254 



MAGNETISM 



Let P be a point in air and Q a point in the body each very close 

 to AB and so near together that PQ is very small compared with the 

 diameter of AB. We may divide the intensity of the field at P 

 into two parts, the one H due to the rest of the system when AB 

 is excluded, the other due to the layer on AB. The latter will be 

 %7T(r along the normal upwards in the figure if <r is positive. The 

 intensity at Q may similarly be divided into two parts, the one due 

 to the rest of the system when AB is excluded, and this will also be 

 H, of the same value and in the same direction as at P, since PQ 

 is very small compared with the distance of either from the nearest 

 parts of the system to which H is due. The other will be STTO- 

 along the normal downwards if a- is positive. 



Let us draw OH, Fig. 197, from a point O in AB to represent H, 

 HC parallel to the normal to AB to represent STTO- upwards, and 

 HD parallel to the normal to represent STTO- downwards. Then 

 OC will represent H^ at P and OU will represent H 2 at Q. 



The force on AB is due neither to H x nor to H r but to H, since 

 AB as a whole exerts no force on itself. The force per unit area 

 of AB, then, is Ho- in magnitude and direction. We may regard 

 OH in Fig. 197 as the resultant of OD and DH, i.e. of H, and STTCT. 



FIG. 197. 



Then we have two forces per unit area. H 2 <r along H 2 and 

 along the normal outwards. 



Putting o- = AcH 2 cos0 2 (p. 253), the pull along the normal 

 outwards may be written 



unit area on each element 



where H 2 makes $ 2 with the normal. 

 The system of forces H 2 <r per 

 and parallel to H 2 may be conveniently represented as the resultant 

 of a system offerees acting throughout the volume in the following 

 way : 



