Is there any electromagnetic radiation associated with the electrons moving in the conductor? Is there any electromagnetic radiation associated with the electrons moving in the conductor (eg copper wire) if the current is constant (DC)?  From what I know, electrons don't move with steady speed but they "leap" from one position to the next and since the "leaping" involves acceleration and deceleration some kind of electromagnetic radiation should arise - true?
 A: I think this is a good question because on one level you're asking about a microscopic theory of conduction, and on another, you're wondering if the microscopic phenomena could lead to a counterintuitive macroscopic effect. I would preface this by noting that there are many theories of conductivity which are appropriate for various physical systems, including the hopping conduction you mentioned. But the one most relevant for your copper wire is probably the Drude free-electron model, which posits that electrons are moving in all directions at any given time, constantly bumping into things which randomize their momentum. The characteristic scattering time for metals is on the order of 10 femtoseconds. This means that the average electron undergoes an acceleration every 10^-14 seconds, even  without an applied field! So where is all the radiation? Well one way to (hand-wavingly) think about it is that there is indeed radiation at the microscopic level, but at any given time for every electron scattering left there is a corresponding electron scattering right, which leads to out-of-phase fields that ultimately all cancel.
