I am looking for an analysis of a disc magnet, I have heard there are 2D analaysis and 3D. Could someone point me in the right direction of a paper or some academic text on the matter.

I don't mind if the solutions are Cartesian, cylindrical or spherical.

I have seen solutions to solving for the \$Z\$ axis (the axis of magnetisation).

\$B = \frac{M}{2}(\frac{h + z}{\sqrt{r^2 + (h + z)^2}} - \frac{z}{\sqrt{r^2 + z^2}})\$

Where \$B\$ is the magnetic flux density at axial distance \$z\$ from the centre of the magnet, \$h\$ is the height of the disc, \$r\$ is the radius of the magnet and \$M\$ is the remanence field (units in flux-density).

I understand if the only practical solve is a finite element synthesis but an indication of this would be nice.


The use of finite element analysis is the easiest approach. If you are a math guru, here is a suggestion for a non-finite-element approach which would seem reasonable for a thin disc magnet: assume that the magnet is actually a group of magnetic dipoles, the effects of which are additive. You could then calculate the fields from the dipoles along on a radius, then rotate this result.


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