scholarly journals FORCES BETWEEN ELECTRIC CHARGES IN MOTION: RUTHERFORD SCATTERING, CIRCULAR KEPLERIAN ORBITS, ACTION-AT-A-DISTANCE AND NEWTON'S THIRD LAW IN RELATIVISTIC CLASSICAL ELECTRODYNAMICS

2008 ◽  
Vol 23 (02) ◽  
pp. 327-351 ◽  
Author(s):  
J. H. FIELD
Keyword(s):  
Special Relativity ◽  
Small Angle ◽  
Classical Electrodynamics ◽  
Classical Electromagnetism ◽  
Newtonian Gravitation ◽  
Keplerian Orbits ◽  
Rutherford Scattering ◽  
Action At A Distance ◽  
Electrodynamic Theory ◽  
Third Law

Standard formulae of classical electromagnetism for the forces between electric charges in motion derived from retarded potentials are compared with those obtained from a recently developed relativistic classical electrodynamic theory with an instantaneous intercharge force. Problems discussed include small angle Rutherford scattering, Jackson's recent "torque paradox" and circular Keplerian orbits. Results consistent with special relativity are obtained only with an instantaneous interaction. The impossibility of stable circular motion with retarded fields in either classical electromagnetism or Newtonian gravitation is demonstrated.

Relativistic analysis of application of Helmholtz theorem to classical electrodynamics

2015 ◽  
Vol 7 (1) ◽  
pp. 1297-1308
Author(s):  
Andrew Chubykalo ◽  
R. Alvarado-Flores ◽  
A. Espinoza
Keyword(s):  
Special Relativity ◽  
Gauge Transformation ◽  
Classical Electrodynamics ◽  
Invariant Solutions ◽  
Helmholtz Theorem ◽  
Action At A Distance ◽  
The Relationship ◽  
Relativistic Analysis

In this work we discuss the relationship between the instantaneous-action-at-a-distance solutions of Maxwell’s equations obtained using Helmholtz theorem and the Lorentz’s invariant solutions of the same equations obtained using Special Relativity postulates. We show that Special Relativity postulates are not consistent with Helmholtz’s theorem in the presence of charges and currents, but in the vacuum, without charges and currents, Helmholtz’s theorem and Special Relativity agree because the instantaneous-action-at-a-distance solutions can be eliminated using a gauge transformation.

On the Equivalence of Physical Theories

2021 ◽  
pp. 192-230
Author(s):  
Jill North
Keyword(s):  
Quantum Mechanics ◽  
Special Relativity ◽  
Classical Electromagnetism ◽  
Classical Physics ◽  
Newtonian Gravitation ◽  
The World ◽  
Metaphysical Equivalence ◽  
Theoretical Equivalence

This chapter argues against formal accounts of theoretical equivalence in physics. It defends the importance of a theory’s picture of the world and its explanations of the phenomena, drawing on examples from classical physics, Newtonian gravitation, classical electromagnetism, special relativity, and quantum mechanics. The discussion draws a distinction between metaphysical equivalence and informational equivalence and argues that these are equally important to the equivalence of physical theories. The chapter concludes that there are fewer cases of wholly equivalent theories in physics than usually thought. However, this is not a problem, for it is still possible to talk about the various respects in which physical theories are, or are not, equivalent to one another.

Electromagnetism and special relativity

2018 ◽  
Author(s):  
J. Pierrus
Keyword(s):  
Electromagnetic Field ◽  
Special Relativity ◽  
Point Charge ◽  
Reference Frames ◽  
Classical Electrodynamics ◽  
Covariant Form ◽  
Field Tensor ◽  
Electromagnetic Field Tensor ◽  
Preferred Reference Frame ◽  
Physical Quantities

In 1905, when Einstein published his theory of special relativity, Maxwell’s work was already about forty years old. It is therefore both remarkable and ironic (recalling the old arguments about the aether being the ‘preferred’ reference frame for describing wave propagation) that classical electrodynamics turned out to be a relativistically correct theory. In this chapter, a range of questions in electromagnetism are considered as they relate to special relativity. In Questions 12.1–12.4 the behaviour of various physical quantities under Lorentz transformation is considered. This leads to the important concept of an invariant. Several of these are encountered, and used frequently throughout this chapter. Other topics considered include the transformationof E- and B-fields between inertial reference frames, the validity of Gauss’s law for an arbitrarily moving point charge (demonstrated numerically), the electromagnetic field tensor, Maxwell’s equations in covariant form and Larmor’s formula for a relativistic charge.

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.

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