due to an Elliptical Current. 109 



where M c = the coefficient of mutual induction of the circle 



and disk circumference, 

 and <r=;H — H c . 



§ 4. To obtain the value of B, we must first find an 

 expression for the intensity of magnetic field (H e ) due to an 

 elliptical current at a point in its plane within it in terms of 

 the semiaxes of the ellipse and the coordinates of the point. 



Let the equation to the ellipse be 



d l ^ b 2 ' 



and let f, rj be the coordinates of the point in question. 



The intensity of the magnetic field at the point (jf , 77) may 

 be expressed by the formula 



«-rs 



where p, 6 are the polar coordinates of a point on the ellipse 

 referred to the point (f, rj) as origin. 



Forming the polar equation to the ellipse with the point 



(f, tj) as origin, solving for — , and substituting in the above 

 equation, we have P 



H = a *b*-b*F-a* V * \ dd ^ C ° S2 ° + 2A ' C0S ° shl 6 +¥&tf #> 

 where f = b 2 - v 2 , 



g 2 = a 2 -?, 



h 2 _ ft. 



Let (j>\ x 2 be determined by the equations 



<$> 2 +x*=f+g 2 \ 



and we have 



a h f* m — 



±ab 



where 



= w *mt) 



E 0/>>X) = [ o 3 dd s/<f> 2 cos 2 0+^j gin8 09 

 an elliptic integral of the second kind. The value of E(<£> %) 



