Alternating current in a perfect conductor

[Txema]

TL;DR Summary

What force accelerates and decelerates the free charges in an alternating current, flowing in a perfect conductor, so that the current increases and decreases cyclically?

Premise: the electric field inside a perfect conductor is zero.
The boundary conditions indicate that the tangential component is continuous, so the tangential component at the surface of the conductor is also zero. In conclusion, the electric field is perpendicular at the surface of a perfect conductor and null inside it.
In these circumstances: what force accelerates and decelerates the free charges in an alternating current, flowing in a perfect conductor, so that the current increases and decreases cyclically.?

 

[Baluncore]

The alternating electric field between your hypothetical perfect conductor, and the perfect (return circuit) conductor, causes a wave of electric field, that propagates along the surfaces of the two conductors. The capacitance between the circuit conductors is charged, making a surface current flow, which causes a magnetic field. Both the electric and magnetic fields propagate in the space between the perfect conductors, guided by the surface currents in the circuit.

 

[Txema]

Thank you very much for your answer. I have a couple of questions.
1) Do the electric field lines, traveling in the dielectric, have a certain curvature so that on the surface of the conductors there is a longitudinal component of this field?
2) The capacitance in the conductors corresponds to non-neutralized surface charge (separated charge). Is the current on the surface of the conductor formed by such charge or is it by the neutralized free charge of the conductor?

 

[Baluncore]

1. Everything in EM has a "certain curvature".
For a hypothetical "perfect conductor", the electric field lines remain exactly perpendicular to the surface of the conductors.
Energy propagates perpendicularly to the electric and the magnetic fields. If the conductor was not perfect, it would be heated by some energy entering through the resistive surface.

2. The net charge balance is neutral. Where the free electrons sink slightly into the surface, the voltage is positive. Where free electrons rise slightly out of the surface, the voltage is negative.
As a voltage wave propagates along a conductive surface, a current appears to flow on that surface. The current on the surface, is a ripple in the surface exposure of the free electron charge, caused by the passage of the external electric field. That surface current reflects the incident magnetic field, preventing it from entering a perfectly conductive surface.
The electric and magnetic fields are intimately coupled. Propagation of the two orthogonal fields, is guided in the space between the perfectly conductive (mirror-like) surfaces, at close to the speed of light.

 

[Txema]

Thank you very much for your answer. I appreciate that the explanation includes both the fields and V-I.

The current on the surface, is a ripple in the surface exposure of the free electron charge, caused by the passage of the external electric field.

Does this mean that an electric field line (to simplify) advances through the dielectric "drawing", with its perpendicular force, free charges from the conductor to the surface and then "releases" them resulting in a charge wave which is equivalent to a current? And does this imply that the charges do not move in the longitudinal direction?

 

[tech99]

Thank you very much for your answer. I appreciate that the explanation includes both the fields and V-I.

Does this mean that an electric field line (to simplify) advances through the dielectric "drawing", with its perpendicular force, free charges from the conductor to the surface and then "releases" them resulting in a charge wave which is equivalent to a current? And does this imply that the charges do not move in the longitudinal direction?

For the AC case consider the conductor as a transmission line. At frequencies below a cut off threshold it can be considered as having discrete series inductors and discrete shunt capacitors. When a wave propagates along the line, there is the ordinary TEM mode, which you describe, but also a longitudinal mode. In this latter mode, an electric accelerating field exists, acting along the wire. You may notice that a voltage arises across each inductor, which is the same thing - this is the longitudinal component of the electric field. There is also a magnetic field which is wrapped around the wire.

 

[Txema]

Thank you very much for your answer.
Yes, I consider the ac circuit as a transmission line. The equivalent circuit to the line with inductors and capacitors is useful to obtain (telegrapher's) equations of V and I as a function of the line parameters, i.e. to forget about fields and charges, but my interest is a qualitative explanation of the essence of the line's working, based on the fields and their sources: charges and currents, identifying, if possible, causes and effects. For some reason, unknown to me, this is not in the books.

but also a longitudinal mode. In this latter mode, an electric accelerating field exists, acting along the wire.

So if possible, I would appreciate clarification on the longitudinal field and what produces it.

 

[Baluncore]

So if possible, I would appreciate clarification on the longitudinal field and what produces it.

AC in a lossless line, what longitudinal field can there be ?

Waves propagate along the perfect conductor, the fields are perpendicular to the axis of the conductor. Only the direction of wave propagation, the Poynting vector, is parallel to the axis of a conductor.

Imagine a single electric field line. It is stretched between the two conductors, with one end on each conductor. The ends of the line are perpendicular to the conductor surface. The field line propagates away from the source, guided by and following the conductors, which lead to the load.

... , but my interest is a qualitative explanation of the essence of the line's working, based on the fields and their sources: charges and currents, identifying, if possible, causes and effects.

Although you can understand the coupling between the fields and charges by following in one direction, there is really no simple cause and effect. Everything is effectively locked intimately, in all directions.

 

[tech99]

For alternating current, the inductance of the wire presents a reactance, across which the flow of current induces a voltage, which acts along the wire.

 

[DaveE]

Charges do move longitudinally on the surface of the wire as the wave passes, just a tiny bit. This means there must be an associated field to create that force, also tiny and quickly canceled by the repositioned charges. As @Baluncore said, it's all coupled together and not really separable as cause and effect. It is the perpendicular e-field that is dominant, so people say it's the only one. One big, one infinitesimally small.

 

[Baluncore]

Imagine a ring of magnetic field around a perfect conductor, on the surface, propagating perpendicular to the axis. That magnetic field line induces a perpendicular (longitudinal) current in the surface of the conductor. The axial surface current causes another magnetic field, opposite to the incident field, that cancels into the conductor, but outwards it appears to be a reflection. That is how the rings of magnetic field are guided to slide along the conductors.

At any instant, the voltage varies along the perfect conductor, but that is due to the gradient of the wave of electric field lines, stretched between the conductors, propagating along the surface. If the conductor was perfect, it would short circuit the ends of any electric field lines, travelling in either direction, unless they were propagating at the speed of light in the surface dielectric insulation.

 

[Txema]

DaveE, Baluncore, tech99, thank you very much for your help. I incorporate the suggestions into my understanding process.

Although you can understand the coupling between the fields and charges by following in one direction, there is really no simple cause and effect. Everything is effectively locked intimately, in all directions.

Ok, I understand that some phenomena present simultaneous manifestations without being able to establish cause-effect relationships between them.

Charges do move longitudinally on the surface of the wire as the wave passes, just a tiny bit. This means there must be an associated field to create that force, also tiny and quickly canceled by the repositioned charges. As @Baluncore said, it's all coupled together and not really separable as cause and effect. It is the perpendicular e-field that is dominant, so people say it's the only one. One big, one infinitesimally small.

If I understand correctly, this is something like a quasi-static equilibrium of electric fields.
The perpendicular e-field waves in the dielectric alter the configuration of the surface charge at each point so that a longitudinal field appears which is cancelled by the immediate reconfiguration of the surface charge itself, and this is repeated continuously. The result is that although the field can be considered null, the charges are momentarily accelerated, and the whole set forms a current on the surface. (Please correct me if I am wrong).
This explanation inspires me a lot to continue thinking and understanding AC circuits and T.L. Thanks again.