436 THE ELECTROMAGNETIC FIELD. [FT. III. CH. XI. 



225. Magnetic Force from Current. Applying Helm- 

 holtz's theorem to the solenoidal vector H, the magnetic force, 

 and calling the components of the vector potential F, G, H* and 

 using the fundamental equations (7), together with 222 (2), we 



obtain 



_dH_dG 



~ > 



(IS) "' G =///>' 



oo 



*-///> 



or the vector potential belonging to the magnetic force is the 

 vector potential of the current density. 



226. Energy of Magnetic Field of Currents. The mag- 

 netic energy of the field is by 118 (10), 



(i) W m = 



and introducing the vector potential this becomes 



- ~- 



dy dzj \bz foj \dx 



00 



Integrating by parts for any volume r bounded by a closed 

 surface 8, 



* It is to be noticed that the letter H is here unfortunately used for both the 

 resultant magnetic force and one component of the vector-potential. This is 

 because we have followed Maxwell in using the letters F, G, H. The ambiguity 

 need cause no confusion. 



