442 THE ELECTROMAGNETIC FIELD. [PT. III. CH. XI. 



electromagnetic equations 222 (2) remain unaltered. When we 

 consider the energy and the mechanical forces, however, we have 

 changes. The potential due to a current is no longer proportional 

 to the solid angle subtended by it, and accordingly we can no 

 longer deduce the forces as simple line-integrals. We must now 

 write for the energy of the field, by 180, 



(i) T = 



so that if a given current is placed in an infinite homogeneous 

 medium, since the distribution of the force is independent of the 

 medium, as long as it is homogeneous, the induction, and therefore 

 the energy, are directly proportional to the inductivity. Contrast 

 this behaviour of a current with that of a permanent magnet, which 

 in different homogeneous media always emits the same total flux of 

 induction, while the force and therefore the energy are inversely 

 proportional to the inductivity. The flux of force emitted by the 

 conductor carrying current is constant. 



Since the magnetic force is no longer solenoidal, it can no 

 longer be represented as the curl of a vector potential. The in- 

 duction, on the contrary, can be so represented, and the vector 

 potential belongs to the magnetic induction. 



aff_8^ 



dy dz ' 



_ 



J\- ~~ ,-v ~ ^ 



ox dy 



On account of this change it is no longer possible to integrate the 

 equations 222 (2) in the same simple manner as in 225, for 

 while the current is the curl of the magnetic force, it is the 

 induction that is the curl of the vector potential. Taking the 

 curl of the induction, 



mm (Mr_Mf\ afc.^ 



dy dz r \8y dz J dy dz 

 or using 222 (2), 



-.Jrfe-Jf|6- 



dy dz 



