362 Permanent Magnetism [OH. xi 



The matter occupying any element of volume dxdydz at this point will 

 be a magnetic particle of which the moment is Idxdydz and the axis is in 

 direction I, m, n. By formula (339), the potential of this particle at any 

 external point is 



~ , i i -o /I '"^-( - If dxdydz, 



dx\rj dy\rJ dz\r)} 



so that, by integration, we obtain as the potential of the whole body at any 

 external point Q, 



On = 1 1 1/ -a - ( ]4-m^ - ( } +n^- I }[ dxdydz (340), 



JJj ( ox\rj oy\rj oz\rj) 



in which r is the distance from Q to the element dxdydz, and the integration 

 extends over the whole of the magnetised body. 



If we introduce quantities A, B, C denned by 



(341), 



then equation (340) can be put in the form 



^49^ 



^. j \*s -. i i r \AJWJ \AJ t/ \AJXS \ J T *j I 



dy\rj dz\rJ) 



The quantities A, B, C are called the components of magnetisation at the 

 point x, y, z. Equation (342) shews that the potential of the original magnet, 

 of magnetisation /, is the same as the potential of three superposed magnets, 

 of intensities A, B, C parallel to the three axes. This is also obvious from 

 the fact that the particle of strength I dxdydz, which occupies the element of 

 volume dxdydz, may be resolved into three particles parallel to the axes, of 

 which the strengths will be A dxdydz, Bdxdydz and C dxdydz, if A, B, C are 

 given by equations (341). 



Potential of a uniformly Magnetised Body. 



413. If the magnetisation of any body is uniform, the values of A, B, G 

 are the same at all points of the body. 



Let the coordinates of the point Q in equation (342) be x', y , z', so that 



= [(*- *') 2 + (y - yj + (*- *?]-* 



Then, clearly, 



a /i\ a /i\ 



5-f- )=-o-/ - , etc. 



dx \rj ox \rj 



