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Faraday and Maxwell conceived the electrostatic and magnetostatic fields as lines of force filling the space around charges and currents, with or without matter. They also established that there are tensions along the lines of force, and compressions around these lines. These ideas are formalized with a stress tensor, whose divergence is a force density. We follow these ideas to show the origin of the electric forces that arise in the case of a dielectric slab partially introduced into a parallel-plate capacitor, and the origin of the magnetic forces that arise in the case of a magnetizable bar partially introduced into a solenoid. We find that these forces have their origin in the abrupt change in permittivity and permeability which produce a difference of pressures at interfaces. This approach permits us to analyze the similarities and differences between both cases. Advanced undergraduate and graduate students can get interesting insights into the electromagnetic forces exerted by electrostatic and magnetostatic fields in vacuum and matter. Faraday y Maxwell concibieron los campos electrostáticos y magnetostáticos como líneas de fuerza llenando el espacio alrededor de cargas y corriente, con o sin materia. Ellos establecieron que hay tensiones a lo largo de las líneas de fuerza, y compresiones alrededor de estas líneas. Estas ideas se formalizan con el tensor de esfuerzos, cuya divergencia es una densidad de fuerza. Nosotros seguimos estas ideas para mostrar el origen de las fuerzas eléctricas que surgen cuando una barra de dieléctrico se introduce parcialmente en un condensador de placas paralelas, y el origen de las fuerzas magnéticas que surgen en el caso de una barra magnetizable parcialmente introducida en un solenoide. Encontramos que estas fuerzas tienen su origen en el cambio abrupto en la permitividad y permeabilidad que produce una diferencia de presiones en la interface. Este enfoque nos permite analizar las similitudes y diferencias entre ambos casos. Los estudiantes no graduados y graduados pueden adquirir una percepción interesante sobre las fuerzas electromagnéticas ejercidas por campos electrostáticos y magnetostáticos en el vacío y en la materia

Though it is generally accepted that electromagnetic radiation fields possess energy and linear and angular momentum, the adscription of these properties to static and quasi-static fields rises some doubts. Some authors consider that in electrostatics the concept of field is superfluous, or that action-at-a-distance and field are equivalent views. However, the interpretation of Poynting’s vector divided by c 2 as a momentum density is consistent and necessary for the conservation laws to hold, even in static conditions. The Feynman paradox exhibits the necessity of assigning linear and angular momentum to static and quasi-static fields, showing in this way that the points of view of action-at-a-distance and field are not equivalent. In the present work we do not intend to present a revision of the literature on this subject, but to show that the concept of hidden momentum is useful to solve the paradox, and we show that it is part of a momentum balance equation derived directly from the macroscopic Maxwell equations. Another consequence of this balance equation is that, in static conditions, the momentum associated to Poynting’s vector equals the hidden momentum and cancels it. Graduate students and researchers interested in conceptual problems of electromagnetism will find a firm foundation of the concept of hidden momentum and an alternative view of the paradox.

A silicalite-1 tubular membrane was prepared on the inner surface of a porous α-alumina support. Helium permeation at different feed volumetric flows (11–41 mL/min) with different sweep flow rates (9–90 mL/min) at STP conditions was measured. The molar fraction was obtained as a function of the residence time ratio. The influences of the geometric parameters of the tubular system and the feed flow rates on the permeation through the membrane were investigated. The dependence of the permeances with the residence time ratio was experimentally obtained and we propose that this dependence is a useful design criterion for tubular membrane permeation systems. The best results in this work were obtained for Q He,in /Q N2,in = 0.22 for V SS /V TS = 7.3. Also, the data showed that an appropriate combination of the flows and the area sections of the system resulted in an optimum value for the Peclet number of 0.3. The experimental data were reproduced by numerically solving the Maxwell–Stefan equations under the assumption that transport across the membrane can be modeled in terms of a Robin-type boundary condition.

In this work we discuss the trick of eliminating infinite potential of reference arguing that it corresponds to a constant of integration, in the problem of determining the electrostatic potential of an infinite line of charge with uniform density, and show how the problem must be tackled properly. The usual procedure is confusing for most students of undergraduate courses, basic or intermediate.

We clarify the contribution of Ragusa and Lazo (2004 Eur. J. Phys. 25 127–31) to the problem of covariance of electromagnetic momentum as given by Poynting's vector and the associated problem of the 4/3 in the electromagnetic mass. In particular, we note that the authors are not conscious of von Laue's theorem which makes their discussion mostly unnecessary.

In order to understand the rise of runaway solutions in the radiation reaction problem a mechanical model is used. An alternative demonstration of Daboul’s theorem, through Hurwitz’s criterion, is given. The origin of runaway solutions in electrodynamics is discussed. They arise when the particle has a negative mechanical mass or when approximations are used in the equation of motion. In the 1-dimensional mechanical model an exact and linear equation of motion for the particle is obtained, the corresponding exact solution is again runaway when the mechanical mass is negative. The exact solution is not runaway when the mechanical mass is positive. However, the use of approximations leads to an equation of motion which has runaway solutions. It is exhibited that the use of approximations in the 3-dimensional mechanical model is completely necessary because the general equation of motion for the particle is non-linear. The analysis of this case proceeds in a very similar way to the one carried out in electrodynamics. This means that the number of dimensions also plays an important role in the analysis.

It is shown that the condition υ > υp (ω), which is necessary in order to trigger the Vavilov-Cherenkov effect, determines the interval of radiated frequencies and it alone cannot establish a strong restriction to the velocity of the particle. It is exhibited that it is possible to define a general lower bound for the velocity of the particle, which does not depend on the frequency when both, a specific response of the medium is taken into account and the mentioned condition is considered. The minimum value of the phase velocity of light in the medium determines the existence of such general lower bound.

An alternative approach to analyze the nonrelativistic quantum dynamics of a rigid and extended charged particle taking into account the radiation reaction is discussed with detail. Interpretation of the field operators as annihilation and creation ones, theory of perturbations and renormalization are not used. The analysis is carried out in the Heisenberg picture with the electromagnetic field expanded in a complete orthogonal basis set of functions which allows the electromagnetic field to satisfy arbitrary boundary conditions. The corresponding coefficients are the field operators which satisfy the usual commutation relations. A nonlinear equation of motion for the charged particle is obtained. A careful consideration of the quantum effects allows the derivation of a linear equation of motion which is free of both runaway solutions and preacceleration, even for a point charge. Also, the electromagnetic mass, which is defined as the coefficient of the acceleration operator, vanishes for a point particle. However, this does not mean that the results are free of ambiguities which are exhibited and discussed.

In this paper the analysis of the classical dynamics of a charged particle is carried out without considering that the electromagnetic field necessarily goes to zero at infinity. A quite general non-linear equation of motion is obtained for an extended charged particle valid for any distribution of charge in the particle and for an electromagnetic field satisfying any boundary conditions. Some common approximations are analyzed with detail to determine how the usual difficulties arise.

The correct definition of electromagnetic momentum in matter, either Abraham's g A = (1/4πc) (E × H), or Minkowski's g M = (1/4πc) (D × B) has been a theme of controversy for a century. Therefore, we can find those who favor one or the other of these proposals. We present here an alternative view, considering that both of the aforementioned equations are equivalent since they pertain to different balance equations derived from the macroscopic Maxwell equations. This is done through their application to a device proposed by Lai in 1980, and recovering his results. Advanced undergraduate and graduate students can find in this work an introduction to a controversial issue and an alternative point of view about it.

In this paper the Vavilov-Cherenkov radiation produced by an electromagnetic pulse propagating, unchanged in shape, inside a medium is analysed. The electromagnetic pulse induces a polarization charge which moves inside the medium with the group velocity. This polarization charge induces time-dependent elemental dipoles in the material medium. If the group velocity is greater than the phase velocity of light in such a medium there is a coherent superposition of the radiation emitted by each elemental dipole that gives rise to Vavilov-Cherenkov radiation. Two methods to obtain the energy spectrum are developed.

The Dirac equation, with minimal coupling, is analysed in order to show that the Zitterbewegung (rapid oscillatory motion) also arises when a static and uniform magnetic field is taken into account. The corresponding equations of motion are solved in the Heisenberg picture with the weak-field approximation.

We analyze some features of the electrodynamics of dual charges and we derive an expression for the self-torque in a simple model of extended dual charge, taking into account, consistently, the retarded condition we compare our results with those obtained for electric or magnetic charges only. The behaviour of a dual charge distribution is radically different from the behaviour of a purely electric or magnetic one.

A proper handling of retarded quantities leads us to a systematic derivation of the Lorentz- Dirac equation. Our basic assumption is that the Lorentz force FΜΝυΝ,where FΜΝ is the electromagnetic field produced by the charge itself, is the radiation reaction force. We exhibit the contribution of each term of FΜΝ to the Lorentz-Dirac equation.

In this work we analyse the Cherenkov effect for non-rotating extended charges. We obtain the energy radiated per unit path length per unit frequency by the charge facing the Cherenkov effect as a radiation reaction problem. The underlying idea is to consider that the power radiated by the charge is equal to the work done by the radiation reaction force. Our results are equal to those obtained using other methods (seeBuskirk F. R. andNeighbours J. R.,Phys. Rev.,28 (1983) 1531;Smith G. S.,Am. J. Phys.,61 (1993) 147;Jackson J. D.,Classical Electrodynamics (Wiley, New York, N.Y.) 1962, pp. 494–499, 783). In the limit of point particle we recover the usual results of the Cherenkov effect.

We review the idea of the generation of time-dependent elemental dipoles in a material medium due to a point charge moving with constant velocity inside it. We obtain that if the velocity of the point charge is greater than the velocity of light in such medium, that is nu >c/ square root epsilon , there is a coherent superposition of the radiation emitted by each elemental dipole; we identify the total coherent radiation as the Cherenkov radiation.

A Hamiltonian approach is presented to study the two dimensional motion of damped electric charges in time dependent electromagnetic fields. The classical and the corresponding quantum mechanical problems are solved for particular cases using canonical transformations applied to Hamiltonians for a particle with variable mass. The Green's function is constructed and, from it, the motion of a Gaussian wave packet is studied in detail., Comment: 14 pages, 4 figures, misprints and figures corrected

We make a thorough non-covariant analysis of the derivation of the equation of motion for a charged particle, including radiation reaction, by means of a simple model for the charge: a dumbbell. This model and our method to expand retarded quantities, based on complex-variable theory, allow us to avoid some of the usual approximations, so we can show several features of the radiation reaction problem.

We present a model of a nematic liquid crystal cell to describe the first and final stages of the reorientation process induced by the action of an obliquely incident optical field. The presence of hydrodynamic backflows associated with the reorientation in both, a homeotropic and a planar geometry, is explicitly taken into account. We study the effect produced by the backflows on two specific optical properties of the nematic, namely, its phase change and its inverse focal length. These quantities are calculated analytically and evaluated for the nematic phase of CBOOA. It is shown that for a homeotropic arrangement, hydrodynamic backflows may produce a significant, and in principle measurable, change as high as 75% in these properties.