Stability of ellipsoidal conductors in microgravity electromagnetic containerless processing facilities

We calculate forces and torques arising on ellipsoidal conductors placed in electromagnetic containerless processing facilities in an ambient of microgravity assuming small displacements from equilibrium. We show that oblate conductors could be unstable to flipping motion when oscillating longitudinal (or heating) magnetic fields are used, while prolate ones are unstable when their elongation is below 2 if only positioning coils are employed.