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The coulomb force and the Ampère force

✍ Scribed by Parry Moon; Domina Eberle Spencer


Publisher
Elsevier Science
Year
1954
Tongue
English
Weight
489 KB
Volume
257
Category
Article
ISSN
0016-0032

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✦ Synopsis


The paper presents a preliminary study of electrodynamics based on an equation for the force between moving but unaccelerated charges. It is proved that the unique equation for force between current elements, consistent with a summation of forces between charges and the Amp&re experiments, is Amp~re's original equation.

The usual "Ampere equation" given in modern textbooks, however, is not the equation used by AmpSre and cannot be derived from a force between moving charges. Since the modern treatment of the magnetic field stems from the so-called "Ampere equation," the entire electromagnetic theory obtained by the customary procedure is open to question.

I. INTRODUCTION

Early developments in electromagnetic theory were based on the force between charged particles (1). 3 The classical experiments (2) of Coulomb on the force between stationary charges were reported in 1785 and led to the well-known Coulomb equation. Gauss (1835) extended the equation to include the effect of motion of the charges (3). Grassmann (4) (1845), Weber (5) (1846), Helmholtz (6) (1873), Riemann (7) (1875), and others made contributions in the same spirit. Amp~re's equation ( 1823) for the force between current elements ( 8) is likewise free of the field concept. All this work was founded directly on experimental data, without the introduction of a magnetic field.

The early formulations were superseded by the Faraday-Maxwell idea of electric and magnetic fields ; and so successful were the Maxwell equations that the older formulation in terms of moving electric charges was almost forgotten. But the field equations encounter certain logical difficulties. In the i~rst place, they violate the classical principle that absolute velocities are meaningless. In Maxwell's formulation, motion is referred to a "stationary" aether, c is a velocity with respect to the aether, and the presence or absence of a magnetic field depends on motion with respect to the aether.

Einstein's famous paper of 1905, "Zur Elektrodynamik bewegter K6rper," which enunciated the theory of special relativity (9), was an attempt to remedy this non-relativistic aspect of electromagnetic theory. Looking back from the vantage point of present knowledge, we may wonder if Einstein's work was not directed up a blind alley. Instead


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