Mutual Induction of a Circle and a Coaxial Helix, $c. 201 



When M has been calculated by (6) it is a simple matter to 

 calculate q, r, -s by the above equations. 



M 

 Let g> / A i \ ~7. = Z. Then equations (7) may be expressed 



thus : 



For the values of 2A , 2', 2oj taken in 10 we have 



n = 17-411370, 



Uc = 4-096932, 



V He = 1-385957, 



F + He' = 6-807907, 



Z = 0-8982254, 

 P (&) = 0-8087238, 

 2 = 1-24629, 

 r = + 2-34593, 

 8 = 0-09964. 



On the Potential Energy of a Circular Current and a Uniform Coaxial 

 Circular Cylindrical Current Sheet. 



12. The current lines in the sheet are circles in planes at right 

 angles to the axis. 



Let the circle have its centre at the origin, and let its equations be 



y = a COS 0"| 



z = a sin J 



and let the equations to the coaxial cylindrical sheet be 



if = A cos & "I 

 z = Asin0'J 



the plane ends of the cylinder being determined by the equations 

 x = XH x = #2. 



Let the current in the circle be / e , and the current per unit length 

 of the cylindrical sheet 7 ; and let the potential energy of the circular 

 current and the current sheet be M'. 



