Sunday, November 25, 2012

Happy Thanksgiving from Nested Tori!

It looks kind of turkey-ish, right? Some numerical imperfections give it a green tail, anyway. It's supposed to be the magnetic field of a spinning solid ball of charge. In some sense, this problem started my quest to become more numerical: I remember being frustrated that I could not rattle off what the magnetic field of this configuration of charge was, despite knowing a whole bunch of theory and equations. And attacking the problem analytically was, to use a different species of fowl, a wild goose chase. It turns out I did find out one possible analytic expression for it, using multipole expansions, but that's still a far cry from being able to come up with interesting visualizations (multipole expansions and spherical harmonics DO have cool visualizations which we will definitely post here someday). Gobble gobble! The field is actually similar to that of a dipole, and aside from the boundary condition that it has to be tangent to the big enclosing cube, the vector field is tangent to, you guessed it, nested tori.

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