MAGNETIC SOLENOIDS. 311 



If such^ a solenoid is closed, the potential is everywhere zero on 

 the outside ; the force is therefore zero, and we can only discover 

 the magnetism in the system by breaking it at a point and separating 

 the ends. 



327. A magnetic filament with a constant or variable section 

 tangential at every point to the direction of magnetisation, and 

 in which the magnetic power is not constant, constitutes a complex 

 solenoid. Such a system may be regarded as several simple sole- 

 noids of unequal lengths united to form one bundle. 



Fig. 75- 



The potential P at an external point of an element of length ds 

 (Fig. 75), whose magnetic power m = a\ is 



mds dr dr 



dN = - cos = -m = - a I . 

 r z r i r i 



The potential at P of the whole filament is 



' A * mdr 



V = 



Integrating the second member by parts, and calling -m^ and 

 2 the masses of th.e extremities Aj_ and A 2 , we get 



'A, rdS 



The potential is the same as if the linear density at each point of 



