90 Effective Resistance and Inductance of a Helical Coil. 



Case of High Frequency. 



We pass to the case of a higher frequency, whose lower 

 limit is determined later. When 



is not less than 8, a four figure accuracy may be obtained by 

 the use of the formulae* 



** M, .... («) 



a small but convenient change in the notation having been 

 introduced. Therefore 



/2 4 9 \ 



and finally 



R= (w) i 1+ V87r/^ 2 ) + l'S7Tfipr 2 j 



-^-^(^-^^{^(^y-K^n (46) 



\2wprV I 4:87rfipr 2 '2\SirfMpr 2 ) j 

 crcos^a-5sin 2 a )/_o L _Yr / <r \» 9 ___^_1 (47) 



A three-figure accuracy in these results will be secured if 

 the conditions 



a>12r, rfi>70 (48) 



are satisfied, in the case of copper wires. No further con- 

 dition as regards a is here needed, as it is satisfied by virtue 

 of the others. In the limiting case of very high frequency 



R =(^) i -32^ cos2a ( 1 - 5sin2a ) W 



T _ ( G ^ V °" cos 2 a (1 — 5 sin 2 a) / <r \l 3a / <t/a \* ,- ft v 



L ~V2^ 2 7 + ~ 327rpm 2 \ 2777^7 "32^\2^ 2 / ,l ° U ' 



* Russell, Z. n p. 532. 



