FORCES ON MAGNETISED BODIES 257 



long that the intensities at the remote ends are negligible. We 

 shall assume that the intensity near the neighbouring ends is 

 parallel to the axis. As above, the volume force gives us a pull 



-/cH 2 2 where H 2 is the intensity just inside the iron. The surface 

 pull 2-7r<7 2 gives us 27nc 2 H./. The total pull is therefore 



8-7T/X 



where Hj is the intensity in the air in the gap. 



The assumptions of constant permeability and of field parallel 

 to the axis in the bar near the facing ends are only very rough 

 approximations to the truth at the best, so that the result obtained 

 has no real value except as an illustration of the formulae. 



Forces on a body of permeability /x 2 placed in a field 

 in a medium of permeability ^ r The field is altered by the 

 introduction of the body just as it would be by the introduction 

 of a layer of magnetism of surface density 



and acting everywhere according to the law m/far 2 (p. 251). The 

 forces due to the body, and therefore the reactions on the body, 

 can be calculated by replacing the body by this layer and finding 

 the forces upon it. The forces on the surface layer a- may be 

 obtained as on p. 254, remembering that now the intensity due to 

 cr is 27r0-/Mi> and that this is now the value of DH or HC in 

 Fig. 197. The intensity H acting on the surface layer may be 

 regarded as the resultant of 27nr/ y u 1 along the normal and of H 2 . 

 The former gives a tension along the normal 



2 7 rc7 2 //x 1 = 2 7T(*2 - *i) 2H 2 2 cos2 a //*r 



The latter may be treated as on p. 255, remembering that now 

 I = (/c 2 A^H. The volume force is then found to be 



1 



2 ( " 2 ~ Kl) ~3Z 



hich may be represented as due to a pressure system 



In para- and diamagnetic bodies in which AC is very small the 

 tension on the surface is negligible. Faraday's experimental 



