Direction of force on bar magnet in solenoid

rj540

A bar magnet with uniform magnetization is inserted half way into a solenoid, and I am wondering what the force is on the magnet?

The magnet's magnetization is pointing up, which means it has bound surface current circling counterclockwise, and a magnetic field pointing up.

The solenoid also has a field pointing up.

If the force on the magnet is effectively I x B, meaning it has direction perpendicular to both the a vector tangent to the magnet and the direction of the field (up), then wouldn't the force direction be perpendicular to the axis of the solenoid?