172 



E. I. Terekhin 



Representing — ^ by q, the potential at any point of the upper layer can 



be expressed thus: 



Uo = 



2]/r^ + 



I B^e"'^ Iq (mr) dm + j A^' 



+ I BQe"'^lQ{mr)dm+ l A^e-""' lQ{mr) dm (3) 



or, using the Weber-Lipshitz formula for negative values of z 



oo 



= / e"^^ L (mr) dm, 







at points in the upper layer above the electrode A, i.e. at points for which 

 z <. 0, we obtain 



U. 



z<Q 



J fe"^^I^{mr)dm+ f B^^ 



e'"^ lQ{mr) dm+ j B^g^^ Iq {mr) dm + 



-j_ / Aq&~^^ lQ{mr)dm, 







(4) 



and 



SU. 



dz 



oo oo 



= — g f /n e"'^ Iq (mr) dm + / mB^e'^^ Iq {mr) dm - 

 2<0 2 ./ J 



oc 



mAQe'"^^ Iq {mr)dm. 



9U 

 According to the condition (4) 



9z 

 and Qq 7^ oo. 



Consequently, for all values of r 



= 0, since in general Qq^ 



oo 



Hi 



qe-'^^o + B^e-'^^o -AQe""^" 



mlQ{mr)dm = 0. 



