# Stability of a dipole magnet undergoing eddy current braking in a cylindrical tube

Consider a cylindrical dipole magnet with strength $$B$$ undergoing eddy current braking in a conductive cylindrical tube with the axis of the magnet aligned with the axis of the tube.

The magnet feels a retarding force $$F_{eddy} =\mathcal{V}vB^2σ$$

The arrangement is in equilibrium (by symmetry) in all directions apart from along the axis. But is it a stable equilibrium in the off-axis directions?

That is, if you knock the magnet sideways by a small amount, is there a restoring force? If you turn the magnet slightly off the axis, is there a restoring couple?

Bonus question: could it be made stable by mechanically attaching some other magnets to the moving magnet? (the goal is to make it stable without significantly reducing the braking force)

• Apparently, we need to create a numerical model. I see no other way how to answer these questions. – Alex Trounev Aug 24 at 4:27