SOLENOIDAL MAGNETS. 355 



This term becomes predominant at a great distance, and the potential 

 reduces then to 



it follows from this (151) that the three products 

 represent respectively the magnetic moments of the sphere in refer- 

 ence to the axes of x, of jy, and of z. Denoting by 3 K the resultant 

 magnetic moment, and by a, /? and y the cosines of the angles which 

 its direction makes with the axes, we have 



K = ^ = 



371. SOLENOIDAL MAGNETS. The potential of a solenoidal 

 magnet (330) only depends on the surfaces formed by the ends 

 of the elementary solenoids which constitute it. 



If all the solenoids are closed, the potential of the magnet is 

 everywhere null, and the magnetic force null. In this case the 

 induction is reduced at each point to 477!, and it is parallel to the 

 magnetisation. 



372. Suppose that a solenoidal magnet is bounded by a channel 

 surface, the magnetisation being everywhere normal to the perpen- 

 dicular section of the channel. The flow of induction across an 

 element dS of the right section is equal to 47rL/S, and the value of 

 the flow of induction is 



Each of the solenoidal filaments forms a closed curve of length /, 

 perpendicular at every point to the right section of the channel. If 

 the structure of the magnet is such that the product of the strength 

 of magnetisation I of a filament, by its length /, is a constant quantity, 

 examples of which we shall see afterwards, the flow of induction 

 could be expressed by the formula 



(20) 



'/ 



A A 2 



