APPENDIX IV 



EVALUATION OF SPACE— CHARGE PARAMETER Q 



Consider the system consisting of a conducting cylinder of radius a and 

 an internal cylinder of current of radius ai with a current 



• jut —Tz /i\ 



te e . (1) 



Let subscript 1 refer to inside and 2 to outside. We will assume magnetic 

 fields of the form 



H,, = Ahiyr) (2) 



H^2 = BhM + CK,M (3) 



From Maxwell's equations we have, 



— {rH^) = jwerE, + rJ, (4) 



or 



Now 



f (s/i(.)) = zh{z) (5) 



oz 



I (zK,{z)) = -zKoiz) (6) 



dz 



Hence 



£.1 = -^ Ahiyr) (7) 



£.2 = ^ (5/0(7/-) - CKoiyr)) (8) 



coe 



at r = a, £22 = 



at r = fli , Ezi = E; 



C = B ^, (9) 



Zl 



Al^iya^ = B { /o(Tai) — 7^^ — c ^'0(7^1) 



Ao(7a) 



^0(7^) /o(7ai) 

 441 



(10) 



