Consider a wire carrying a steady current, I placed in a uniform magnetic field B perpendicular to its length. Consider the charges inside the wire. It is known that magnetic forces do no work. This implies that,

motion of charges inside the conductor is unaffected by B, since they do not absorb energy

some charges inside the wire move to the surface as a result of B

if the wire moves under the influence of B, no work is done by the magnetic force on the ions, assumed fixed within the wire.

if the wire moves under the influence of B, no work is done by the force