68 Mr. W. A. Price on Alternating 



§7. Suppose an alternating current 27rAcosw£ to be 

 introduced into the central conductor at A where 0=0, and 

 a current 27rB cos (cot + <£) into the same conductor at B where 



The charge at B on the central conductor due to the current 

 introduced at A is, writing 



^/jjLu ft and ^/- M y, 



Acj 



--; { sin <otf 3 (0) + co? cot f ,(13)] 



A c g 

 H {sin totf 3 (y)+ cos cotf^ry)}. 



The charge at B on the central conductor due to the 

 current introduced at B is 



~ {sin (cot + 0)A(/3) + cos(a>t + </>)/ 2 (/3)} 

 Be 



+ -j{S™ (cot + <f>)f 1 (y) + COS (cot + <f>)f 2 (ry)}. 



The charge at B induced on the concentric conductor by 

 the current introduced at A is 



" ^7 (1 ~ m ^ *t °7 {sin mtfi{ ® + cos at f*Wl 



1 Ac 



" w/ Q--™") uj * sin at Mr) +■ cos ^A(y)}. 



The charge at B induced on the concentric conductor by 

 the current introduced at B is 



~ t^7 (l " mfir) To c {sin (w ' "* ^ )/l(/9) + cos {o3t + W>W \ 



-" ™'( 1- mvr ) ~ °H &in i wt + <£)/i(7) + cos (cot + </>)/ 2 ( 7 )} . 



The potential of the central conductor at the point B is 



^ , where s s' are the total charges on the two 



mn 



conductors respectively, and is 



