198, 199] DIELECTRICS AND MAGNETIZABLE BODIES. 381 



For a uniform external field 



the internal field is uniform, and given by 



,.L 



If b/a = 9/10, fjL 2 /^ = 1000, the internal field is 1/67 of the ex- 

 ternal. 



The sphere thus shields more effectively than the cylinder, 

 as might be expected. A table of the relative strengths of the 

 internal field for various ratios of b/a and for ^l^\ = 100 and 

 = 1000, is given by J. J. Thomson, Elements of the Mathematical 

 Theory of Electricity and Magnetism, p. 264. 



If 6 = the results of this section agree with those of 194. 

 For instance in the sphere 



agreeing with 194 (3). 



199. Forces acting on the Polarized Body. In virtue 

 of the polarization of a body whose inductivity differs from that 

 of the surrounding medium the body experiences certain forces. 

 These forces may be calculated by considering the work done 

 when the induced body is moved from one part of the field to 

 another, during which motion its polarization will in general 

 change. 



Before considering the general problem, let us, to fix the ideas, 

 examine the case of an electrical condenser. We have seen that 

 the capacity is proportional to the inductivity of the dielectric. 

 Accordingly for a given charge, the difference of potential of the 

 plates is inversely as the inductivity, consequently the force of 

 the field varies in the same ratio. The energy being proportional 

 to the product of the charge by the difference of potential is 

 accordingly inversely proportional to the inductivity. Now since, 

 the charge being given, the energy tends to decrease, if the di- 

 electric is movable, and its inductivity variable, it will tend to 



