Why do magnetic fields decay exponentially with depth in a conductor?

[Orlando]

Homework Statement

I am a HS student researching the penetration depths of magnetic fields in conductors. Specifially, I am investigating the exponential decay of eddy currents induced within a conductor in the presence of a rapidly changing magnetic field. I am a bit confused as to why the eddy current density is strongest at the surface of the conductor in a high frequency time-varying magnetic field - can someone explain to me in very simple terms why this occurs?

The Attempt at a Solution

I can only reason that the magnetic fields generated by the eddy currents at the surface shield the rest of the conductor, however this is very weak reasoning. Does anyone have any ideas?

 

[marcusl]

Your intuition is correct. The induced eddy current is proportional to the magnetic flux enclosed by the path, which in this case is proportional to the field strength. Since a thin layer of eddy current "shields" (partially cancels) the applied field, the next layer down sees a smaller field and carries a smaller current, and so on. The equations governing the exponential decay with depth behave like those governing diffusion (e.g., the conduction of heat into a slab).

 

[Orlando]

Thank you for your response, would you also by any chance know how to calculate the power loss due to eddy currents? I found this from wikipedia:

Under certain assumptions (uniform material, uniform magnetic field, no skin effect, etc.) the power lost due to eddy currents can be calculated from the following equations:

For thin sheets: http://upload.wikimedia.org/math/5/e/e/5ee57c87a0a7375257720d65c5a75198.png

As I am investigating the skin effect, would I be correct to incorporate the exponential decay of the magnetic field as it penetrates the conductor (a function of depth) into this expression if I wanted to calculate the power loss at a particular depth in the material? Or is there a better way to do this?