Force on a current carrying wire

Question based on Force on current carrying wire

Force on current carrying wire || Self inductance

Force on current carrying wire

A current carrying wire is placed along the axis of a uniformly charged circular ring. If the ring starts rotating about its central axis what will be force on the current carrying wire due to the moving charges of ring.

the force on current carrying wire placed in uniform magnetic field B as shown in figure is

Prove that the force acting on a current carrying wire, joining two fixed points a and b in a uniform magnetic field, is independent of the shap of the wire.