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Let’s consider a perfect electric conductor which is connecting the terminals of an ideal voltage source (it is a short circuit in practice). What happens from an electromagnetic point of view?

We know that for a perfect electric conductor:

1) The electric field inside the material is 0

2) The electric field on its surface is purely orthogonal

If I understood correctly, these properties are always true, also in absence of equilibrium, since the conductor is ideal.

The property 2) implies that the voltage across the conductor's surface is 0. But there is a voltage source applied on it: which is the solution?

Moreover, voltage source means electric field between the two terminals: is this electric field inside the conductor or on its surface?

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Remember that ideal voltage sources and perfect conductors are idealizations. They are simplifications that approximate the behavior of real devices. Both real voltage sources and real conductors deviate from ideal behavior at high currents.

So, with that in mind, from a purely theoretical perspective you have set up a circuit that is represented by a set of equations with no solution. Specifically, if $V$ is the voltage across both elements and $V_0$ is the voltage of the source then the equations are $V=V_0$ and $V=0$. This clearly has no solution.

Now, from a practical standpoint we can consider alternative, more realistic, models of the components. For example, we could consider the voltage source to be ideal, and the wire to have 0 resistance but nonzero inductance. This would lead to a standard inductor circuit; it is a more realistic model of the wire since even a superconductor necessarily has inductance. As another example you could consider the voltage source to have an internal impedance, which would determine the short circuit current.

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  • $\begingroup$ The model where the source has zero impedance and the wire has inductance may be mathematically possible but the current will increase over time without bounds which is not at all realistic. The model where the wire has zero impedance and the load has an internal impedance will give a better approximation to something that can actually be realized. Some voltage sources are designed to withstand short-circuit and for that sort of case this would actually be a very good approximation. $\endgroup$ – Rodney Nov 2 at 11:55
  • $\begingroup$ Completely agree! Circuit elements need to be understood as easy approximations that are only valid within a certain range. That range can easily be exceeded by poorly designed circuits. $\endgroup$ – Dale Nov 2 at 12:14

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