FORCES ON MAGNETISED BODIES 



259 



FIG. 201. 



Now let the bar be inclined at any angle to the field, as in Fig. 201. 

 The mutual action of the cubes tends to increase the end 

 magnetisation and to weaken the side magnetisation. Neglecting 

 this mutual action, that is, neglecting the effect of the surface 

 distribution on the intensity, the bar, as we have seen, will be in 

 equilibrium that is, the "centre of polarity 11 of the end A and 

 of the side B must be at c in the line of force OH through the 

 centre O, Fig. 201 . But taking into account the increase of polarity 

 at A and the decrease at B, the mag- 

 netic axis will be thrown on to the A 

 side of oc to c v say, and the force, 

 acting through c will tend to pull the 

 bar into the direction of the field. 



Now take a diamagnetic bar made 

 up in the same way of cubes. If it is 

 held longitudinally in the field, we 

 represent its polarity by supposing 

 that a NSP induces a NSP, while a 

 SSP induces a SSP. At the plane of 

 contact of two cubes where there are 

 opposite polarities each therefore tends 

 to weaken the other, and the net result 

 is that the end magnetisation is de- 

 creased. Now put the bar transversely. 

 Since like induces like, each cube will tend to strengthen its neigh- 

 bours and the side magnetisation is increased. 



If the bar is inclined at an angle to the field the mutual action 

 of the cubes tends to increase the side magnetisation and to 

 decrease the end magnetisation, and the centre of polarity is 

 thrown towards B, say to c ir This is a SSP, and the force 

 due to the intensity H will push it. The moment round the 

 centre O will tend to make the bar turn round parallel to the lines 

 of force. 



The magnetic moment of a small paramagnetic or 

 diamagnetic body placed in a magnetic field. If the 

 field intensity is H before the body is introduced, that value is 

 almost unaltered by its introduction when ju. 1 is exceedingly 

 small. The magnetisation at any point may therefore be taken as 

 I = /cH. Any small cylinder of length / and cross-section a and with 

 axis along H may be regarded as a magnet with poles la = /cHa, 

 and with moment Mai = /cH X volume. The total magnetic 

 moment will be the resultant of all such moments, and if the body 

 is so small that H may be regarded as uniform in it, its moment 

 will be /cH X volume. 



Force on the small body. We showed in Chapter XVIII 



that the force on a small magnet of moment M in direction x is -^ . 

 If its volume is dv. this is equal to 



