STRESSES IN THE DIELECTRIC 137 



The tensions being 2-TrD^/K and ^7rD 2 2 /K, the resultant pull 

 inwards is 



And substituting from the previous equation the total pull 

 inwards is 



But now suppose there is a transverse pressure P normal to the 

 surfaces of the rim of the lamina between ABCD and A'B'C'D'. 

 The area of ABB' A' is R^c. That of BCC'B' is R 2 <j> 2 S. 



Resolving P along the normal to ABCD and perpendicular to 

 it, the latter gives resolutes neutralising each other in pairs. The 

 former gives 



so that there is equilibrium if 



= 



There may be other solutions of the problem. Faraday 

 was led to the idea of longitudinal tension and lateral pressure by 

 considering the nature of electric induction. He says : * " The 

 attractive force which exists amongst the particles of the dielectric 

 in the direction of the induction is accompanied by a repulsive or 

 a diverging force in the transverse direction." Clerk Maxwell 

 showed that equilibrium would be maintained if the tension were 

 equal to the pressure. But it is to be remembered that the system 

 thus obtained is only a possible solution of the problem of the 

 stresses in the medium. It is a solution, but there may be others. 

 Meanwhile its simplicity recommends it as worthy of trial, and we 

 shall assume henceforth that it is the solution. 



These stresses will not produce equilibrium if K is 

 not uniform. It is important to observe that if we assume the 

 existence of these stresses the medium is not necessarily in equili- 

 brium unless K is constant. Thus a solid dielectric body suspended 

 in air behaves like a magnetic body in a magnetic field, and 

 Boltzmann's method of determining K by the force on a small 

 sphere hung up in a field radiating from a centre depends upon 

 this fact. Even in a system in equilibrium stresses other than the 

 electrical stresses must intervene if there is a change of value of K. 



* E*p. Re*., i. p. 409, 1297. 



