﻿726 Mr. A. Bramley on Radiation. 



F e = E + - {H* . u r -H r . u z ] 



e — u 1 1 _~ 



= 4tt * ~J~ ' s/\~]& ' (r 2 + R 2 + ~ 2 -2rRcos0 1 ) 1 '' 2- = ' 



where F represents the force acting on unit charge and U^ is 

 the tangential velocity. 



The force acting on an element of volume dr' at any point 

 P is therefore 



F r =0, 



F« = 



e 



— u 1 pdr' 



4tir' c 2 ' x/l- ^' (r'-l-W + z 2 -2rR cos O^ 2 ' 



-j-, _ e —u 1 pdr 



o'^r'^' VW? 3 '^ 2 +^ + ~ 2 -2rR cos^) 1 ' 2 * 



If we suppose that an electron is composed of a perfectly 

 conducting sphere surrounded by an electrically charged 



shell ol uniform surface-density, then the - 1 1 [E . H] r ds over 



the entire inner surface of the shell is equal to zero. Thus 

 we see that no energy is radiated inwardly. 



Suppose we take any spherical element of volume dr, then 

 the energy radiated from it, if it is of uniform density, is 

 cn[E . H] r <is over any surface enclosing the element 



_?!_ ?L l 



~ 87^ , wc 2, l-/3 2, 



where e is the elementary charge on this volume element. 



Thus we see that each element of the electronic shell 

 radiates the same amount of energy. 



We shall now make use of the idea of electromagnetic 

 mass in dealing with radiation. If electromagnetic energy 

 possesses mass, then there ought to be an equilibrium estab- 

 lished between the mutual force of attraction and the radiation 

 forces. Thus the energy will condense around the electron 

 until this equilibrium value is attained, when it will be 

 emitted in quanta. The force acting on the element of 

 volume due to the radiated energy is per unit volume 



= -|[E.H]. 



