Modeling a bar magnet's magnetic flux inside a coil

A bar magnet and a coil arranged alongside their common axis is a common setting in teaching. But how does the magnetic flux H(x) (where x is the distance of the bar magnet's center relative to the coil's center) look like? Is there a good approximation? I guess it should look like a Gaussian function, but how close does that resemble reality?

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Can you expand your question a bit: maybe with a diagram. It looks as if your asking what the flux through the coil is, which I think is the same as asking what the magnet's field strength is as a function of distance from the magnet. –  John Rennie Jun 10 '12 at 19:04
@john Yes, flux through the coil as a function of distance between coil and magnet. As this is different from the field's strength (which does not take the area i.e. the number of turns and cross section into account) and I don't know to what extend the two functions differ, I stated my question in it's current from--just to be sure to get a precise answer. –  artistoex Jun 10 '12 at 19:22
I don't think there is a precise answer for a real bar magnet. The closest analytical result is for a magnetic dipole, which works well a long way away from the magnet but is a poor approximation close up. See en.wikipedia.org/wiki/Magnetic_dipole for the dipole calculation. You'd need to integrate the field over the area of the coil then multiply by the number of turns. It's not a trivial calculation. –  John Rennie Jun 10 '12 at 19:36