/'A'( »/'.»(;. 7 //o.v oj/K i:ii\'.ii.i.ii. ( (».\7'(t /('Ms .w 



In the dielectric space inside the lube where r<«, the axial elerlric 

 force may l>e written 



00 



E,= y^CnJn(p)cn»ne. (1) 



or replacini; tlu- liesscl functions by their \alucs for vaiiihliinnly 

 small argunuMiis, 



£, = V" p^r' cos ti9 (2) 



where A.. Di . . . D„ are constants determined !>>• the bounfl.irx- condi- 

 tions. Applying Maxwell's law relating the normal and tauten li.il 

 magnetic forces //, and IIq to the axial electric force, gives 



nii^-Ilg = '' ^ -1 n [Jn'ip) + X„A."„(p)l cos nO, (3) 



pi=() 



nioiIlr = -^A„ (y„(p) + X„A'„(p)lsin ne, (4) 



for the s()ace inside the conductor, and 



iuillg = ^ nPnr"-^ cos }iO. (5) 



n=0 



foi//, = V" nn„r"-^ sin uO, (6) 



«=o 



for the inner dielectric (/i = l). Equating the two expressions for 

 the tangential magnetic force Hf, and for the normal magnetic in- 

 duction nH, term b>- term at the surface r = a, 



Ify,'(M-,i«A(f)l+X,lfAV(f)-|x«A',(nl = 0. (7) 



Whence, for the practically important case of non-magnetic con- 

 ductors in which n = l, we have 



and 



£' = 2 ^" [•^"(P) - ^;^j ^-(P)] cos >,0. (9) 



