# Skin effect prevailing the drift velocity effect

In general, an electron will propagate randomly in a conductor at the Fermi velocity( produced due to thermal energy of the conductor). An applied electric field will give this random motion a small net flow velocity in one direction. Wikipedia

Skin effect is the tendency of an alternating electric current (AC) to become distributed within a conductor such that the current density is largest near the surface of the conductor, and decreases with greater depths in the conductor. Wikipedia

I’m curious about situations in between. For example for a lightning bolt, running down a wire, the skin effect is prevailing. For low frequent AC currents perhaps the drift velocity is more important.

Implying a DC current with a highfrequent pulses, will the skin effect dominate or - more general - for which boundary conditions the skin effect will dominate the drift velocity effect?

First of all, the Wikipedia article on drift velocity is misleading and wrong. Check out the Talk of that page. In short, a more correct introduction could be

Following the free electron model, in a conductor the few free electrons that can take part in electrical conduction propagate randomly in at speeds near the Fermi velocity. An applied electric field will perturb the electrons that are going in the field's direction at the Fermi velocity, to change their momentum in the opposite direction with approximately the same speed. The net result is a small drift velocity in the opposite direction than the electric field.

Thus in reality only very few free (quasi)electrons are perturbed by the electric field, and their velocity is roughly constant in magnitude but changed in direction. The magnitude of the speed is about two orders of magnitude slower than the speed of light in vacuum. The net effect of this, is that indeed mathematically it is the same as if all the free electrons had acquired a very small ($$\sim 10^{-4} m/s$$) drift velocity, but what really happened physical is quite different.

Now onto your question. It seems like you believe that the skin effect competes with the "drift velocity effect" (first time I've heard of that term), but this isn't the case. With DC there is no skin effect, and there is a non zero drift velocity. This means the current is made by a uniform current density within the wire. With pure symmetrical AC there is a skin effect, which might, or not, be noticeable. Depending on the frequency of the AC, resistivity, magnetic permeability and permittivity of the material if the skin depth $$\delta= \sqrt{\frac{2\rho }{\omega\mu}} \sqrt{ \sqrt{1 + \left({\rho\omega\epsilon}\right)^2 }+ \rho\omega\epsilon}$$ is much larger than the radius of the assumed cylindrical wire, then the skin effect (which manifest itself as a higher resistance/impedance) will be a small perturbation and the case is almost like DC. On the other hand, if that quantity is very small compared to the radius of the wire, then the skin depth effect will be more noticeable. To give you a rough idea, the skin depth of copper at 60 Hz is about 8.5 mm. This means a very small radius wire will be much less impacted than one with a very big radius, where small and big are meant to be relative to 8.5 mm. So the impedance of a thin wire would not change much compared from a DC case, whilst the one of a thick wire would.

Thus, the skin effect does not really compare to the drift velocity. It impacts on the resistance/impedance of the material (say a copper wire) in that the electrons that participate in conduction are mostly near the surface of the material and less so at its center. As you know, $$R = \rho L/A$$, where $$\rho$$ is the resistivity, $$L$$ is the length of the material and $$A$$ its cross section. The skin effect reduces $$A$$, hence $$R$$ is increased. So, for a given constant voltage source $$V$$, from Ohm's law one gets that when $$R$$ increases, $$I$$ the current decreases. But you could have as well chosen a constant current source, in which case the voltage would have increased. As such, the real effect of the skin depth phenomenon is that it impacts on the resistance/impedance, not necessarily on the current itself, and so on the drift velocity.

Edit: In response to the comment

I hoped to get special knowledge about pulsed DC. The only difference to AC is that in the second case the electrons wiggling around a point while for DC they wiggling AND moving in one direction. In both cases the accelerations induce magnetic fields and a skin effect should appear for pulsed AC too.

I suppose you meant "DC too" as your two last words. I would say that pulsating DC should be similar to AC in that the changing current would indeed create a changing magnetic field that gives rise to the skin effect. The above answer is still applicable in that case.

• tttt, I hoped to get special knowledge about pulsed DC. The only difference to AC is that in the second case the electrons wiggling around a point while for DC they wiggling AND moving in one direction. In both cases the accelerations induce magnetic fields and a skin effect should appear for pulsed AC too. – HolgerFiedler Jan 17 at 15:06
• @HolgerFiedler I've added a comment in my answer regarding your comment. – thermomagnetic condensed boson Jan 17 at 19:52