Is current carrying wire have any electric field?
Yes, there is usually an implicitly applied electric field in the wire itself that gives rise to the current. Usually this electric field is ignored for the purposes of a simple static problem. However, if we have an alternating current, then this current is excited by an electromagnetic wave that propagates between the wire and the return/ground. This electromagnetic wave permeates the space around the wire. By convention, we do not regard the fields to penetrate the wire. A perfect conductor restricts all currents to the surface of the wire and prevents any fields from being present inside the wire. A realistic conductor can still be reasonably estimated to have this property as well.
author = "Assis, A. K. T. and Rodrigues, W. A. and Mania, A. J.",
title = "The electric field outside a stationary resistive wire carrying a constant current",
journal = "Foundations of Physics",
year = 1999,
volume = 29,
number = 5,
pages = "729-753",
(I am not an author)
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