Simple circuit theory and the solution of two electricity problems from the Victorian Age

Two problems from the Victorian Age, the subdivision of light and the determination of the leakage point in an undersea telegraphic cable are discussed and suggested as a concrete illustrations of the relationships between textbook physics and the real world. Ohm's law and simple algebra are the only tools we need to discuss them in the classroom.Comment: 8 pages, latex fil

An exercise on Gauss' law for gravitation: The Flat Earth model

We discuss the flat and hollow models of the Earth as a pedagogical example of the application of Gauss' law to the gravitational field.Comment: 4 pages, Latex file. More typos correcte

A note on the electrostatic energy of two point charges

The electrostatic field energy due to two fixed pointlike charges shows some peculiar features concerning the distribution in space of the field energy density of the system. Here we discuss the evaluation of the field energy and the mathematical details that lead to those peculiar and non-intuitive physical features.Comment: 9 pages, 3 figure

Duality Transformations and temperature inversion symmetry

We argue that the temperature inversion symmetry present in the original Casimir setup and also in other Casimir systems for which symmetrical boundary conditions are imposed is not related to the duality transformations that in the context defined in Ref. [1] are transformations relating spatial extension and temperature, and pressure and energy density. We provide an example of a Casimir system for which in principle there is no temperature inversion symmetry but nevertheless these duality transformations can be found.Comment: 5 pages, no figures, standard Late

Entropy bounds for massive scalar field in positive curvature space

We consider a massive scalar field with arbitrary coupling in $\mathbf{S}^{1}\times \mathbf{S}^{3}$ space, which mimics the thermal expanding universe, and calculate explicitly all relevant thermodynamical functions in the low- and high-temperature regimes, extending previous analysis of entropy bounds and entropy/energy ratios performed in the conformal case. For high temperatures, new mass-dependent entropy ratios are established which, differently to the conformal limit, fulfil Bekenstein's and Verlinde's bounds in the physical region.Comment: 19 pages, 1 figur

On the Casimir energy of a massive scalar field in positive curvature space

We re-evaluate the zero point Casimir energy for the case of a massive scalar field in $\mathbf{R}^{1}\times\mathbf{S}^{3}$ space, allowing also for deviations from the standard conformal value $\xi =1/6$, by means of zero temperature zeta function techniques. We show that for the problem at hand this approach is equivalent to the high temperature regularisation of the vacuum energy.Comment: Four pages, latex file; submitted for publication in the Proceedings of the XXIV Brazilian National Meeting on Particles and Fields held in Caxambu MG, Brazil September 30 -- October 4, 200

A note on the Lorentz force, magnetic charges and the Casimir effect

We show that in order to account for the repulsive Casimir effect in the parallel plate geometry in terms of the quantum version of the Lorentz force, virtual surface densities of magnetic charges and currents must be introduced. The quantum version of the Lorentz force expressed in terms of the correlators of the electric and magnetic fields for planar geometries yields then correctly the Casimir pressure.Comment: Simple latex file: six pages, no figure

Remarks on the conservation of mechanical energy in introductory mechanics

We discuss the work-kinetic energy theorem and the mechanical energy conservation theorem in the context of general physics courses. The motivation is the fact that all modern texts on introductory mechanics show the same conceptually dangerous statement that besides obliterating the concept of mechanical work, diminishing the importance of the work-kinetic energy theorem, leads to erroneous applications of the energy conservation theorem and at the same eliminates its relationship with the principle of the conservation of the mechanical momentum.Comment: Latex file, 8 pages, no figures; typos correcte

An alternative calculation of the Casimir energy for kappa-deformed electrodynamics

A simple, but effcient way of calculating regularized Casimir energies suitable for non-trivial frequency spectra is briefly described and applied to the case of a kappa-deformed scalar field theory. The results are consistent with the ones obtained by other means.Comment: Four pages, latex file. Submitted for the Proceedings of the XXIV Brazilian National Meeting on Particles and Fields held in Caxambu MG, Brazil, September 30 -- October 4, 200

An English translation o Bertrand's theorem

A beautiful theorem due to J. L. F. Bertrand concerning the laws of attraction that admit bounded closed orbits for arbitrarily chosen initial conditions is translated from French into English.Comment: This is English version of a beautiful theorem due to Joseph Bertrand; simple latex file, no figures, six page