Equivalence between Ampere and Grassmann's forces

1996/03/01 by A. K. T. Assis, A.K.T. Assis, M.A. Bueno +1
Physics and Astronomy · Engineering · #Experimental and Theoretical Physics Studies #Electromagnetic Launch and Propulsion Technology #Geophysics and Sensor Technology

paper · doi:10.1109/20.486529

Abstract

We calculate the force on part of a single closed circuit due to the remaining circuit in four different geometries according to the forces of Ampere and Grassmann. All analytical calculations are performed using surface or volume current elements in order to avoid the divergences which appear with linear current elements of zero diameter. We conclude that when we consider the action of a closed circuit as a whole and utilize only circuits with closed lines of current, there will be an equivalence between the expressions of Grassmann and Ampere. This means that both of them are compatible with the experimental findings related to Ampere's bridge, contrary to the opinion of some authors.

Related

• On the interaction between a current density and a vector potential: Ampère force, Helmholtz tension and Larmor torque
• The Electric Force Between Two Straight Parallel Resistive Wires Carrying DC-Currents in the Asymptotic Limit of Infinitely Thin Wires
• Applying the method of cases of equilibrium: from the unprecedented ‘case of equilibrium of Ampère’s motor’ to a contemporary deduction of Ampère’s electrodynamic force
• Ampère, the Etherians, and the Oersted Connexion
• Surface charges on circuit wires and resistors play three roles