33$ PARTICULAR CASES. 



CHAPTER III. 

 PARTICULAR CASES. 



354. POTENTIAL OF A UNIFORM MAGNET. The magnetic 

 action of a body uniformly magnetised being equivalent to that 

 of two layers of gliding (320), the potential V may be readily 

 deduced from that of a homogeneous mass which would fill the 

 volume. Let P be the value of this potential at a point M, when the 

 density of the mass is equal to unity, its value will be pP if the 

 density is p. 



The potential of the system of the two layers is evidently the sum 

 of the potential /oP of the positive mass, and of the potential - pP' of 

 an identical negative mass which has been displaced in the opposite 

 direction to that of the magnetisation, by an infinitely small quantity 

 dx = 8. The potential pP' is that of the positive mass at the point M', 

 whose co-ordinates are the same as that of the point M, except the 

 abscissa parallel to the magnetisation, which has increased by dx. 



We thus obtain 



,, ,--,(,***).-, 



Consequently the potential of a uniform magnet is equal, and of 

 opposite sign, to the product of the intensity of magnetisation by the 

 partial differential, referred to the direction of the magnetisation, 

 of the potential, which a uniform mass, of density equal to unity 

 occupying the whole volume of the body, would have at the point 

 in question. 



The components X, Y, and Z of the magnetic force are equal, 

 and of opposite sign, to the partial differential of the potential, 

 which gives 



