Volume 17: Pages 301-306, 2004
On the Directional Dependence of the Field of a Charge Moving in Three Spatial Dimensions
A. C. Lehum 1, J. Lucinda 2
1Universidade de São Paulo, Caixa Postal 66318, 05315‐970, São Paulo, SP, Brazil
2Universidade Federal do Paraná, Caixa Postal 19044, 81531‐990, Curitiba, PR, Brazil
The customary Lorentz transformation, with relative motion along the direction of one single Cartesian axis, seems to suppose that this restricted transformation is enough for the analysis of any other case where it is necessary to shift from one frame to another. Contrary to this implicit expectation is an unnoticed property of the angular dependence, in the denominator of the electric and magnetic fields of a moving charge in three spatial dimensions; that is, it changes with a change in the direction of the position vector of the test charge by a rotation around any one of the Cartesian axes. Further, the rotation‐invariant symmetry of the denominator before the transformation is preserved. This result contrasts with that given in the literature, where this symmetry is not maintained and the angular dependence does not change by a rotation of this position vector around the Cartesian axis parallel to the direction of the motion. In view of the extensive literature devoted to the problem describing the interaction between two moving classical charges, this directional dependence is depicted in a figure, and we compare the electric fields, at the same point, due to two identical charges moving with the same speed along different directions. It is worth emphasizing that the novelty in this paper is borne out by a more careful analysis within the framework of SR, without alternative structures or new speculations.
Keywords: magnetic force, general boost, force law, magnetic field, electric field
Received: September 24, 2003; Published online: December 15, 2008