When two cylindrical magnets are brought close together so that the North pole of one is close to the south pole of the other, there is an attraction force between them. But what is the nature of this force? I used to think that this force is nothing but Lorentz force that the magnetic field of one magnet exerts on the the equivalent current densities of the other. If it was so, there must be no force on the circular face of the magnet because the net current density is zero there. So what is the nature of the fore? The force is usually understood and calculated from the energy points of the view and the principle of virtual work. Can it be explained by Maxwell's equations as well? Thanks.