270 Methods for the Solution of Special Problems [OH. vin 



plate at distance 2h instead of an infinite plane at distance h. The equi- 

 potentials and lines of force for either problem are shewn in fig. 91. 



- U), 



- V+TT). 



V 



FIG. 91. 

 Separating real and imaginary parts in equation (243), 



m-( * 



7T 



--( u si 



7T 



Thus the equipotential V is the line y = h, the equipotential F= TT is 

 the line y = 0. 



On the former equipotential, the relation between x and U is 



r(pU_7J\ {9AA<\ 



\h l(> ^ / y^fjDTC/, 



7T 



When U= oo,# = + oo; as 7 increases, a? decreases until it reaches a 

 minimum value x hJTr when 7 = 0; and as 7 further increases through 

 positive values x again increases, reaching #=oo when 7= + 00. Thus as 

 U varies while F=0, the path described is the path PQR in fig. 91. 



The intensity at any point is 



R 



dW 

 dz 



7T 



h\e w -I\' 



