Re: Can a permanent magnet be made which mimics a current carrying conductor?

Dear Pius!

Sorry that this has taken so long, but you know how it is during Christmas time...

In order to understand the answer to your question you first have to realize the physicist's view of a magnet and how the magnetic field is produced there. A magnetic material is modelled as a very large array of small magnetic dipoles which react to an external magnetic field. In some cases, the dipoles align to the external field and more or less stay in this position even when the external field is switched off. This is a ferromagnet: Its magnetization depends on its ``magnetic history''. Now we have a microscopic understanding of what's going on, but how does the magnetic field look like when the magnetization is given? A tiny dipole magnet can be modeled by a small circular current. In a bunch of dipoles which are aligned (either due to an external field or due to their interaction among each other), the small circular currents largely compensate each other, because neighbouring dipoles belong to currents which flow (locally) into opposite directions. The only place where the currents do not cancel is the surface of the material! So a permanent magnet can be viewed as a current flowing on its surface (if the magnet is cylindrical and magnetized along its axis, the current flows around the axis on the surface; there is no current on the `bottom' and `top' pieces of the cylinder).

The magnetic field of the setup that you have described in your question would thus be zero. That is because the current flow generated by your `angular slices' on the outer surface of your tube is accompanied by the current that flows on the inner surface of the tube (small as it may be); the magnetic fields generated by the two currents exactly cancel outside the material (by the way, the magnetic field outside the wire decreases as the inverse of the distance, not its square). The `outer' current does flow into the right direction to account for the desired magnetic field, but unfortunately the `inner' current destroys it again. There is a magnetic field inside the material, but it depends strongly on the exact way the stuff is magnetized. However, one can roughly expect a 1/r behaviour, just like outside the usual current-carrying conductor. There is also a problem with the usual picture we have of a current-carrying wire: We always assume that the current density is constant among the whole transverse section - which leads to the linear behaviour of the magnetic field -, but that ceases to be the case already if the current is not steady any more, i.e. if it varies with time. You can look this up under `skin effect' in any textbook on electrodynamics.

Hope that helps,
happy new year,
Georg.