How do we know that any two points of an ideal wire must be equipotential whether or not there is a current flowing through it?
I fully understand that how the electric field in a conductor in electrostatic condition will be zero. My question is primarily for a conductor which is not an electrostatic condition.
In any circuit in which circuit elements like batteries, resistors etc. are connected by "ideal wires" we assume that any two points on the ideal wires are at the same potential. What is the justification behind this assumption?
The popular explanation is as follows:
Since from Microscopic form of Ohm's Law, we know that "E = ρ J", and for an ideal wire, the ρ (resistivity) tends to zero, so E (electric field) must tend to zero and if electric field inside the ideal wire is zero, so potential drop across idea wire must be zero.
The question which then comes is, why and how exactly the electric field inside an ideal wire becomes zero? Mathematically I agree that it turns out to be zero, but how do we understand this idea "Intuitively"?
I read the above post on why electric field inside a wire becomes zero. It explains the following reason:
In the steady state condition, there is no electric field inside a perfect conductor because the electrons have moved to cancel out any electric field. That is because electrons will move whenever there is an electric field.
Does it and will it always happen that electrons rearrange themselves in such a way that electric field inside the ideal wire will always become zero?
Is there a fundamental law which governs this idea that electric field inside an ideal wire should be zero? If yes, then what that is?
Is it just an inductive/recurring fact that it always becomes zero (like Sun rises from the east) that we assume this fact to be true? Or there is some fundamental reality which is governing this fact?