The Electric Origin of the Magnetic Force between Two Filamentary Current Elements

The magnetic force was considered different in origin from the electrostatic force between charges because the current-carrying wires are intrinsically charge-neutral. An earlier explanation of the magnetic force described it as a natural consequence of special relativity and purely electrostatic forces. But neither the electric field nor the magnetic field is a relativistic effect. This talk will discuss an explanation of the magnetic force between two filamentary current elements as a result of electric force interactions between current charges. This explanation applies for both none-relativistic frames and relativistic frames. I will demonstrate an analysis to the electric field spreading in the space due to the movement of charges inside current elements. This spreading electric field contains discontinuity points to indicate the changes in positions of the moving charges. Applying Gauss's law at these discontinuity points indicates the existence of electric charges. I will show that the electric interactions of these charges with the moving charges inside current elements produce a force that is exactly equivalent to the observed magnetic force. This work is helpful in explaining magnetic force properties and how an electric current produces a magnetic field around it.