3 ms·
There are two things here. The force magnetic fields apply is always perpendicular to the field: F ~ v × B (right hand rule, and all that). So if you want F
by evanb 10y ago
There are two things here.
The force magnetic fields apply is always perpendicular to the field: F ~ v × B (right hand rule, and all that). So if you want F to point inward, the one component of B that doesn't matter is its radial component---ie. the tangent component is all that counts. But it's not clear to me that you can't compensate for the restrictions of the hairy ball theorem by having a nonuniform velocity distribution. Of course, there's no "hairy torus" theorem (because it's not true!) and this immediately suggests the tokamak design.
It's also not possible to take a sphere and have the radial magnetic field point inward everywhere (or outward everywhere), because Maxwell's equations prohibit magnetic monopoles.
- vecter 10y agoIt's been too long since E&M. I forgot about magnetic fields being normal doh. And of course, the last point about no magnetic monopoles should be sufficient to make a spherical field impossible.