Suppose we are looking at the cross-section of a cylindrical current-carrying wire. Due to the motion of the electrons in the wire, it can be said that at all points at the surface of the wire a magnetic field tangential to the wire exists. Since there are electrons moving in that region as well, a radial Lorentz force arises on these electrons. The questions: 1. Is this analysis correct? Does this force exists? 2. And if it does, wouldn't this cause all the electrons in the wire to pile up at its center? This is fundamentally a problem concerning the effect of a wire's magnetic field on itself.