250 BELL SYSTEM TECHNICAL JOURNAL 



W = 2W, = '^ 



W = — ° E' 



4/3 



Jo 



(15) 



and 



(F?/l3^Py'' = 6.20 (v/vsY" (16) 



The surface charge density a on one side of the array of wires (say, y > 0) 

 is given by the y component of field at y = 0. 



2x 

 0" = eEy = eE sin /5.r cos — z (17) 



This is related to the current 7 (flowing in the z direction) per unit distance 

 in the .v direction by 



dz di 



From (18) and (17) we obtain for the current on one side of the array 



I = — —z — E sm i5x sm — z (19) 



/TT Xo 



If we use the fact that a;Xo/27r = c and c e = l/\//x/€, we obtain 



—jE, . . 2x 



/ = '/=F sin ^x sin — z (20) 



VM/f Xo 



If R is the surface resistivity of either side (y > 0, y < 0) of the wires, when 

 the wires act as a resonator (a standing wave) the average power lost per 

 unit length for both sides is 



P = ii?Xo£7(MA) (21) 



In this case the stored electric energy is half the value given by (15), and 

 we find 



Q = (ViuA/i?) {v/c) (22) 



