Differential Equations Describing Magnetic Fields Around Magnets

[EroticNirvana]

The magnetic field around a magnet very much looks like the solution of a differential equation (which I guess it is, at least apprx). Now, can anyone give my a few simple exaples of such differential equations describing a magnetic field around a magnet?

 

[Meir Achuz]

If you are not too close to the magnet, the field around it is the field of a magnetic dipole $${\bf m}$$. In vector notation, the magnetic field is given by
[tex{\bf B=-\nabla\left(\frac{\bf m\cdot r}{r^3}\right)
=\frac{3({\bf m\cdot{\hat r}){\hat r}-m}}{r^3}.
[/tex]

 

[EroticNirvana]

browser malf?

i see only strange symbols in the above msg. Does my browser not work properly?

 

[dfx]

$${\bf B=-\nabla\left(\frac{\bf m\cdot r}{r^3}\right) =\frac{3({\bf m\cdot{\hat r}){\hat r}-m}}{r^3}.$$

I think he forgot to close a ] around the tex notation. :)