426 



CURRENTS AND MAGNETIC SHELLS. 



The magnetic potential of the current at a point is not, therefore, 

 a simple function of the co-ordinates, but a function having an 

 infinity of values, which differ from each other by a multiple of 



ki 



477 ; that is to say, of the work which would be represented by 



the complete rotation about the current of a magnetic mass equal 

 to unity. This property may be easily generalised. 



447. POTENTIAL OF AN ANGULAR CURRENT. Let us consider 

 two unlimited currents AA' and BB' (Fig. 97) of the same strength, 



situated in the same plane, and moving in the directions indicated 

 by the arrows. Let Q be the projection of the pole P on this plane. 

 The potential at P of the current AA' is proportional to the 

 apparent surface of the plane AA'X; that of BB' is proportional 

 to the apparent surface of the plane BB'X. 



With the actual direction of the current, and assuming that their 

 planes extend indefinitely on the right, these two apparent surfaces 

 must be taken with contrary signs, and the resultant potential is 

 equal to their difference. But the part in common, AOBX, dis- 

 appears; the potential is therefore proportional to the apparent 

 surface of the angle BOA', diminished by the apparent surface of 

 the angle AOB'. 



On the other hand, the system of two unlimited currents is 

 identical with that of two angular currents BOA' and AOB', the 

 first of which turns its positive face to the front, and the second its 

 negative face. 



We may accordingly assert that the potential at a point P of an 

 angular current, such as BOA', is proportional to its apparent surface, 



