# Small charged sphere's motion in earth's magnetosphere?

Suppose that a spherical metal sphere with mass $m=10^{-16}kgr$ radius $R=10μm$ charge $Q=10^{-9}C$ travels with $v=c/3$ and is trapped in the earth's magnetosphere at a distance around $r = 1000km$. The exact numbers are not that important, I am providing them for order of magnitude considerations.

Assuming a non-zero velocity component parallel to the field lines:

• Will magnetic mirroring and magnetic drift be the same as with plasma (i.e. can one use the same equations to calculate the motion of the sphere)? Will the eddy currents in the sphere affect mirroring/drift and how?
• If the sphere is already spinning, what effect will the spin have on its motion and vice-versa?
• If instead of a solid sphere we had a spherical shell with the same characteristics, would it behave differently and how?

I am looking for a qualitative answer, or a pointer to work that has been done along these lines.

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