$\begin{array}{1 1} \text{motion of charge inside the conductor is unaffected by $\overrightarrow{B}$ since they do not absorb energy } \\ \text{Some charges inside the wire ,move to the surface as a result of $\overrightarrow{B}$} \\ \text{if the wire moves under the influence of $\overrightarrow{B}$ no work is done by the force } \\ \text{if the wire moves under the influence of $\overrightarrow{B}$ no work is done by the magnetic force on the ions, assumed fixed within the wire.} \end{array} $