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Gil. The Effective Capacity of Multilayer Coils toith Square 

 and Circular Section. By Gregory Breit, PA.1?.* 



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

 capacity of a coil can be computed as :, i 



where 



x is an arbitrary parameter along the wire, 

 L is the inductance of the coil, 



M(x)dx is the mutual inductance of the section between 

 x and x-\-dx to the rest of the coil, 



l-T.)*($)dx is the charge on the element dx, i being the 

 current through the coil terminal, 



x u x 2 are the values of x at the terminals of the coil, 

 the value x x corresponding to the ungrounded 

 terminal of the coil. 



In the paper mentioned, the formula has been applied 

 to short single-layer solenoids. In this paper the same 

 formula will be applied to two types of multilayer coils 

 having a large diameter. To be specific, consider a multi- 

 layer coil having a circular cross section. A section of 

 such a coil by a plane through its axis is shown in fig. 1. 

 Here AB is the axis. The circles FGH, F'G'H' represent 

 the cross section of the coil. The centres of these cross 

 sections are represented by and 0'. The radius of either 

 of the circles FGH, F'G'H' is denoted by a. The radius 

 of the circle through and 0' and having its centre at D 



(the point of intersection of AB and 00') is denoted by ^— . 



Thus the circumference of the circle last mentioned is /. 



It has been assumed that / is large compared; "with a. 

 Thus (see G. Breit, loc.cit.) the flux through one. turn' of the 

 coil is the same as that through any other. If, ..therefore, 

 the manner in which the layers of the coil are arranged is 

 known, then the relative potential of the various parts of the 

 coil is known. - •■■.,/■■ 



* Communicated by the Director of the Bureau of Standards, 

 "Washington. 



t G. JBreit, " The Distributed Capacity of Inductance Coils-,'' Phys. 

 Rev. xvii. pp. 649-677 (June 1921). ,:.■■-" 



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