Classical electrodynamics: the equation of motion

1974 ◽  
Vol 76 (1) ◽  
pp. 359-367 ◽  
Author(s):  
P. A. Hogan
Keyword(s):  
Electromagnetic Field ◽  
Charged Particle ◽  
Scalar Field ◽  
World Line ◽  
External Electromagnetic Field ◽  
Equation Of Motion ◽  
The Self ◽  
Classical Electrodynamics ◽  
Field Equations ◽  
The World

In this paper we derive the Lorentz-Dirac equation of motion for a charged particle moving in an external electromagnetic field. We use Maxwell's electromagnetic field equations together with the assumptions (1) that all fields are retarded and (2) that the 4-force acting on the charged particle is a Lorentz 4-force. To define the self-field on the world-line of the charge we utilize a contour integral representation for the field due to A. W. Conway. This by-passes the need to define an ‘average field’. In an appendix the case of a scalar field is briefly discussed.

scholarly journals Classical electrodynamics without singularities

1948 ◽  
Vol 195 (1042) ◽  
pp. 323-336 ◽  
Keyword(s):  
World Line ◽  
Equations Of Motion ◽  
The Self ◽  
Classical Electrodynamics ◽  
Dirac Equations ◽  
Form Function ◽  
The World ◽  
Extended Charge ◽  
Electron Radius ◽  
Mass Component

It is shown that it is possible to construct a theory of the electron with an extended charge distribution in a Lorentz invariant way by introducing a four-dimensional form function. The electromagnetic field quantities reduce to those given by the ordinary theory at distances large compared with the electron radius r 0 , but remain finite on the world line. The equations of motion, after elimination ’of the self field, become integro-differential equations. In the case of small accelerations an expansion in powers of r 0 similar to that of Lorentz is obtained, in which only odd powers of r 0 occur. The first term endows the electron with a mass component of electromagnetic origin. For accelerations small compared with the characteristic frequency l/ r 0 of the electron, the Lorentz-Dirac equations are a good approximation; for larger accelerations, higher terms become important.

scholarly journals THE SELF-FORCE OF A CHARGED PARTICLE IN CLASSICAL ELECTRODYNAMICS WITH A CUTOFF

1999 ◽  
Vol 13 (03) ◽  
pp. 315-324 ◽  
Author(s):  
J. FRENKEL ◽  
R. B. SANTOS
Keyword(s):  
Charged Particle ◽  
Special Relativity ◽  
Point Charge ◽  
Equation Of Motion ◽  
The Self ◽  
Classical Electrodynamics ◽  
Exact Equation ◽  
Electromagnetic Mass ◽  
Self Force

We discuss, in the context of classical electrodynamics with a Lorentz invariant cutoff at short distances, the self-force acting on a point charged particle. It follows that the electromagnetic mass of the point charge occurs in the equation of motion in a form consistent with special relativity. We find that the exact equation of motion does not exhibit runaway solutions or non-causal behavior, when the cutoff is larger than half of the classical radius of the electron.

A Proposed Experiment of Direct Detecting of the Vector Potential within Classical Electrodynamics

1997 ◽  
Vol 11 (12) ◽  
pp. 531-540
Author(s):  
V. Onoochin
Keyword(s):  
Magnetic Field ◽  
Electromagnetic Field ◽  
Charged Particle ◽  
Vector Potential ◽  
Energy Exchange ◽  
Short Pulse ◽  
Classical Electrodynamics ◽  
Direct Influence ◽  
Ultra Short Pulse ◽  
The Magnetic Field

An experiment within the framework of classical electrodynamics is proposed, to demonstrate Boyer's suggestion of a change in the velocity of a charged particle as it passes close to a solenoid. The moving charge is replaced by an ultra-short pulse (USP), whose characteristics should depend on the current in the coil. This dependence results from the exchange of energy between the electromagnetic field of the pulse and the magnetic field within the solenoid. This energy exchange could only be explained, by assuming that the vector potential of the solenoid has a direct influence on the pulse.

PARAXIAL APPROXIMATION OF THE VLASOV-MAXWELL SYSTEM: LAMINAR BEAMS

1994 ◽  
Vol 04 (02) ◽  
pp. 203-221 ◽  
Author(s):  
A. NOURI
Keyword(s):  
Electromagnetic Field ◽  
Charged Particle ◽  
Initial Data ◽  
Global Existence ◽  
Local Existence ◽  
Sufficient Conditions ◽  
External Electromagnetic Field ◽  
Evolution System ◽  
Lagrangian Coordinates ◽  
Maxwell System

The Vlasov-Maxwell stationary system for charged particle laminar beams is studied with a paraxial model of approximation. It leads to a degenerate evolution system, which local existence is proved. Then, using lagrangian coordinates, with sufficient conditions on the initial data and the external electromagnetic field, it is shown that global existence is possible.

Braneworld mimetic f(R) gravity

2019 ◽  
Vol 16 (03) ◽  
pp. 1950042 ◽  
Author(s):  
Kourosh Nozari ◽  
Naser Sadeghnezhad
Keyword(s):  
Scalar Field ◽  
Recent Work ◽  
Friedmann Equation ◽  
Equation Of Motion ◽  
Einstein’S Field Equations ◽  
Field Equations ◽  
Einstein's Field Equations ◽  
Bulk Scalar Field ◽  
Codazzi Equations ◽  
Mimetic Gravity

Following our recent work on braneworld mimetic gravity, in this paper, we study an extension of braneworld mimetic gravity to the case that the gravitational sector on the brane is modified in the spirit of [Formula: see text] theories. We assume the physical 5D bulk metric in the Randall–Sundrum II braneworld scenario consists of a 5D scalar field (which mimics the dark sectors on the brane) and an auxiliary 5D metric. We find the 5D Einstein’s field equations and the 5D equation of motion of the bulk scalar field in this setup. By using the Gauss–Codazzi equations, we obtain the induced Einstein’s field equations on the brane. Finally, by adopting the FRW background, we find the Friedmann equation on the brane in this [Formula: see text] mimetic braneworld setup.

Nonrelativistic motion of a charged particle in an electromagnetic field

1998 ◽  
Vol 59 (3) ◽  
pp. 555-560
Author(s):  
C. J. McKINSTRIE ◽  
E. J. TURANO
Keyword(s):  
Electromagnetic Field ◽  
Charged Particle ◽  
Plane Wave ◽  
Particle Motion ◽  
Wave Amplitude ◽  
Equation Of Motion ◽  
Analytic Solutions

The nonrelativistic motion of a charged particle in the electromagnetic field of a plane wave is studied. New analytic solutions of the equation of motion are found that manifest the dependence of the period of the particle motion on the wave amplitude.

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