Energy in the Electromagnetic Field. 155^ 



The Lagrangian operator then gives 



ac 1 dt + c 2 dt} r 



_ e ^ r {UM+YM^V[Hi dv 



c 1 Bar J r 



^vj r 

 with corresponding equations for the y, z co-ordinates.. 



Since — 2^ s ^ ne mass or " tne charge e, these equations give for 



O.C 



x= _ 1^1 I'M ,7,._ MM 



the force on unit E.S. charge at rest 



c J r a^ J r 



and for the additional force on the charge £ due to its motion 



P= _ £ ( u|_ + v A +w |_) 1 I'M (/l , 

 c\ d«<' oy ozj cj r 



c { oa' c J ?■ qxcj r 



+ w a lfxefj.^i q, &c . ;R , &c . 



... x=- 1 f-|^ ! Y,Ac . . (14) 

 c di ox 



and 



_ W (| M'W^IH'H,,.)! 



V <jr cj r d^ cj r / J 



-i;nl-|',)-"(f-l?)}''«- R ' fc -("> 



