EQUIVALENCE BETWEEN AMPERE AND GRASSMANNS FORCES

We calculate the force on part of a single closed circuit due to the r emaining circuit in four different geometries according to the forces of Ampere and Grassmann. All analytical calculations are performed usi ng surface or volume current elements in order to avoid the divergence s which appear with linear current elements of zero diameter. We concl ude that when we consider the action of a closed circuit as a whole an d utilize only circuits with closed Lines of current, there will be an equivalence between the expressions of Grassmann and Ampere. This mea ns that both of them are compatible with the experimental findings rel ated to Ampere's bridge, contrary to the opinion of some authors.