By W. G. V. Rosser M.Sc., Ph.D. (auth.)
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Extra resources for Classical Electromagnetism via Relativity: An Alternative Approach to Maxwell’s Equations
The calculation of the electric and the magnetic forces between two convection currents using the theory of special relativity. (a) The charge distributions are at rest in L'; there is only an electric force between the charges in L'. 3(b). 14) ELECTROMAGNETISM AS A SECOND ORDER EFFECT According to the theory of relativity the laws of electromagnetism are the same in all inertial reference systems. Hence, the problem can be considered from the reference frame l:', moving with uniform velocity v relative to l: along the common x axis.
Choose the zero of time such that q2 is at the origin of ~ at the time t = 0. 1(a). The force on the charge ql due to the charge q 2 will be calculated in the inertial frame ~ at the time t = 0, when q2 is at the origin. 1(b). Let ql be at P' at a distance r' 29 • POINT' CHARGE MOVING WITH UNIFORM VELOCITY from the origin 0' and have co-ordinates x', y', z', t' in ~' corresponding to the point P, which has co-ordinates x, y, z, t = 0 relative to ~. 1. (a) In the inertial reference frame ~. the charge q2 moves with uniform velocity v.
C:::~-------_x is the total microscopic electric intensity at P due to all the charges in the complete system. Let p be the macroscopic charge density in the vicinity of P. l! 20) can now be rewritten f pdV e. 21) &V If the Gaussian surface AV is made very small on the laboratory scale, but still large enough to contain many microscopic (atomic) ~4 THE EQUATION V. E = pleo charges. so that p can be treated as a continuous function of position. 3, the local microscopic electric field e will vary enormously from point to point on the surface of AV.