Physics

In this article we have illustrated how is possible to formulate Maxwell's equations in vacuum in an independent form of the usual systems of units. Maxwell's equations, are then specialized to the most commonly used systems of units: International system of units (SI), Gaussian normal, Gaussian rational (Heaviside-Lorentz), C.G.S. (electric), C.G.S. (magnetic), natural normal and natural rational. Both, the differential and the integral formulations of Maxwell's equations in vacuum, are illustrated. Also the covariant formulation of Maxwell's equation is illustrated.

The electromagnetic scattering from interconnections of high-permittivity dielectric thin wires with sizes smaller than (or almost equal to) the operating wavelength is investigated. A simple lumped element model for the polarization current intensities induced in the wires is proposed. The circuit elements are capacitances and inductances between the wires. An analytical expression for the induced polarization currents in terms of the magneto-quasistatic current modes is obtained. The connection between the spectral properties of the loop inductance matrix and the network's resonances is established. The number of the allowed current modes and resonances is deduced from the topology of the circuit's digraph. The coupling to radiation is also included, and the radiative frequency shifts and the quality factors are derived. The introduced concept and methods may find applications both at the microwaves and in nanophotonics.

The discovery of Electromagnetism by Oersted (1820) started an 'extraordinary decennium' ended by the discovery of electromagnetic induction by Faraday (1831). During this decennium, in several experiments, the electromagnetic induction was there, but it was not seen or recognized. Faraday built up a local theory of electromagnetic induction based on the idea that there is an induced current when there is an intersection between lines of magnetic force and a conductor in relative motion. In 1873, Maxwell, within a Lagrangian description of electric currents, wrote down a 'general law of electromagnetic induction' in which a fundamental role is played by the vector potential. A modern reformulation of Maxwell's general law is based on the definition of the induced emf as the line integral of the Lorentz force on a unit positive charge and the use of the equation that relates the electric field to the potentials. Maxwell's general law has been rapidly forgotten; instead, the "flux rule" has deeply taken root. The "flux rule" not always yields the correct prediction, it does not say where the induced emf is localized, it requires ad hoc choices of the integration paths. It is not a physical law but only a calculation tool. To understand why Maxwell's `general law' has been forgotten, also a sample of representative textbooks, distributed over about a century, has been analyzed. In this framework, a part of the paper deals with the idea of rotating lines of magnetic force, falsified by Faraday, but common in the first decades of the Twentieth century and astonishingly resumed recently. It is shown that this hypothesis is incompatible with Maxwell - Lorentz - Einstein electromagnetism and that it is falsified also by recent experiments. Finally, the electromagnetic induction in some recent research papers is briefly discussed.

For an oscillating electric dipole in the shape of a small, solid, uniformly-polarized, spherical particle, we compute the self-field as well as the radiated electromagnetic field in the surrounding free space. The assumed geometry enables us to obtain the exact solution of Maxwell's equations as a function of the dipole moment, the sphere radius, and the oscillation frequency. The self field, which is responsible for the radiation resistance, does not introduce acausal or otherwise anomalous behavior into the dynamics of the bound electrical charges that comprise the dipole. Departure from causality, a well-known feature of the dynamical response of a charged particle to an externally applied force, is shown to arise when the charge is examined in isolation, namely in the absence of the restraining force of an equal but opposite charge that is inevitably present in a dipole radiator. Even in this case, the acausal behavior of the (free) charged particle appears to be rooted in the approximations used to arrive at an estimate of the self-force. When the exact expression of the self-force is used, our numerical analysis indicates that the impulse-response of the particle should remain causal.

A uniformly-charged spherical shell of radius R , mass m , and total electrical charge q , having an oscillatory angular velocity Ω(t) around a fixed axis, is a model for a magnetic dipole that radiates an electromagnetic field into its surrounding free space at a fixed oscillation frequency ω . An exact solution of the Maxwell-Lorentz equations of classical electrodynamics yields the self-torque of radiation resistance acting on the spherical shell as a function of R , q , and ω . Invoking the Newtonian equation of motion for the shell, we relate its angular velocity Ω(t) to an externally applied torque, and proceed to examine the response of the magnetic dipole to an impulsive torque applied at a given instant of time, say, t=0 . The impulse response of the dipole is found to be causal down to extremely small values of R (i.e., as R→0 ) so long as the exact expression of the self-torque is used in the dynamical equation of motion of the spherical shell.

The self-force of a point charge moving on a rectilinear trajectory is obtained, with no need of any explicit removal of infinities, as the negative of the time rate of change of the momentum of its retarded self-field.

Thermostatics of CARNOT engines has been extended by more recent research based on endo-reversible model. Our model assumes exo-reversibility but endo-irreversibility to determine new upper-bound to thermomechanical conversion. We propose a functional expression of entropy production related to transformation cycle durations. This approach analyses the energy, entropy and power consequences. We introduce a new concept of entropy production actions that results in three optimums : maximum energy related to transformation durations, maximum energy associated with equipartition of entropy actions, optimal power for given period cycle.

The Bertrand theorem concluded that; the Kepler potential, and the isotropic harmonic oscillator potential are the only systems under which all the orbits are closed. It was never stressed enough in the physical or mathematical literature that this is only true when the potentials are independent of the initial conditions of motion, which, as we know, determine the values of the constants of motion E and L . In other words, the Bertrand theorem is correct only when V≡V(r)≠V(r,E,L) . It has been derived in this work an alternative orbit equation, which is a substitution to the Newton's orbit equation. Through this equation, it was proved that there are infinitely many energy angular momentum dependent potentials V(r,E,L) that lead to closed orbits. The study was done by generalizing the well known substitution r=1/u in Newton's orbit equation to the substitution r=1/s(u,E,L) in the equation of motion. The new derived equation obtains the same results that can be obtained from Bertrand theorem. The equation was used to study different orbits with different periodicity like second order linear differential equation periodicity orbits and Weierstrasse periodicity orbits, where interestingly it has been shown that the energy must be discrete so that the orbits can be closed. Furthermore, possible applications of the alternative orbit equation were discussed, like applications in Bohr-Sommerfeld quantization, and in stellar kinematics.

Inhomogeneous small-amplitude plane waves of (complex) frequency ω are propagated through a linear dissipative material which displays hereditary viscoelasticity. The energy density, energy flux and dissipation are quadratic in the small quantities, namely, the displacement gradient, velocity and velocity gradient, each harmonic with frequency ω , and so give rise to attenuated constant terms as well as to inhomogeneous plane waves of frequency 2ω . The quadratic terms are usually removed by time averaging but we retain them here as they are of comparable magnitude with the time-averaged quantities of frequency ω . A new relationship is derived in hereditary viscoelasticity that connects the amplitudes of the terms of the energy density, energy flux and dissipation that have frequency 2ω . It is shown that the complex group velocity is related to the amplitudes of the terms with frequency 2ω rather than to the attenuated constant terms as it is for homogeneous waves in conservative materials.

We apply a simple decomposition to the energy of a moving particle. Based on this decomposition, we identify the potential and kinetic energies, then use them to give general definitions of momentum and the various kinds of forces exerted on the particle by fields, followed by the generalization of Newton's second law to accomodate these generally defined forces. We show that our generalization implies the Lorentz force law as well as Lagrange's equation, along with the usually accepted Lagrangian and the associated velocity dependent potential of a moving charged particle.