Analysis of Biot-Savart’s law in comparison with Ampère’s force between current elements

Abstract

Nowadays, we use Biot-Savart’s Law and Grassmann’s force to study the magnetic fields effects. We can observe that this force apparently do not always satisfy the principle of action and reaction. In contrast, Ampère’s force always satisfies this principle explicitly and always along the straight line connecting the two currents elements. The present work presents a historic analysis of the development of these two forces, which have been developed based on interpretations of the Ørsted’s experiment. We also compare these two forces in order to verify if both have the same result. We show that the Grassmann’s expression, in fact, does not satisfy to the principle of action and reaction. Ampère’s force not only follows the principle of action and reaction in the strongest way, but it also explains the phenomena based action at a distance, which is easier to be observed and has many other powerful results, not only in the electromagnetism. In order to compare these two approaches, we calculate the force that an infinite rectilinear wire exerts on a loop of conductive material, both with current.