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VI. The Impulsive Motion of Electrified Systems. By 

 G. F. C. {Seaele, M.A., F.E.S., University Lecturer in 

 Experimental Physics, Cambridge*. 



§ 1. "\X7"HEN an electrified system is suddenly set into 

 H motion, a pulse of electromagnetic disturbance 

 travels outwards from the system in all directions with the 

 velocity of light, and this pulse carries energy and electro- 

 magnetic momentum away to infinity. In the following- 

 paper, a method is given of calculating the radiated energy 

 and momentum for any given system, and the results are 

 applied to a number of simple systems. The principles of 

 electromagnetism are then applied to deduce the electric and 

 the magnetic energies and the momenta of the systems, 

 when they are in steady motion. Some of the results, as 

 will be indicated in footnotes, have already been published 

 by Dr. Oliver Heaviside and by Dr. M. Abraham, but others 

 are, I believe, now given for the first time. 



The method employed in calculating the electric and 

 magnetic forces in the pulse is simply an extension to finite 

 speeds of Prof. J. J. Thomson's investigation f of the pulse 

 gfven off when the infinitesimal velocity of a charged sphere 

 is suddenly destroyed. 



§ 2. When a charged particle has been at rest at a given point 

 for an infinite time, the lines of electric force are uni- 

 formly distributed round the particle. At the time £ = 0, let 

 the particle be impulsively set into motion at a speed u, which 

 is maintained constant in direction and magnitude. Then, at 

 any subsequent time t, the field can be divided into two parts 

 by a sphere of radius vt described about as centre, v being 

 the velocity of light. The field outside this sphere is the same 

 as if the particle had remained at rest, while the field inside 

 the sphere is the same as if the particle had been in steady 

 motion for an infinite time. 



On the other hand, suppose that a charged particle, which 

 has been moving along a straight line, with uniform velocity 

 u, for an infinite time, is suddenly stopped, at £ = 0, as it 

 reaches a given point 0. Then, at any subsequent time t, a 

 sphere of radius vt will again divide the field into two parts. 

 The field outside this sphere is the same as if the particle had 

 continued in steady motion, while the field inside the sphere 



* Communicated by the Author. 



T Elements of the Mathematical Theory of Electricity and Magnetism. 

 Third edition (1904), § 287. 



