No, because there is no electric field inside of the wire. This is because there is no gradient of charge in the wire; both sides have a positive charge rather than one side having an excess negative charge and the other having an excess positive charge. Recall that we learned that the direction of an electric field points from positive to negative. If there were an electric field in this wire, what would be the direction of the field since there is only a positive charge in the wire? Again, because there isn't an electric field, there is no surface charge.
Work Step by Step
No work is needed for this problem.