In a conductor, free electrons keep on moving but no magnetic force acts on a conductor in a magnetic field.
Force on free electrons due to magnetic field always acts perpendicular to its direction of motion.
Free electrons move randomly within a conductor. Each moving electron will experience a magnetic force based on the Lorentz force equation given as:
Since, in the absence of an applied potential, such movement of free electrons doesn't constitute a net current in the conductor. So, the conductor as a whole will not behave as a current element in such a case and hence, the magnetic force acting on it will be zero.