POTENTIAL ANALOGUE METHOD OF NETWORK SYNTHESIS 



321 



E = - ^ = - ^ 



dx dy 



— re 



dW 



dz ' 



Ey=^ - 



dV d^ 



dy 



dx 



im 



dW 



dz 



(17) 



(a) 



Fig. 3 — Flux of electric intensity; (a) across an arc, (b) through a circle surrounding 

 a charge. 



The stream function^ may be interpreted in terms of the flux of the field 

 intensity across a curve in the z-plane. The flux of a vector across a given 

 curve is the line integral of the normal component of the vector, 



JEnds, 



(18) 



hence the flux of E crossing the curve of Fig. 3(a) between the points Zo 



and z is 



$ 



= f {-Ey dx + E, dy) 



-a 



dx 



dx 



dy 



dy 



j = ^ 



(19) 



(zo) - ^{z), 



in the clockwise direction when viewed from Zo . The flux depends only 

 on the values of ^ at the ends of the curve. 



For a point charge q at the origin the stream function is 



y^r = —q(p-\- constant, 



(20) 



