429-433] Force inside a Magnetised Body 



373 



FIG. 108. 



At the same time it must be remembered that H Q has not been shewn to 

 be the true value of the potential except when the point Q is outside the 

 magnetic matter. The true potential inside magnetised matter will vary 

 rapidly as we pass from one magnetic particle to another. 



431. Let us next suppose that the length I of the cylindrical cavity is 

 very small compared with the linear dimensions of an 



end. The force, as before, is that due to the distributions 

 I, II and III of 428. The force from distribution III | 

 however, will no longer vanish, for this distribution con- 

 sists of distributions + / over the ends of the cavity, 

 and the force from these is not now negligible. From 

 analogy with the distribution of electricity on a parallel plate condenser, it 

 is clear that the force arising from distribution III is a force 4?r/ in the 

 direction of magnetisation. The forces from distributions I and II are 

 easily seen to be the same as in the former case. Thus the force on a unit 

 pole placed at a point Q inside a cavity of the kind we are now considering 

 is the resultant of 



(i) the magnetic force at Q, as defined in 429, 



(ii) a force 47r/ in the direction of the intensity of magnetisation at Q. 



The resultant of these forces is called the magnetic induction at Q. 



432. The magnetic force will be denoted by H, and its components 

 by a, & 7. 



The induction will be denoted by B and its components by a, b, c. 



We have seen that the force B is the resultant of a force H and a force 

 47r/. The components of this latter force are 4-TrJ., 4?rj5, 47r(7. Hence we 

 have the equations 



a = a + 4?rJ. "j 



6=/3 + 47rJ9 I (359). 



c = y + 4>7rC ) 



433. Let us next consider the force on a unit pole inside a cylindrical 

 cavity when the cavity is disc-shaped, as in 431, but its 



axis is not in the direction of magnetisation. The force can, 

 as in 428, be regarded as arising from three distributions. 



Distributions I and II are the same as before, but 

 distribution III will now consist of charges both on the 

 ends and on the side- walls of the cylinder. By making the 

 length of the cylinder small in comparison with the linear 

 dimensions of its cross-section, the force from the distri- 

 bution on the side-walls can be made to vanish. And if 6 is the angle 

 between the axis of the cavity and the direction of magnetisation, the 



Fm. 109. 



