I still wonder about this. A simple results of this equation is: If a charge has a velocity in the positive y direction [v = (0,1,0)] and it accelerates in the positive x direction (it curls) then there will be a magnetic field in the positive z direction. There will be no magnetic field in the negative z direction. The problem here is that negative and positive z are symmetrical, there is no physical difference, and the xy plane is orthogonal so there is no interaction with the z plane to choose one direction or another. Yet nature always chooses the same direction to put the field based on the motion of an electric charge in an orthogonal plane. Because of this I do not see how the magnetic field is a field at all. It only appears to be a mathematical object used for simplification in describing the physical interactions of electric charges.