568 A DYNAMICAL THEORY OF THE ELECTROMAGNETIC FIELD. 



Mechanical Force on an Electrified Body. 



(79) If there is no motion or change of strength of currents or magnets 

 in the field, the electromotive force is entirely due to variation of electric 

 potential, and we shall have (65) 



~dx' V ~ 



Integrating by parts the expression (I) for the energy due to electric 

 displacement, and remembering that P, Q, R vanish at an infinite distance, it becomes 



or by the equation of Free Electricity (G), p. 561, 



By the same demonstration as was used in the case of the mechanical 

 action on a magnet, it may be shewn that the mechanical force on a small 

 body containing a quantity e t of free electricity placed in a field whose 

 potential arising from other electrified bodies is ,, has for components 



(D). 



' dz~ 



So that an electrified body is urged in the direction of the electromotive 

 force with a force equal to the product of the quantity of free electricity and 

 the electromotive force. 



If the electrification of the field arises from the presence of a small 

 electrified body containing e l of free electricity, the only solution of , is 



*.- < 43 >' 



where r is the distance from the electrified body. 



The repulsion between two electrified bodies e lt e t is therefore 



( . ? = __' (44) 



* dr 47r r 1 ' 





