in a wire remain parallel to the wire even if it is randomly curved (current still flows)?
In school, technicians are taught simply that electric energy travels with the current, through the wires. It is then quite a surprise to realised that the opposite is actually true.

The presence of a voltage and a current of electrons on the surface of the wandering wires, generates the electric and magnetic fields around the wires. That in turn orients the Poynting vector field that directs energy towards the load, through the insulation outside the conductors. Energy that follows Poynting vectors into the wires is lost as heat and so does not reach the load.

• Dale