Nature of Coil and magnet fields?

Ruptor

I find it difficult to visualise how the magnetic field generated by a coil can be the same as the field of a permanent magnet. Are the magnetic fields the same or is it just that the effects are the same in that they both attract iron or magnets in the same fashion?
Visualising the field produced by a coil is straightforward because the current flows along the wire and emanates a nice ring of magnetic field but I can't see how the orbital magnetic moments of individual atoms clumped in to domains sum up to the same rings of field.

tiny-tim

Hi Ruptor!
It makes (almost) no difference to the magnetic field whether you have a current coil with a wide diameter,

or lots of current coils with tiny diameters (and the same current) filling the same volume.