INDUCED MAGNETISATION 243 



and that its field is superposed on H. We have shown (p. 226) 

 that a sphere radius a, uniformly magnetised with intensity of 

 magnetisation I, has a field without it the same as that of a small 



4 



magnet with moment - ?r 3 I placed at its centre, and with axis 



in the direction of I, and that it has a field within the sphere 

 uniform and equal to - r TT!. We are to find the value of I 

 which will satisfy the conditions of continuity of potential and 



TtlsLrv 0. 



FIG. 189. 



flux of induction. The supposition to which we have already 

 referred (p. 231) is that this gives the actual magnetisation. 



Consider a point P at the end of a radius OP making with 

 the direction of H. We may resolve the small magnet equivalent 



4 



to the sphere into two, one along OP with moment ~ 7ra 3 I cos 0, 



o 



4 



and the other perpendicular to OP and with moment 5 ira*l sin 



o 



respectively. 



The intensity of the field just outside P due to the former will 



Q 



be along OP and equal to - TT! cos 0. That due to the latter will 



4 

 be perpendicular to OP and equal to ^ TT! sin 0. The field intensity 



parallel to the surface is obtained by combining this with the 

 component of H and is 



4 



H sin - TT! sin 0. 

 o 



4 

 Just within the magnet'sed sphere its own field is ^ ?rl parallel 



4 

 to H, so that, adding II, the total intensity of field is H - ^ xl. 



