Question

“Speed sorting” in electric field and inhomogeneous magnetic field?

Answer 1

Let's say you add an electric field to a inhomogeneous magnetic field, oriented as in the picture; what would that lead to? There is a grad B drift upwards in the picture, that the electric field opposes. Would this lead to "speed sorting", where the fast particles gather at the top and the slow at the bottom, if we ignore collisions? Would the (positive) charged particles describe circles or some other shape of orbit, if we ignore movement into and out of the screen/paper.

Answer 2

The direction and strength of the electric field matter here. As an aside, a grad-B drift will already act as a velocity filter since there will be some particles that ballistically plow through a magnetic field gradient like this. Changing the gradient scale length changes the energy range of particles that will undergo a grad-B drift.