416 Prof. S. R. Milner : Does an Accelerated 



In the light of this solution it seems desirable to examine 

 with some care the proof of the presence of radiation as a 

 necessary accompaniment to the accelerated motion of 

 charges. The proof, as given by Larmor in ' iEther and 

 Matter' (Chapter XL V.), and by Lorentz in 'The Theory 

 of Electrons' (§39), is based on the solution in terms of 

 retarded potentials for the field of a point-charge in a pre- 

 scribed state of motion. This solution shows that the 

 alteiations in the field at any point can be considered as due 

 to disturbances which emanate from the charge at each 

 point of its path, and are propagated outwards with the 

 velocity of light. Outside a moving boundary, marking 

 the farthest points to which the disturbances have travelled, 

 the previously existing field is unaffected by the motion of 

 the charge. It is now found that in the resulting field, at a 

 sufficiently great distance from the charge, there is an 

 outward flux of energy proportional to the square of the 

 acceleration, which clearly seems to represent an irreversible 

 loss by radiation. 



Let us first test this general conclusion by applying the 

 method to Schott's solution, as originally limited by the 

 moving boundary. The point law of: retarded potentials 

 gives for the field of a point-charge moving arbitrarily * 



E = e 



["--i- ( El "^) {(vIl)+6 ' 2 " v2} l 



L c 2 K 2 R + ' c 2 K 3 R 2 J' 



H=[R 1 E], where K=/l- V ^V 



E, H are here the electric and magnetic forces which exist 



at the time t = r-\ at any point which is at a distance R 



from the point where the charge was at the time t. For 

 simplicity take t = 0, so that the disturbances considered are 

 those emitted at the turning-point A, (k, 0), of the charge, 

 whence in the formula we shall have v = and v = c 2 /k 

 parallel to x. Then at the time t = ~R/c, and on the spherical 

 surface of radius R described about A as centre, E and H 

 will be given by 



■-(-Tifr+iW' H=[RlE] ' 



where a is the angle between the axis of x and R, and P l7 Ri 



* Schott, ' Electromagnetic Radiation/ p. 23. 



