222 MAGNETISM 



CT 1 CQ 1 NP 1 . 

 tan ( = CP = 2CF = 2CP = 2 bl ' ia 



Either from an easy geometrical construction or from the trigo- 

 nometry of the two triangles CPM CPN it can be seen that CM 



= oCN. Hence the following somewhat simpler construction: 



Draw PN perpendicular to CP, meeting the axis in N ; trisect CN 

 in M. Then MP is the direction of the intensity at P. 



We may easily work out the force on one small magnet due, to 

 another, for particular cases. For these we refer the reader to J. J. 

 Thomson's Elements of Electricity and Mu<*neti.fm, chap, vi, as 

 we shall not need them in what follows. 



Uniform magnetic shell. Imagine a very thin steel or 

 iron plate of uniform thickness bent into a surface of any form. 

 The plate will of course be bounded by a closed curve. Let the 

 plate be magnetised uniformly at each point and normal to the 

 surface. This is equivalent to the supposition that it is built up 

 of equal small magnets, placed side by side, the axis of each 

 perpendicular to the surface of the plate ; or it is equivalent to the 

 supposition that a layer of North magnetism of uniform densitv i> 

 spread over one face of the plate and that a lavcr of South 

 magnetism of equal uniform density is spread over tin- other fare. 

 This system is termed a uniform magnetic shell. If & is the 

 uniform surface density and t the uniform thickness, a-t is the 



moment of the plate per unit ana. 

 The product rrt is termed the 

 "strength "of the shell We shall 

 denote this strength by 0. 



Though we ne\er meet with a 

 uniform magnetic shell in practice, 

 the conception is very useful, since 

 the magnetic field, for \\hicli \\r 

 can find a simple- explosion, is. the 

 IM(I - lb<J - same ru TV u here outside the shell 



as that of an electric current of 

 a certain strength circulating round the rim of the shell. 



Potential of a magnetic shell. Let AH, Fiir. l(><), represent 

 a cylindrical element of the shell with cm --Action . [U poles are 

 cur, and its moment is ao-t = a(f). 



The potential at P of the element is : 



art cos _ cos 

 ~^~ =* 



If dw is the solid angle subtended by a at P, du = \. projection of 

 a 011 a plane perpendicular to AP = q ^ S ^. Then the potential 



