Martin Rivas

An example of surface charge distribution on conductors carrying steady currents

In order to constrain electrons to move along ohmic conductors carrying steady currents, there must be a surface charge density that is usually very difficult to calculate. An approximate analytic expression for this surface charge density on a conducting square ring is presented here where the only source of emf is a changing external magnetic field. The corresponding electric field is determined and it is checked that the energy balance for this system holds.

δ -function converging sequences

We discuss the usefulness and physical interpretation of a simple and general way of constructing sequences of functions that converge to the Dirac delta function. The main result, which seems to have been largely overlooked, includes most of the δ-function converging sequences found in textbooks, is easily extended, and can be used to introduce many useful generalized functions to physics students with little mathematical background. We show that some interesting delta-function identities are simple consequences of the one discussed here. An illustrative example in electrodynamics is also analyzed, with the surprising result that the formalism allows as a limit an uncharged massless particle which creates no electromagnetic field, but has a nonzero electromagnetic energy–momentum tensor.

Linear momentum density in quasistatic electromagnetic systems

We discuss a couple of simple quasistatic electromagnetic systems in which the density of electromagnetic linear momentum can be easily computed. The examples are also used to illustrate how the total electromagnetic linear momentum, which may also be calculated by using the vector potential, can be understood as a consequence of the violation of the action–reaction principle, because a non-null external force is required to maintain constant the mechanical linear momentum. We show how one can avoid the divergence in the interaction linear electromagnetic momentum of a system composed by an idealization often used in textbooks (an infinite straight current) and a point charge.

Magnetic braking revisited

The braking force acting on a conducting disk rotating under the influence of an external magnetic field of axial symmetry is calculated in a quasi-static approximation and the role played by the charge distributions induced in the disk is shown. The two cases of infinite and finite radius are considered to analyze the influence of edge effects and we obtain a general expression for the braking torque when the magnetic field has axial symmetry. The particular case of a uniform external magnetic field is used to show the working of a simplified model of a cylindrical battery. Analytical results are compared with those obtained by other authors.

The dynamical equation of the spinning electron

We obtain by invariance arguments the relativistic and non-relativistic invariant dynamical equations of a classical model of a spinning electron. We apply the formalism to a particular classical model which satisfies Diracs equation when quantized. It is shown that the dynamics can be described in terms of the evolution of the point charge which satisfies a fourth-order differential equation or, alternatively, as a system of second-order differential equations by describing the evolution of both the centre of mass and centre of charge of the particle. As an application of the found dynamical equations, the Coulomb interaction between two spinning electrons is considered. We find from the classical viewpoint that these spinning electrons can form bound states under suitable initial conditions. Since the classical Coulomb interaction of two spinless point electrons does not allow for the existence of bound states, it is the spin structure that gives rise to new physical phenomena not described in the spinless case. Perhaps the paper may be interesting from the mathematical point of view but not from the point of view of physics.

A pure kinematical explanation of the gyromagnetic ratio g=2 of leptons and charged bosons

Abstract By analysing the structure of the spin operator, we give a pure kinematical explanation of the origin of the gyromagnetic ratio of elementary particles.

On generalized Boltzmann equations for reacting systems

A quantum-statistical treatment of chemical kinetics is presented which does not differ between non-reactive scattering and rearrangement processes. This treatment is done in such a way that the standard methods of nonequilibrium statistical mechanics become applicable. Kinetics equations of the Waldmann-Snider, and Wang Chang and Uhlenbeck type are derived for the reduced density operator of different species related to an homo-geneous, dilute gaseous system of the type AB+C⇌2AC+B⇌2BC+A. Global rate coefficients for the different rearrangement processes are defined and derived when starting with Waldmann-Snider type equations.

The atomic hypothesis: physical consequences

The hypothesis that matter is made of some ultimate and indivisible objects, together with the restricted relativity principle, establishes a constraint on the kind of variables we are allowed to use for the variational description of elementary particles. We consider that the atomic hypothesis not only states the indivisibility of elementary particles, but also that these ultimate objects, if not annihilated, cannot be modified by any interaction so that all allowed states of an elementary particle are only kinematical modifications of any one of them. Therefore, an elementary particle cannot have excited states. In this way, the kinematical group of spacetime symmetries not only defines the symmetries of the system, but also the variables in terms of which the mathematical description of the elementary particles can be expressed in either the classical or the quantum mechanical description. When considering the interaction of two Dirac particles, the atomic hypothesis restricts the interaction Lagrangian to a kind of minimal coupling interaction.

Falling elastic bars and springs

We analyze the initial motion of an elastic bar that is suddenly released after being hung from one end. The analytical solutions uncover some unexpected properties, which can be checked with a digital camera or camcorder in an alternative setup in which a spring is substituted for the bar. The model and the experiments are useful for understanding the similarities and differences between the elastic properties of bars and springs. Students can use the simple experiments to improve their understanding of elastic waves.

Surface charges and energy flow in a ring rotating in a magnetic field

An ohmic ring that rotates with constant angular velocity in an external uniform magnetic field is considered as a simple model for a current generator. Under the assumption that all quantities vary slowly in time, the lowest‐order approximation to the surface charge density is found. The flux of the Poynting vector through the loop surface is also computed. Unlike in the examples that are given in textbooks, this flux is not always incoming: It has the outgoing direction around the loop parts where the electrons are moving against electrostatic forces.