Moving Point Charge Research Articles

Model estimation of the polarization forces generated by a moving point charge in carbon nanotubes

Two models of polarization forces generated inside a carbon nanotube by a moving point charge are considered. In the first model, carbon atoms are replaced by equivalent spherical dielectrics; in the second model, the carbon nanotube is replaced by a homogeneous hollow dielectric tube.

On the Field of a Moving Charge

An electro-magnetic field appearing in a laboratory due to moving charges has unusual properties. In particular, such a field of kinematical origin does not obey the wave equation with a non-relativistic velocity instead of light speed; so its movement resembles that of a rigid body. The present article deals with kinematical field in two extreme cases: non-relativistic and relativistic. A non-standard approach to the familiar laws deduced from a primary principle, on the one hand, and a new idea of the direct experimental verification for the well-known formula concerning the field of a uniformly moving point charge, on the other, are suggested.

Charge/mass dynamic structure factors of water and applications to dielectric friction and electroacoustic conversion

We determine time correlation functions and dynamic structure factors of the number and charge density of liquid water from molecular dynamics simulations. Using these correlation functions we consider dielectric friction and electro-acoustic coupling effects via linear response theory. From charge-charge correlations, the drag force on a moving point charge is derived and found to be maximal at a velocity of around 300 m/s. Strong deviations in the resulting friction coefficients from approximate theory employing a single Debye relaxation mode are found that are due to non-Debye-like resonances at high frequencies. From charge-mass cross-correlations the ultrasonic vibration potential is derived, which characterizes the conversion of acoustic waves into electric time-varying potentials. Along the dispersion relation for normal sound waves in water, the ultrasonic vibration potential is shown to strongly vary and to increase for larger wavelengths.

Space–time diagram approach in derivation of Lienard–Wiechert potential for a moving point charge

In classical electrodynamics, electric and magnetic fields at a point due to moving charges are calculated from the electric scalar potential and magnetic vector potential. For a moving point charge, this potential is known as Lienard–Wiechert potential and is derived in many different ways in textbooks. In this paper, we derive the retarded Lienard–Wiechert potential in a new graphical manner using space–time diagrams so that the derivation becomes more appealing and we can visualize the reason for the presence of an additional velocity-dependant factor in the denominator of the expression for the Lienard–Wiechert potential. The derivation is valid even for charged particles moving at relativistic speeds.

TE TM electromagnetic fields and potentials

TE, TM harmonic Fields are obtained from Potentials in cartesian and cylindrical coordinadtes. In both cases and, in presence of charges and currents, these potentials for the Lorentz gauge, are solutions of 2D in homogeneous Helmholtz equations, solved with the help of Green functions. Solutions are made explicit for currents generated by moving point charges.

Polarizability of screened Coulomb potential

We have obtained the co-ordinate space wavefunction by the inverse Fourier transform of the momentum space wavefunction for the screened Coulomb potential, $$ V\left( r \right)\; = \; - {\text{e}}^{{{ - }\mu {\text{r}}}} /{\text{r}} $$ , problem. The dipole polarizability αd is evaluated in the closure approximation. In this approximation $$ \alpha_{\text{d}} \; = \;\frac{2}{3}\frac{{\langle r^{2} \rangle }}{\Updelta } $$ , where ∆ is the mean excitation energy which is related to the information entropy via Bethe theory for the stopping cross-section for a moving point charge interacting with a bound quantum mechanical system. We find that αd increases with μ. Near the Coulomb limit, we find $$ \alpha_{\text{d}} \left( \mu \right)\; = \,\alpha_{\text{H}} \left( {1\; + \;2.9245 \mu^{2} } \right), $$ where α H is the polarizability of hydrogen atom. Results have been compared with the recent theoretical works.

Sources, potentials and fields in Lorenz and Coulomb gauge: Cancellation of instantaneous interactions for moving point charges

We investigate the coupling of the electromagnetic sources (charge and current densities) to the scalar and vector potentials in classical electrodynamics, using Green function techniques. As is well known, the scalar potential shows an action-at-a-distance behavior in Coulomb gauge. The conundrum generated by the instantaneous interaction has intrigued physicists for a long time. Starting from the differential equations that couple the sources to the potentials, we here show in a concise derivation, using the retarded Green function, how the instantaneous interaction cancels in the calculation of the electric field. The time derivative of a specific additional term in the vector potential, present only in Coulomb gauge, yields a supplementary contribution to the electric field which cancels the gradient of the instantaneous Coulomb gauge scalar potential, as required by gauge invariance. This completely eliminates the contribution of the instantaneous interaction from the electric field. It turns out that a careful formulation of the retarded Green function, inspired by field theory, is required in order to correctly treat boundary terms in partial integrations. Finally, compact integral representations are derived for the Liénard–Wiechert potentials (scalar and vector) in Coulomb gauge which manifestly contain two compensating action-at-a-distance terms.

A Study of Divergence on still Point Charge and Moving Point Charge in the Vacuum Passive Space

The divergence of still point charge is zero in the vacuum passive space, but the divergence of moving point charge is not zero. In order to make the divergence of moving point charge in the vacuum passive space being zero, we must choose the coordinate in which moving point charge has the same velocity with the coordinate as a reference system.

On the holomorphic solutions of Hamiltonian equations of motion of point charges

The Maxwell–Lorenz system of electromagnetic fields interacting with charged particles (point charges) is studied in the Darwin approximation in which the Lagrangian and Hamiltonian of the particles are not coupled with the field. The solution of the equation of motion of particles with approximate Darwin Hamiltonian is found in a finite time interval by using the Cauchy theorem. The components of this solution are represented as holomorphic functions of time.

Electromagnetic field of a moving charge in the presence of a left-handed medium

We analyze the electromagnetic field of a moving point charge in the presence of a 'left-handed' medium (LHM). First, the case of uniform motion of the charge in infinite LHM was considered. Using complex function theory methods, we decomposed the total field into a 'quasi-Coulomb' field, a wave field (Cherenkov radiation) and a 'plasma trace'. In addition, an effective numerical algorithm was developed for the total field computation, and typical plots were presented. It was shown that the wave field in LHM lags behind the charge more so than it does in ordinary medium. Furthermore, we investigated a charge intersecting the interface between vacuumlike medium and LHM. Asymptotic expressions for the field components were obtained and algorithms for their computation were developed. The spatial radiation can be separated into three distinct components, corresponding to ordinary transition radiation with a relatively large magnitude, Cherenkov radiation and reversed Cherenkov-transition radiation (RCTR). Rigorous conditions for generating RCTR were obtained: RCTR in the vacuum area was found to be the double threshold effect in both frequency and charge velocity domain. The RCTR decay in vacuum due to the losses in LHM was studied. Areas of the RCTR significance were determined and were found tomore » be sufficiently large for observation. Possible applications to the beam diagnostics and the characterization of metamaterials were suggested.« less

Hydration Dynamics at Femtosecond Time Scales and Angstrom Length Scales from Inelastic X-Ray Scattering

We use high resolution dynamical structure factor S(q,omega) data measured with inelastic x-ray scattering to reconstruct the Green's function of water, which describes its density response to a point charge, and provides a fundamental comparative model for solvation behavior at molecular time scales and length scales. Good agreement is found with simulations, scattering and spectroscopic experiments. These results suggest that a moving point charge will modify its hydration structure, evolving from a spherical closed shell to a steady-state cylindrical hydration "sleeve".

A Simplified Proof of the Relativistic Nature Behind Magnetism

The relativistic nature behind magnetic forces is well understood. It is commonly demonstrated via thought experiment by imagining a free charge in between a pair of moving capacitor plates. This paper presents a greatly simplified version of the same thought experiment, by deriving equivalent results from a system of two moving point charges. The derivation only requires knowledge of Coulomb's law, the Biot-Savart law, and the Lorentz force, and can therefore be readily presented to an introductory-level course in applied electromagnetics.

On magnetic fields generated in a dielectric half-space by a slowly moving point charge outside

A point charge moving with speed u ≪ c / n outside a non-dispersive dielectric half-space having refractive index n produces, inside the material, magnetic fields of the same order as and in fact larger than they would be in wholly empty space. The part of the field generated directly by the polarization currents is parallel to the surface, and has even parity with respect to it. For 1≪ n ≪ c / u , these fields are practically independent of n , and, by a remarkable coincidence, the same as the (already known) fields that the same charge would produce in a half-space occupied by material having high (but not infinite) ohmic conductivity.

Regularization of fields for self-force problems in curved spacetime: Foundations and a time-domain application

We propose an approach for the calculation of self-forces, energy fluxes and waveforms arising from moving point charges in curved spacetimes. As opposed to mode-sum schemes that regularize the self-force derived from the singular retarded field, this approach regularizes the retarded field itself. The singular part of the retarded field is first analytically identified and removed, yielding a finite, differentiable remainder from which the self-force is easily calculated. This regular remainder solves a wave equation which enjoys the benefit of having a non-singular source. Solving this wave equation for the remainder completely avoids the calculation of the singular retarded field along with the attendant difficulties associated with numerically modeling a delta function source. From this differentiable remainder one may compute the self-force, the energy flux, and also a waveform which reflects the effects of the self-force. As a test of principle, we implement this method using a 4th-order (1+1) code, and calculate the self-force for the simple case of a scalar charge moving in a circular orbit around a Schwarzschild black hole. We achieve agreement with frequency-domain results to ~ 0.1% or better.

An interpretation of the energy conservation law for a point charge moving in a uniform electric field

The standard interpretation of the energy conservation law accepted in the theory of electromagnetism maintains that a change in the field energy occurring in a volume is the sum of the energy increment in the volume due to the Poynting vector flow and the energy dissipated as heat in the interaction of charge carriers with the medium in which these carriers move. We show that the work done by an external electric field on a moving point charge is due to two sources: the energy arriving at the charge with the Poynting vector flow and a specific channel of energy supply to the charge originating from the interaction of the charge's field with the external field. Interestingly, at nonrelativistic charge velocities (v ≪ c), 2/3 of the energy is supplied by the Poynting vector flow and 1/3 by the second channel. In the ultrarelativistic case (v c), all of the energy comes with the Poynting vector flow.

Wake fields in the electron gas including transverse response

Relativistic electrons have transverse electric fields comparable in magnitude to the longitudinal fields. We determine the effects of transverse and longitudinal fields of a moving point charge subject to the dielectric response of a uniform electron gas, using Lindhard's longitudinal and transverse dielectric functions and, separately, the Drude dielectric function. The formalism of the transverse response is presented, including forms for the electromagnetic potentials of a point charge moving at a constant velocity in the Lorentz, Hamiltonian, and Coulomb gauges, how these are screened, and how the screening is affected by both the relevant dielectric functions and Maxwell's equations. The longitudinal fields have screening, resonance enhancement, or antiscreening depending upon the frequency in question. The transverse fields are always screened. Transverse fields dominate at large impact parameters, but longitudinal fields dominate for small impact parameters. The implications of the results for electron energy loss experiments in electron microscopy are discussed.

String formulation of space charge forces in a deflecting bunch

The force between two moving point charges, because of its inverse square law singularity, cannot be applied directly in the numerical simulation of bunch dynamics; radiative effects make this especially true for short bunches being deflected by magnets. This paper describes a formalism circumventing this restriction in which the basic ingredient is the total force on a point charge comoving with a longitudinally aligned, uniformly charged string. Bunch evolution can then be treated using direct particle-to-particle, intrabeam scattering, with no need for an intermediate, particle-in-cell, step. Electric and magnetic fields do not appear individually in the theory. Since the basic formulas are both exact (in paraxial approximation) and fully relativistic, they are applicable to beams of all particle types and all energies. But the theory is expected to be especially useful for calculating the emittance growth of the ultrashort electron bunches of current interest for energy recovery linacs and free-electron lasers. The theory subsumes coherent synchrotron radiation and centrifugal space charge force. Renormalized, on-axis, longitudinal field components are in excellent agreement with values from Saldin et al. [DESY Report No. DESY-TESLA-FEL-96-14, 1995; Nucl. Instrum. Methods Phys. Res., Sect. A 417, 158 (1998).]

The fields of a moving point charge: a new derivation from Jefimenko's equations

We give a derivation for the fields of a moving point charge from Jefimenko's equations without the usual cumbersome differentiation of retarded quantities.

Potentials of a uniformly moving point charge in the Coulomb gauge**This paper is written by V Hnizdo in his private capacity. No official support or endorsement by the Centers for Disease Control and Prevention is intended or should be inferred.

The Coulomb-gauge vector potential of a uniformly moving point charge is obtained by calculating the gauge function for the transformation between the Lorenz and Coulomb gauges. The expression obtained for the difference between the vector potentials in the two gauges is shown to satisfy a Poisson equation to which the inhomogeneous wave equation for this quantity can be reduced. The right-hand side of the Poisson equation involves an important but easily overlooked delta-function term that arises from a second-order partial derivative of the Coulomb potential of a point charge.

Nota sobre os potenciais de uma carga em movimento

Na maneira usual de se obter os potenciais de uma carga em movimento, os potenciais de Liénard-Wiechert, toma-se como ponto de partida os potenciais retardados, expressos em termos de uma distribuição volumétrica de carga. Argui-se aqui que aqueles potenciais podem também ser obtidos diretamente dos potenciais retardados de uma carga pontual, corrigidos por efeitos do tipo Doppler, característicos de grandezas propagadas e que são devidos ao movimento do emissor em relação ao ponto de observação.