The Field of Force due to a Moving Electron
Arthur William Conway · Proceedings of the London Mathematical Society · 1904
THE following paper treats of the field of force due to the motion of an electron.No assumption is made as to the nature or shape of an electron except to regard it as a simple singularity of the differential equations which is changing its position in three-dimensional space in any continuous manner whatever.The results will, however, be correct as long as the distance of the point at which the field of force is calculated is great compared with the dimensions of the electron.In § 1 the case of an electron moving in a general manner with a speed less than that of radiation is considered.In § 2 the results are extended to moving distributions of electric charge.Without making an hypothesis concerning the distribution of the charge of the electrical nucleus or electron it it is impossible to obtain the total amount of energy of the system, but the amount of energy radiated, or "wasted," is calculated in § 3.In § 4 the form which the results of § 1 assume when the speed of the singularity is greater than that of radiation is considered.1.The Electromagnetic Field due to an Electron moving with a Velocity less than that of Radiation.The differential equations which hold in any space free from singulariarities are, the origin being fixed in the aBther,where (X, Y, Z) is the electric force in electromagnetic units, (a, ft y) is the magnetic force, K is the specific inductive capacity, and /* is the magnetic permeability.From the above equations it follows that (X, Y, Z) is circuital and that X, Y, and Z are solutions of V 2 U = V~2d 2 Uldf where F" 2 = Kfi.Let f x {u), / 2 (&), /Q(U) be any functions of u which are real and uniform where u is real, and which are finite and continuous for all finite * Heaviside, Electromagnetic Theory.