Equivalent Shell of a Circular Current. 135 



B x S is constant, imposes certain conditions on the equiva- 

 lent shell, if we are to get the proper direction and magni- 

 tude of the induction at all points. 



For instance, it is clear the shell cannot be of the form 

 shown in thick continuous line in fig. 1. The inductions at 



Fig-. 1. 



A, I), and C are entirely different in direction and line of 

 action from that of the slab indicated by dotted lines, 

 although the magnitude in both cases is the same and equal 

 to 4ttN. 



It is, a priori, evident that the equivalence can be extended 

 to all points in space, (1) by making the rim of the magnetic 

 shell a line instead of a cylinder as in fig. 1, and (2) by 



Efc. 2. 



making the two surfaces of the shell coincide with two 

 equipotential surfaces close to each other as in S t , S 2 , and 

 S 3 in fig. 2. We can still choose the equivalent shell in an 

 infinite number of ways, although we cannot make it pass 



