408 Prof. 8. R. Milner : Does an Accelerated 



The field, as given by Schott. is limited by a moving- 

 boundary, formed by the plane x-\-ct=-Q (AB at t= —k/c, 

 A'B' at t=+k/c, fig. i ; OY, fig. 2). The boundary is a 

 transition layer (of a thickness comparable with the radius 

 of the electron) in which the electric and magnetic forces 

 vary from the values given in (4) on the right of the 

 boundary to zero beyond it. For a point-charge it forms a 

 layer of discontinuity, in which the lines of force emanating 

 from the charge suddenly change their direction, and thence- 

 forth lie in the plane. 



It will readily be seen that this field gives an irreversible 

 .radiation of energy. The direction of the energy-flux shows 

 that, except at the moment £ = when the moving boundary 

 crosses if, no energy ever passes through the median plane. 

 Thus the field energy which, at positive values of t, exists to 

 the left of the origin, must, along with the boundary, 

 constitute a permanent loss by radiation from the system. 



A very simple modification of Schott's solution eliminates 

 from it the presence of irreversible radiation. Consider the 

 equations (4) for E and H, and let them now be valid over 

 all space and all time, the moving boundary being dispensed 

 with. The electromagnetic field thus expressed possesses 

 the following properties : — 



(1) It satisfies Maxwell's equations 



E = ccurlH, H=— ccurlE, 

 div E = 47rp, div H = 0, 



at every point of space and time from — oo to + x> . 



(2) The third equation is satisfied in the sense that 

 div E = everywhere except at the points # = + f, where it 

 becomes go in such a way that \E n ^S round any closed 

 surface surrounding the point is equal to ±4:7re. The 

 solution thus forms throughout all space and time an electro- 

 magnetic field which can be associated with two point- 

 charges, + e and — e, moving with the particular type of 

 accelerated motion defined by (1). 



The two charges start with the velocity of light at t= -co 

 from positive and negative infinity of x respectively ; they 

 move symmetrically along the axes inwards towards the 

 origin, come to rest at £ = at the points %= +k, and then 

 move outwards to infinity, ultimately acquiring again the 

 velocity of light. The lines of force are as in figs. 1 and 2, 

 except that the image is now a real charge and there is no 

 boundary, the lines extending from one charge right up to 

 the other. 



