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LXIII. The Effective Capacity of a Pancake Coil. 

 By G. Bkeit *. 



Purpose. 



IT has been shown in a previous paper f that the effective 

 capacity of a coil may be computed as 



where 



x is an arbitrary parameter along the wire ; 



L is the inductance of the coil ; 



M(a?)dx is the mutual inductance of the section between 

 x and x -f dx to the rest of the coil ; 



\Tt) a (^)^ * s ^ ne cnar g e on the element dx, i being the 

 current through the coil terminal ; 



a?!, x 2 are the values of x at the coil terminals, the 

 value x 1 corresponding to the ungrounded ter- 

 minal of the coil. 



The conditions which were assumed in deriving this 

 formula are : — 



(1) The constant C exists. 



(2) The product of the frequency used into the con- 



ductivity is so high that the wire of the coil may 

 be considered as a perfect conductor: i.e., the 

 electric intensity is practically perpendicular to 

 the surface of the wire at any instant. 



(3} The dimensions of the coil are sufficiently small to 

 make it legitimate to neglect the phase differences 

 introduced into the retarded potentials by currents 

 and charges in different portions of the coil. 



(4) The formula still applies if C is not a constant in 

 general, but is constant within a range beginning 

 at very low frequencies. 



It is the purpose of this paper to apply this formula to the 

 case of a pancake coil. 



* Communicated by the Director of tlie Bureau of Standards, 

 "Washington. 



t See " The Distributed Capacity of Inductance Coils," by G. Breit, 

 Phys. Rev. xviii. p. 649 (1921). 



