A. K. T. Assis

On Mach's principle

We propose the postulate that the resultant force acting on any body is zero. With this postulate and with a Weber force law for gravitation, we obtain equations of motion and conclude that all inertial forces are due to gravitational interaction with other bodies in the universe, as suggested by Mach. We then obtain the same value for the advance of the perhelion of the planets as is given by general relativity. All this is accomplished in a strictly relational theory. Finally, we relate these points to topical questions of electrodynamics raised by the experimental studies of Graneau and Pappas.

A new method for inductance calculations

A new method for calculating inductances is presented. The method results in analytically simple expressions that replace the traditional tables and working formulae. Moreover, it overcomes the diverging self-inductances of thin wires.

The Electric Field Outside a Stationary Resistive Wire Carrying a Constant Current

We present the opinion of some authors who believe there is no force between a stationary charge and a stationary resistive wire carrying a constant current. We show that this force is different from zero and present its main components: the force due to the charges induced in the wire by the test charge and a force proportional to the current in the resistive wire. We also discuss briefly a component of the force proportional to the square of the current which should exist according to some models and another component due to the acceleration of the conduction electrons in a curved wire carrying a dc current (centripetal acceleration). Finally, we analyze experiments showing the existence of the electric field proportional to the current in resistive wires.

Equivalence between Ampere and Grassmann's forces

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 Amperes bridge, contrary to the opinion of some authors.

Changing the Inertial Mass of a Charged Particle

We calculate utilizing Webers law the force on a moving charge exerted by a stationary charged spherical shell surrounding it. We obtain a net force different from zero which is proportional to the acceleration of the test particle relative to the spherical shell. This result can be interpreted by saying that the inertial mass of a test particle should change if it is placed inside a charged spherical shell. We conclude that this modification in the inertial mass is proportional to the electrostatic potential of the charged spherical shell and to the electric charge of the test particle. Then we present some possible experiments which could be performed to test this prediction.

The potential, electric field and surface charges for a resistive long straight strip carrying a steady current

We consider a long resistive straight strip carrying a constant current and calculate the potential and electric field everywhere in space and the density of surface charges along the strip. We compare these calculations with experimental results.

A limitation of Weber's law

Abstract We present Webers law and its main properties. We discuss its relation with the experiments of mass variation with velocity. Then we calculate the energy and force on a charge moving inside and outside a capacitor according to Webers electrodynamics. We discuss the consequences of this relation, and in particular we show that in this model a charge could attain velocities larger than the light velocity in a limited space due do a finite and feasible voltage difference. As this has never been observed we conclude that Webers electrodynamics should not be applied to charges moving near the light velocity.

Surface charges and fields in a resistive coaxial cable carrying a constant current

We calculate the surface charges, potentials, and fields in a long cylindrical coaxial cable with inner and outer conductors of finite conductivities and finite areas carrying a constant current. It is shown that there is an electric field outside the return conductor.

The Influence of Ernst Mach in the Teaching of Mechanics.

We present Newtons main ideas for the formulation of classical mechanics as given in the Principia. Then we discuss Ernst Machs criticisms of Newtonian mechanics as contained in his book The Science of Mechanics. We analyze the influence of Machs ideas in the teaching of classical mechanics considering five representative textbooks: those of Kittel, Knight and Ruderman; Marion and Thornton; Symon; Feynman, Leighton and Sands; and Goldstein. We conclude that the influence of Machs ideas has been very great, being incorporated in the textbooks, although not always with the deserved acknowledgment.

Weber's law and mass variation

Abstract Due to the renewed interest of the last few years in Ampere and Webers laws of force we decided to apply Webers law to the situation of Bucherers experiment. We calculate, according to Webers expression, the force on a charge in regions of uniform electric and magnetic fields. Then we show that Webers law agrees with the relativistic calculation only up to second order, inclusive, in v / c . So the special theory of relativity remains as the only model in perfect agreement with Bucherers experiment.