CHAPTER XX 



FORCES ON MAGNETISED BODIES. STRESSES 

 IN THE MEDIUM 



The forces on a body of constant permeability fj, placed in a magnetic field 

 in air Illustrations The forces on a body of permeability /j. 2 placed in 

 a field in a medium of permeability ^ Forces on an elongated bar in a 

 uniform field in air when its permeability differs very slightly from 1 

 The magnetic moment of a small paramagnetic or diamagnetic body 

 placed in a magnetic field Time of vibration of a small needle with 

 fj. - 1 very small suspended in the centre of the field between the poles of 

 a magnet Stresses in the medium which will account for the forces 

 on magnetic bodies The stresses on an element of surface separating 

 media of permeabilities ^ and /i 2 - 



The forces on a body of constant permeability /u 

 placed in a magnetic field in air. We can obtain useful 

 expressions for the forces on a body in a magnetic field when the 

 permeability is constant, that is, for a body which is paramagnetic 

 or diamagnetic with permeability very near to unity. 



We have seen (p. 239) that the field outside the body is altered 

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

 introduction of a layer of magnetism occupying the position of the 

 surface of the body and of density 



, cos 0. = f-^ H 2 cos 2 = /cH 2 cos 2 



T?7T 



and acting everywhere according to the law ra/r 2 . 



The forces on the poles or bodies producing the field can be 

 calculated by replacing the magnetised body by this layer, and, 



FIG. 196. 



equally, the reactions on the body can be calculated by replacing 

 it by the layer and finding the force on each element of the surface. 

 Let AB, Fig. 196, be an element of the surface so small that it may 

 be regarded as plane and as having a layer of magnetism of uniform 

 dcnsitv <r all over it. 



253 



