Ingeniare. Revista chilena de ingeniería, vol. 16 No 2, 2008, pp. 273-274





by Andre Koch Torres Assis and Julio Akashi Hernandes 2007

(Available in pdf format at

 por H. Torres-Silva1

 1 Instituto de Alta Investigación. Universidad de Tarapacá. Arica, Chile. E-mail:


Prof. Andre K.T. Assis of the State University of Campinas in Brazil has written a new book in collaboration with Prof. J. A. Hernandes, the focus of which is refuting the charge levelled by R. Clausius, J. C. Maxwell, and others, that the alleged failure to detect a force between a current-carrying wire and a nearby stationary charge invalidates Weber's fundamental law.

This book provides good teaching material that is important to take into account in the consideration of some areas of electromagnetism and electromagnetic engineering, in systems where the existence of a force of between a conductor and static charges must be considered as a main aspect.

The goal of this book is to analyze the force between a point charge and a resistive wire carrying a steady current, when they are at rest relative to one another and the charge is external to the circuit. Analogously, the authors consider the potential and electric field inside and outside resistive conductors carrying steady currents. The authors also discuss the distribution of charges along the surface of the conductors which generate this field. This is an important subject for understanding the flow of currents along conductors. Unfortunately, it has been neglected by most authors writing about electromagnetism. The main aim is to present the solutions to simple cases which can be solved analytically in order to show the most important properties of this phenomenon.

The book is written for undergraduate and graduate students in programs of physics, electrical engineering, mathematics, and history and philosophy of science. Chapters 1, 2, 3, 5, 6, 7 and 8 are appropriate for undergraduate students. The intention of the authors is to help develop critical thinking in students and to deepen their knowledge of this fundamental area of science.

They begin by showing that many well-known authors held incorrect points of view regarding steady currents, not only in the past but also in recent years. They then discuss many experiments proving the existence of a force between a resistive conductor carrying a steady current and an external charge at rest relative to the conductor.

This first topic shows that classical electrodynamics is a lively subject in which there is still much to be discovered. Another goal is to show that electrostatics and steady currents are intrinsically connected. The electric fields inside and outside resistive conductors carrying steady currents are due to distributions of charges along their surfaces, maintained by the batteries. This presentation unifies the treatments of the subjects of electrostatics and steady currents, contrary to what we find nowadays in most basic books on these topics.

In addition to this consideration of electrostatics, later chapters also deal with pure electrostatics, namely, the force between a conductor and an external point charge at rest relative to it. That is, they deal with electrostatic induction, image charges and related subjects. In particular the authors calculate in detail the force between a long cylindrical conductor and an external point charge at rest relative to the conductor.

The authors then move to the main subject of the book by considering the force between a resistive wire carrying a steady current and a point charge at rest relative to the wire, outside the wire. In particular, they consider the component of this force which is proportional to the voltage of the battery connected to the wire (they discuss the voltage or electromotive force of a battery, together with its distinction from the concept of potential difference, in chapter 5).

They embark on this analysis by first considering straight conductors of arbitrary cross-section in general and a general theorem on their surface charges. Next they deal with a long straight conductor of circular cross-section. Then they treat a coaxial cable and a transmission line (twin lead). They subsequently discuss conducting planes and a straight strip of finite width.

In the third part they consider cases in which the closed current follows curved trajectories through resistive conductors. They then move onto the force between this conductor and an external point charge at rest relative to it. Initially they deal with a long cylindrical shell with azimuthal current. Then they consider the current flowing in the azimuthal direction along a resistant spherical shell. And finally they posit the case of a toroidal conductor with steady azimuthal current. Although this last situation is much more complicated than the previous cases, it is extremely important, as it can model a circuit bounded in a finite volume of space carrying a closed steady current, such as in a resistant ring. This third part is appropriate for graduate students and it can be utilized as a complementary text in courses on electromagnetism, electrical circuits, and mathematical methods of physics.

The intention of authors in including analytical solutions of all these basic cases in a single work is to make it possible to utilize this material in the undergraduate and graduate courses mentioned earlier. Although the mathematical treatments and procedures are more or less the same in all cases, they are presented in detail for conductors of different shapes, so that the chapters can be studied independently from one another. It can then easily be incorporated in standard textbooks dealing with electromagnetism and mathematical methods for scientists.

As an example, in the traditional Electricity & Magnetism curriculum, electrostatics and circuits are treated as almost completely separate topics. Electrostatic phenomena are analysed in terms of charge and field, but circuits are analysed in terms of current and potential, and the connection between these two sets of concepts is not made salient. This dissociation undermines the claim that physics can analyse a wide range of phenomena starting from a small number of powerful fundamental principles. This book is aims to understand macro-micro connections and the integration of electrostatics and circuits.

This book engages students in the analysis of circuits from a microscopic point of view in terms of the relation between the drift speed, the mobility of the mobile charges, and the electric field. The field inside circuit wires can be shown to be due not only to charges in and on the battery, but also to those on the surfaces of the circuit elements. Students can learn to analyze both DC and AC circuits directly in terms of the Coulomb interaction and the atomic nature of matter. This analysis in terms of charge and field makes a strong connection with electrostatics, unifying the two topics, and it provides a strong sense of mechanism for the behavior of simple circuits.

At the end of this work the authors present open questions and future prospects. Later chapters in the book are devoted to theoretical calculations related to the Weber force, including an original treatment of the resistant spherical shell. An appendix, "Wilhelm Weber and Surface Charges", contains a penetrating study of Weber's significant paper in the Electrodynamic Measurements series, devoted to resistance measurement.

A second appendix, on Gustav Kirchoff's derivation of the telegraphy equation, in which he demonstrated that the propagation of current in a wire would be limited by the velocity of light, sets the record straight that both Weber and Kirchoff had preceded Maxwell by several years in this discovery.

These later chapters can be appropriate to Research & Development. One case is the Aharonov-Bohm effect that is usually believed to be an indication of the fundamental importance of electromagnetic potentials in nature. Although, several non-conventional explanations of this effect have been suggested in the literature, as far as I know, there are no attempts to interpret this effect in terms of direct interactions between particles. This material could fill that gap by suggesting a simple description of the Aharonov-Bohm effect within the Weber action-at-a-distance theory. This explanation does not involve the notions of electromagnetic potentials, fields, and non-trivial space topologies.