Is the surface of a Perfect Electric Conductor Equipotential in any Condition?

Question

It is known that the surface of a PEC (Perfect Electric Conductor) is equipotential. This is true, in theory, in any situation (equilibrium or not), since the conductor is perfect and so the electric field on its surface is always orthogonal to it, and this means that the electric potential is the same on its surface.

Now let's consider for instance a transmission line of length L, which starts from position z = 0 and arrives at z = L. This line is connected to an AC Voltage Source. Now let's consider one of the two conductors: obviously the voltage between them is function of time (since the source is AC), but what I want to focus on is the fact that it is function of the position z on the conductor (precisely, it has a waveform behaviour).

This dependence on position seems to be in contrast with the fact that the potential on a PEC is constant on its surface.

Answer 1

An equipotential surface is always perpendicular to the electric field line. The surface of a (perfect) charged conductor works as an equipotential surface and it satisfies the above condition,i.e, the electric field lines are perpendicular to the surface of the charged conductor. BUT, once you apply a voltage or potential difference across the conductor (the AC source in your question), it no longer applies because now the electric field lines are affected by the electric field due to the voltage source and they are no longer perpendicular to the surface of the conductor. In summary, the surface of the conductor is NO LONGER an equipotential surface due to the applied voltage across the conductor. For more information, follow this link https://openpress.usask.ca/physics155/chapter/3-5-equipotential-surfaces-and-conductors/