By W. G. V. Rosser M.Sc., Ph.D. (auth.)
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Extra info for Classical Electromagnetism via Relativity: An Alternative Approach to Maxwell’s Equations
Originally Maxwell's equations were developed in the nineteenth century, from experiments based on matter in bulk form, before any precise atomic theory had been developed. It is now known that macroscopic charge and current distributions are built up of a finite number of microscopic (atomic) charges, namely electrons, protons and positive ions. The principle of superposition will be used to extend Maxwell's equations relating the fields of 'point' charges into a macroscopic theory for charge and current distributions of finite dimensions.
11) 21t8 or The force on the positive ions in conductor 2 due to the stationary positive ions in conductor 1 is a repulsive force given by f++ = y E A? 2. The forces between two conduction currents I. In the simplified model used, the positive ions are at rest and the negative electrons all move with the same uniform velocity v. \. 2 cancel out to zero, leaving only the second order magnetic forces that are observed experimentally. 3. 2 using Maxwell's equations will now be considered from the viewpoint of the theory of special relativity.
A second proton is moving with uniform velocity 0·6c along the y axis. The second proton is at a position y = 10- 4 metres, when the proton, which is moving along the x axis, is at the origin. Calculate the magnitude and directions of the electric and the magnetic forces between the charges at this instant. 1. INTRODUCTION In Chapter 3, the electric intensity E and the magnetic induction B of a 'point' charge q, such as an electron or a proton, moving with uniform velocity u were developed from Coulomb's law, by taking the principle of constant electric charge and the transformations of the theory of special relativity as axiomatic.