Relations of the Magnetic Field. 075 



The second term on the right represents the internal elastic 

 energy stored in the media on account of the magnetic polarity 

 induced in them. The first part therefore represents the true 

 magnetic potential energy of the field, and on a tentative 

 theory we could regard it as distributed throughout the field 

 with the density 



at any place. In the case of the linear isotropic law of 

 induction, we have 



H = ^B-47rI , h = kB ; 



so that BTi = kSB, 



fodh) = *f. 



and thus 



The total work done in the field is thus 



.1 8 



87T 



These relations are somewhat simpler than those obtained 

 on the only consistent form of the older theory, as the 

 permeability is again restored to the numerator of the 

 expression for the energy and in addition the unknown 

 local terms are entirely absent. 



When the field is statical and the magnetic force proper 

 possesses a potential function, the characteristic equation 

 satisfied by this function is slightly different from that usually 

 given. The induction vector B is always circuital, so that 



divB = ^ + | B '+^=0, 

 dx dy oz 



and when the mechanical force H is derived from the 

 potential <f> we have 



B = — grad </> + kirl, 



