248 BELL SYSTEM TECHNICAL JOURNAL 



APPENDIX III 



STORED ENERGIES OE 

 CIRCUIT STRUCTURES 



A3.1 Forced Sinusoidal Field 



If i; <3C c, the field can be very nearly represented inside the cylinder of 

 radius a by 



_ T. hW jp^ _ E /o(/3r) y^. 



and outside by 



Inside 



F = Fo ^^ e-^'^ (2) 



K{ya) 



^=-y^;_^.-^^Fo (4) 



Outside 



^=_y,|^.-Fo (6) 



Because there is a sinusoidal variation in the z direction, the average stored 

 electric energy per unit length will be 



"'"' " (0C2) /=o ^''^'"'^^'^' + (£.max)'j(27rr dr) (7) 



Here Er max and Ez max are maximum values at r = a. The total electric 

 plus magnetic stored energy will be twice this. This gives 



