Classical Electromagnetism via Relativity: An Alternative by W. G. V. Rosser M.Sc., Ph.D. (auth.)

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By W. G. V. Rosser M.Sc., Ph.D. (auth.)

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20), vxrQ2{1-v 2/e 2) B2 -- - v X E 2 -_ 2 e e24neor3[1- (v 2/e 2) sin 2 0]3/2 (3 22) . 1(a). The quantities r and 0 relate to the position of the charge at the time the field is determined at the field point P. 23) is less than uv/e 2 • According to the theory of special relativity both u and v must be less than c, the velocity of light in empty space, so that the magnetic force between the two moving charges is always less than the electric force between the charges. 2. 22) will now be rewritten for the general case of any charge of magnitude q moving with uniform velocity u relative to an inertial reference frame L.

At this stage, the theory can be extended to field points inside stationary dielectrics. When a stationary dielectric is in an applied electric field, there is a separation of the positive and negative charges in atoms giving rise to induced atomic dipole moments. Polar molecules will tend to align themselves in the direction of the applied electric field, and any ions in crystals will tend to be displaced in the direction ofthe applied electric field. The macroscopic polarization P is defined as the resultant electric dipole moment per unit volume.

And () = n - rt.. The sense of rotation of the lines of B about the direction of u is the same in both cases. 37 , POINT' CHARGE MOVING WITH UNIFORM VELOCITY The direction of B is consistent with the right-handed corkscrew rule, if qu is treated as a current element Idl. According to the righthanded corkscrew rule the direction of B is the direction in which a right-handed corkscrew would have to be rotated in order that it should advance in the direction of current flow. As the velocity of the charge tends to the velocity of light, the lines of E bunch closer and closer to the direction perpendicular to the direction of motion of the charge, with B remaining perpendicular to E.

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