A.C. Tort

A note on the conservation of mechanical energy and the Galilean principle of relativity

A reexamination of simple examples that we usually teach to our students in introductory courses is the starting point for a discussion about the principle of conservation of energy and Galilean invariance.

Gauss's law, infinite homogenous charge distributions and Helmholtz theorem

We rediscuss the validity of Gausss law in the case of homogenous discrete and continuous charge distributions fulfilling all space.

Uma introdução aos métodos de cálculo da energia de Casimir

The Casimir effect is one of the most intriguing aspects of modern physics. The prediction of the existence of a macroscopic force of quantum origin between two neutral conductors and its subsequent experimental verification is without doubt the hallmark of quantum field theory. The present work complements a conceptual introduction recently published in this journal by presenting some of the methods of evaluation of the Casimir energy which gives rise to the Casimir effect.

Electromagnetic field correlators, Maxwell stress tensor, and the Casimir effect for parallel walls

We evaluate the quantum electromagnetic field correlators associated with the electromagnetic vacuum distorted by the presence of two plane parallel conducting walls and in the presence of a conducting wall parallel to a perfectly magnetically permeable one. Regularization is performed through the generalized zeta funtion technique. Results are applied to rederive the atractive and repulsive Casimir effect through Maxwell stress tensor. Surface divergences are shown to cancel out when stresses on both sides of the material surface are taken into account.

Uma tradução comentada de um texto de Maxwell sobre a ação a distância

A commented Portuguese translation of a text by James Clerk Maxwell published in 1873 is offered. In this important paper, Maxwell discusses arguments in favour and against the concept of action at a distance.

A commented Portuguese translation of a paper by Maxwell on action at a distance

A commented Portuguese translation of a text by James Clerk Maxwell published in 1873 is offered. In this important paper, Maxwell discusses arguments in favour and against the concept of action at a distance.

Galileo's kinematical paradox and the expanding circle of simultaneity

Consider a vertical circle and the diameter BA and representative chords BC, BD, which start from point B at the top of the circle, and also the chord EA and the line segment GF (see figure 1). If we simultaneously release two or more beads from B in such a way that one of the beads falls along diameter BA and the others slide along chords BC and BD or EA, then the beads will hit the circumference of the circle at the same instant, even though the chords have different lengths [1, 2]. This apparent paradox can easily be explained if we relate the length of diameter BA, let us call it h, to the length of a chord, say EA, let us call it . Then, by making use of Thales’ theorem, which states that any triangle inscribed in a semicircle is a right triangle, we can write

Another look at Helmholtz's model for the gravitational contraction of the Sun

We take another look at the Helmholtz model for the gravitational contraction of the Sun. We show that there are two other pedagogically useful ways of rederiving Helmholtzs main results that make use of Gausss law, the concept of gravitational field energy and the work–kinetic energy theorem. An account of the energy balance involved in the gravitational contraction process is also discussed.

A forma da superfície de uma massa de água girante como um problema variacional

Variational methods have a long and remarkable role in theoretical physics. Few of our students when first exposed to them fail to admire their elegance and efficacy in the formulation and solution of physical problems. In this paper we apply the variational approach that leads to the Euler-Lagrange equations to the determination of the shape of the surface of a mass of water that partially fills a cylindrical bucket that rotates with constant angular velocity (Newtons bucket). Here this approach will lead us to the principle of minimization of the effective potential energy associated with the system. The effect of an external pressure on the equilibrium shape is also taken into account and two models, the constant pressure model and the linear model are discussed. The level of the discussion is kept accessible to undergraduates taking an intermediate level course in classical mechanics.

Michell, Laplace e as estrelas negras: uma abordagem para professores do Ensino Médio

The modern concept of a black hole as a region of spacetime from which light cannot escape owns its origins to John Michell (1724-1793) and Pierre Simon Laplace (1749-1827). In the present work we review the approaches of these distinguished scientists in an attempt to provide the high school teacher with tools to understand those early ideas before the advent of the modern black hole of Einsteins gravitational theory.