Hi Yuze:

I believe there will be eddy currents even if the thickness is less than the skin depth, but the amount of current will be less and there will be a residual field on the other side of the thin conductor. In your example the conductor thickness is less than 8% of the skin depth so you could approximate the current density as being piece-wise  linear in it, so the amount of current in that small depth would be roughly 8% of the total current that would be induced in an infinitely thick conductor. So if the current density at the surface is J and the skin depth is d, the total induced current in an infinitely-thick conductor would be d*J, and in the small depth y

I agree with the comments by  Alan P Letchford. It is a common situation that 

material has the thickness which is smaller than the skin depth e.g. thin metal films

or graphene. Eddy currents are still present there. Electromagnetic field and current

distribitionin the direction perpendicular to the film depend on frequency and 

conductivity. Some informationa  about such phenomena at MW frequencies  can be found in: Journal of the European Ceramic Society 27 (2007) 2823–2826

The answer is yes.  There is even such a terminology as "thin conductive sheets and shells".

Dear all,

Thank you so much for your kind explanation, there will be eddy current in the particle. The ideas from Marek and Alan for eddy current calculation inspire me a lot.

If we go a littile bit further, what is the Lorentz force in this case?

For instance, a conducting particle at a low frequency magnetic field, the calculated skin depth is much larger than the particle size, in this case, based on a patent (Saveliev, Vladimir. "System and method for separating electrically conductive particles." U.S. Patent No. 5,772,043. 30 Jun. 1998), the induced eddy current will be lagged the external magnetic field by pi/2, therefore, their conclusion is that the average Lorentz force on the particle will be zero for this case. 

If that theory is right, can we use that theory for the case of a conducting particle travels through a non-uniform magnetic field? Specifically, the characteristic scale  of the non-uniform magnetic field is L, the particle travelling speed is relatively low with value v, then the equivalent frequency f=v/L, in this case, can we say that, as the particle travelling speed is low, the equivalent frequency f=v/L is low, therefore the skin depth is much larger (skin depth is proportional to f^(-1/2)) than the particle size, and the induced eddy current is lag the external magnetic field by pi/2, thus, the average Lorentz force on the particle is zero. Is this correct?

Thank you so much,

Thank you, Professor Alan, the inductance should be considered here, it is much clearer now. 

Dear Yuze,

What has been said by the colleagues is okay. It is so that alternating current will cause an alternating magnetic field in a plane normal to the flow of the original ac current. This alternating magnetic field will induce secondary alternating current which aids the current nearer the surface and opposes the primary current flowing in nearer the interior. It follow that the current will be nonhomogeneously distributed at the cross section of the conductor where the current is more concentrated at the surface region.

So, the skin effect is the consequence of the induced secondary eddy currents. This effect is always present irrespective of the thickness of the conductor. It is advisable not to make the conductor thicker than the skin depth to save materials of the conductors. However the skin effect is always present irrespective of the thickness of the conductor.

Best wishes

Thank you, Professor Abdelhalim.

The main conclusion about shielding of thin (compared to the skin depth) conductive layers is a clear YES and NO depending on the boundary conditions. We all know that shielding in the near field of a magnetic antenna with such layers does not work very well. One way to visualize this is the pricture of a homogeneuous plane wave impinging on such a thin layer..for normal incidence there are very simple formulae for the reflected and transmitted wave as a function of the resistance per unit sqaure of this layer and in this case a layer which is very thin compared to the skin depth can already be very efficient in shielding. However for the grazing incidence of a homogeneous plane wave with vertical polarisation the shielding efficienty is very low..the layer is in the case a kind of "equipotential surface"where one should not talk about (scalar) potential in the context of time dependent field. In simple words:if there is any significant current flowing in this layer it shields more or less well, if not ..then not..The question..does this current (caused by the incident field) flow depends on the direction of the electric or magnetic field wrt the surface normal of the layer and the external boundary condiction..if the current can find an easier way than through this layer..it will use it...

We know all this very well from shielding performance of thin layers in coated ceramic beampipes.

Thank you for the nice discussion here. I am wondering if it is possible to induce eddy current on a single layer graphene sheet (one atom thick)? If there would be sufficiently large eddy current, one may use alternating magnetic field to sort graphene according to their size. However, it seems to me that even graphene has very high mobility, the electron concentration is too low to support eddy current. Is there any experiment on magnetic field induced eddy current in graphene?

Dear Prof Jer, I haven't majored in physics and no idea if that is possible to generate eddy current in graphene sheet that is only one atom thick. But I found an article named as " Potential-driven eddy current in rippled graphene nanoribbons,arXiv:1210.1727v2", in which they proposed a method to generate nano-scale eddy current in rippled graphene nanoribbons.