460 Prof. D. 1ST. Mallik on Magnetic 



we have in the first place to find the mean value of V, 



i. e. calculate (V Tr j i 



\\ Vac da 



jj dc da 



lea) 

 where <; = distance of any winding of wire from the origin, 



ISIv 



and a= radius of the winding 



=h vV 2 -i Vi-/^ 2 . 



8. We shall suppose the meridian section of the coil to be 

 a curvilinear area bounded by confocal ellipses (r= constant) 

 and confocal hyperbolas (0 = constant), so that r and juu may 

 be treated as independent variables. 



This will enable us to obtain an approximate solution of 

 the problem of induction in a soft iron rod in the form of a 

 very prolate spheroid, due to a coil of small depth. 



Now 



"b(ca) _ B c ~d a __ "bc_ B<2 



L Vi-V vV 2 -iJ 



.". the potential 



tfdcdajj LVl-ya 2 v/»- 2 -l-l 



+(i-/OK« a -i)»}*^/»] 



= -29rmt'pQo(i-'){l + (^ ^— 1 cosh" 1 »— >■ n/?^l\ VI-/T 2 . ;£} 



+ (1-^)^-1)*] drd^J; 



where m — total number of windings in the coil and 

 §dcda 





