# How do electrons lose their kinetic energy in ideal wire?

Electrons keep accelerating due to the electric field (produced by the battery) along the circuit. So electrons gain kinetic energy, hence their drift velocity changes. But this is not the case: electrons flow in average with constant drift speed so they must lose kinetic energy. So how do electrons lose their kinetic energy in ideal wire?

Since there is no resistance in ideal wire, there would be no collisions. So how do electrons lose their kinetic energy?

• "Electrons keep accelerating due to the electric field (produced by the battery)" - There is no electric field within an ideal wire. See, for example, Perfect conductor: "an idealized material exhibiting infinite electrical conductivity or, equivalently, zero resistivity (cf. perfect dielectric)." Jul 16 '19 at 10:24
• This is not the case, no, because no wire is ideal. In a theoretically ideal wire, charges would accelerate to an infinitely high speed. In a non-ideal but still low-resistance wire, you will also see acceleration happening to a very high speed, and most possibly this will cause the wire to melt at some point. Therefor the smallest viable circuit contains a resistor as well, in order to control and limit the current. Jul 16 '19 at 10:34
• @MohammadAlshareef The premise is wrong in this part of your question: "So how electrons lose their kinetic energy in ideal wire." The answer is that they don't. Charges only lose kinetic energy in non-ideal wires. Or in components. In a typical circuit we can usually assume that the wires are ideal, so energy only is lost in components. This makes it much easier to work with, and it is usually a very good assumption, because components usually cost much more energy loss, so any tiny loss in the wires is negligible. Jul 16 '19 at 10:48
• @MohammadAlshareef No, the current can be constant in an ideal wire, if there is a resistor further up along the wire. Then it is the resistor, which limits and slows down the current - it is in the resistor that kinetic energy is lost as heat. Surely, if the charges are slowed down at a resistor, they further incoming charges will "queue up" in front it. they will have to slow down to the same lower and constant speed. This happens at an instant, and after this "queuing up", all charges move at the same drift speed. But kinetic energy is still only lost in the resistor; not in the wire. Jul 16 '19 at 11:00
• Mohammad, the current density in a conductor is given by $\vec{J} =\sigma\vec{E}$ where $\sigma$ is the conductivity. Note that as $\sigma\rightarrow\infty$, the electric field goes to zero for finite current density, i.e., in the limit of infinite conductivity (ideal wire), there can be non-zero current density with zero electric field. Also note that in the idealization to a perfect conductor, the mobile charge in the conductor responds instantaneously to any external electric field so that the electric field inside is zero. Yes, this is non-physical thus the term ideal wire. Jul 16 '19 at 11:49

Well, they don't.
An ideal wire would have no resistance so no charge carrier electron collisions with the wire lattice electrons. This would mean that no energy is lost, similar to assuming no friction on an ideal surface.

It could mean that electrons have the speed of light as drift speed. This idea probably doesn't sound right! That's because the wires are ideal, not real. In reality, they would lose kinetic energy.

As an analogy, if you rolled a ball on an ideal surface without friction, it would keep going in theory. But realistically, this real surface would have friction and the ball would lose kinetic energy.

We make these ideal assumptions to simplify problems, not to represent reality.

1. zero electrical resistance, a steady current will flow without losing energy

2. requires a constant magnetic flux, inside the perfect conductor, the magnetic flux must be constant with time. Any external field applied will have no effect to the internal field.

A perfect conductor or perfect electric conductor (PEC) is an idealized material exhibiting infinite electrical conductivity or, equivalently, zero resistivity (cf. perfect dielectric). While perfect electrical conductors do not exist in nature, the concept is a useful model when electrical resistance is negligible compared to other effects. One example is ideal magnetohydrodynamics, the study of perfectly conductive fluids.

As you see in the comments, perfect conductors do not exist.

The answer is that electrons will not lose their kinetic energy in a perfect conductor. Their drift velocity will be the speed of light.

Since the perfect conductor needs a constant magnetic flux, that will keep the electrons move infinitely at speed c.

• Does that mean that speed of light is the maximum speed that electrons can reach ? Jul 19 '19 at 10:34
• @MohammadAlshareef correct, that is because they are inside a perfect conductor. It's like vacuum for photons. Jul 19 '19 at 11:17