The angular momentum of a classical electromagnetic plane wave of arbitrary extent is predicted to be, on theoretical grounds, exactly zero. However, finite sections of circularly polarized plane waves are found experimentally to carry angular momentum and it is known that the contribution to the angular momentum arises from the edges of the beam. A mathematical model is described that gives a quantitative account of this effect and resolves the paradox.
A capacitor paradox is an electromagnetic problem designed to show the limits of circuit theory which considers the connection of two ideal capacitors, one charged and the second discharged. A blind solution to this problem leads to the non-conservation of energy and, thus, to a paradox. In this text an attempt is made to isolate the inductance part of the problem in the form of wave-guiding phenomenon, providing yet another point of view of this intriguing educational problem.
It is shown that the famous paradox of two charged capacitors is successfully resolved if all the energy changes in the system are properly considered when some of the charges are transferred from one capacitor to the other. It happens so even when the connecting wire has an identically zero resistance, giving rise to no Ohmic losses in the wire. It is shown that in such a case the "missing energy" goes into the kinetic energy of conducting charges. It is shown that radiation plays no significant role in resolving the paradox. The problem can be formulated and successfully resolved in a novel …
Mechanical angular momentum is not conserved in systems involving electromagnetic fields with non-zero electromagnetic field angular momentum. Conservation is restored only if the total (mechanical and field) angular momentum is considered. Previous studies have investigated this effect, known as "Feynman's Electromagnetic Paradox" or simply "Disk Paradox" in the context of idealized systems (infinite or infinitesimal solenoids and charged cylinders etc). In the present analysis we generalize previous studies by considering more realistic systems with finite components and demonstrating explic…
The incorporation of a relativistic momentum of a nonelectromagnetic nature into macroscopic problems of electrodynamics obviates the lack of correspondence between the electromagnetic mass and the electromagnetic momentum of macroscopic bodies, allowing, in particular, the resolution of the well-known 4/3 paradox.
It is pointed out that Coleman and Van Vleck make a major blunder in their discussion of the Shockly-James paradox by designating relativistic hidden mechanical momentum as the basis for resolution of the paradox. This blunder has had a wide influence in the current physics literature, including erroneous work on the Shockley-James paradox, on Mansuripur's paradox, on the motion of a magnetic moment, on the Aharonov-Bohm phase shift, and on the Aharonov-Casher phase shift. Although hidden mechanical momentum is indeed dominant for non-interacting particles moving in a closed orbit under the in…
In this work we suggest very simple solution of the two capacitors paradox in the completely ideal (without any electrical resistance or inductive) electrical circuit. Namely, it is shown that electrical field energy loss corresponds to works done by electrical fields of both capacitors by movement of the electrical charge. It is all and nothing more (some dissipation processes, e.g. Joule heating and electromagnetic wave emission effects) is necessary. Additionally, we shortly demonstrate a simple mechanical analogy of mentioned paradox and its solution. Concretely we consider two water bucke…
Maxwell's equations are formulated in arbitrary moving frames by means of tetrad fields, which are interpreted as reference frames adapted to observers in space-time. We assume the existence of a general distribution of charges and currents in an inertial frame. Tetrad fields are used to project the electromagnetic fields and sources on accelerated frames. The purpose is to study several configurations of fields and observers that in the literature are understood as paradoxes. For instance, are the two situations, (i) an accelerated charge in an inertial frame, and (ii) a charge at rest in an …
In this Chapter the time-domain analysis of the velocity of the electromagnetic field pulses generated by a spatially compact source in free space is presented. Recent simulations and measurements of anomalous superluminal, subluminal, and negative velocities are discussed. It is shown that such velocities are local and instantaneous in nature and do not violate either causality or special relativity. Although these effects are mainly confined to the near- and intermediate-field zones, some of them seem paradoxical and still lack adequate physical interpretation.
We discuss here the famous paradox of a continuous power drainage from the source at the input of an otherwise lossless infinite transmission line. The solution of the paradox lies in the realization that in an open-circuit finite transmission line/ladder network, there is an incident as well as a reflected wave and the input impedence is determined by the superposition of both waves. It is explicitly shown that the reactive input impedance of even a single block, comprising say a simple LC circuit, is determined at all driving frequencies from the superposition of incident and reflected waves…
The electromagnetic energy $U_{em}$ stored in the magnetic field of an ideal solenoid at rest appears for a moving observer as $U'_{em} $, a sum of magnetic and electric energies satisfying: $U'_{em} > γU_{em}$. We explain this seemingly paradoxical result calculating the stresses in the solenoid structure and showing that the total energy of the solenoid transforms by the expected relativistic factor $γ$.
A very simple system like a parallel-plate capacitor reveals striking features when we examine the peculiar phenomena appearing when it is moving at low speed in different directions. Both hidden momentum and hidden energy appear and their addition, with their sign, to the corresponding electromagnetic component results in the expected ordinary kinetic momentum or energy of the electrostatic mass equivalent. What's happening is that passing from one inertial reference frame to another, part of the energy or momentum is transferred from the electromagnetic component to the material part of the …
A model calculation using the Darwin Lagrangian is carried out for a magnet consisting of two current-carrying charges constrained by centripetal forces to move in a circular path in the presence of the electric field from a distant external point charge. In the limit that the magnet's two charges are non-interacting, the calculation recovers the only valid calculation for hidden mechanical momentum. However, if the magnet's charges are mutually interacting, then there is internal electromagnetic linear momentum associated with the perturbed magnet's electrostatic charge distribution and the m…
