# Do surface currents (in EM scattering) really exist?

When an EM wave impinges on a target, it generates surface currents on that target, and these currents radiate the scattered fields.

However, this approach, namely finding the surface currents and calculating the fields, is just a mathematical construction to make the problem easier to solve. It is either the induction equivalence, or the physical equivalence principle (see Advanced Engineering Electromagnetics, by Balanis, Sections 7.9-7.12). In other words, to make the problem easier to solve, the object is replaced by surface currents so that the background constitutive parameters (epsilon,mu) remain the same.

So it is my understanding then, that these currents really do not exist. Do surface currents really exist?

• Most of the things in physics are mathematical abstractions. Currents don't exist either, it's just a superposition of wave functions of electrons... Oh, wait. Wave functions? Another abstraction.. – Eugene Sh. Aug 2 '17 at 14:59
• Yes, the surface currents exist. The electrical field of the EM wave causes any mobile charges in the target to move. Any time you have free charges in the presence of an electric field, the free charges will move. – mkeith Aug 2 '17 at 15:42

It's just a question of levels of models.

At any given level, its abstractions 'exist', in the sense that they're what you do the sums with. So yes, surface currents exist in that model. If you know what underpins that model, then you can explain those abstractions in lower terms.

The lowest level model we have is quantum mechanics. If your maths is up to setting up the wave equation for the reflection situation, then go ahead. I think it's generally agreed that QM is not necessarily the lowest level model there is, as it doesn't agree with the other good model, GR. But, it's all we have at the moment.

So it is my understanding then, that these currents really do not exist. Do surface currents really exist?

Yes, they exist. Lets look at a DC example:

A different view for an impinging field would be this but the result is the same, because for an impinging field the magnetic field still generates a current and then all the laws that govern current come into effect. It doesn't matter how the current is generated.

Source: Muon Ray

The DC currents taper off to zero at the core because of the internal magnetic field of the material of the conductor. So its a real effect from the interaction of the current and electric field.

As we increase the frequency of the alternating field only the electrons on the surface move. Why? because the core of the wire has a higher impedance. High frequency currents take the path of lowest impedance, which happens to be near the outside of the wire. One thing that would be interesting to try would be to come up with an expression for impedance vs radius.

Another thing to not is the electric and magnetic field outside of the wire, which also carry energy.

If you look below, you can see what portion of the wire is actually carrying current. If you move to high enough frequency, only the outside of the wire carries the current.

Source: Quora

• Your answer, while detailed is about conduction through a wire via a driving current. That is not what I am asking about. My question is about the INDUCED currents caused by an external, impinging electromagnetic wave. – user41178 Aug 2 '17 at 17:47