In this case, we must remember that the magnetic field acts with a magnetic force on the moving charge. The Lorentz equation describes the magnitude of this force:
Fm = q(v x B)
q, is the electric charge of the particle in motion.
v, is the speed of the charged particle.
B, is the magnetic field induction.
In a conductor carrying current, the electrons move in a preferred direction from the negative terminal to the positive terminal of the supply. The net charge is zero because, during the same time interval, the number of electrons that come from the negative terminal of the source, is equal to the amount of these that enter in the source by the positive terminal.
Therefore, although the net charge of the conductor is zero, there are electrons moving in its interior. In these conditions we have that the magnetic field exerts a force on each electron moving with velocity v along the conductor. The sum of all the forces acting on the electrons in motion will manifest as a force that acts on the conductor.