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. 
 A: 
Will magnetic mirroring and magnetic drift be the same as with plasma

No. It's behaviour will be vastly different than that for a particle. Large metal objects have free electrons/ions which will attract the charged particles in the magnetosphere. Ultimately the magnetospheric plasma will shield the metal object such that the net electromagnetic force on the sphere is zero. 
This phenomena is called Debye shielding. 
Now, how much of a force is provided by radiation pressure is another question altogether ...

If the sphere is already spinning, what effect will the spin have on its motion and vice-versa?

From the above answer, we can assume that the electromagnetic forces on the sphere are negligible. Hence, its motion will be determined by laws of motion and gravitation. A spinning sphere will have angular momentum, and details for its motion can be found in any orbital mechanics textbook. 

If instead of a solid sphere we had a spherical shell with the same characteristics, would it behave differently and how?

Well yes, but this is a complex question dealing with electrostatics and the principles of spacecraft charging, and also orbital mechanics. In theory, the moment of inertia ($I$) of a sphere and shell are very different. Refer to the textbook mentioned above for an in-depth explanation and relevant equations. 
