Re: Sphere/Toroid Comparison Chart

["Tesla list" <tesla-at-pupman-dot-com>]

Original poster: "by way of Terry Fritz <twftesla-at-uswest-dot-net>" <Mddeming-at-aol-dot-com>

In a message dated 5/8/01 8:17:07 PM Eastern Daylight Time, tesla-at-pupman-dot-com 
writes: 


>
> Original poster: "Luc by way of Terry Fritz <twftesla-at-uswest-dot-net>" < 
> ludev-at-videotron.ca> 
>
> Hi guy 
>
> I post again the same question: If you look at the chart you'll 
> see that until you hit 18" of exterior diameter the toroid with a 
> thickness of 4" have more capacity than one of 6" thickness. 
> Please could some of you explain to me how a toroid with an area 
> bigger could have a smaller capacity. I already know that the 
> surface facing the center ( the hole of the donut ) don't 
> participated as far as the exterior. But the exterior of a 6" 
> thick toroid is bigger than the area of a 4" one. 
>
> Tx 



Hi Luc, All! 

        I was wrong about the C-C diameter. It is actually the exterior 
diameter. I believe the mystery of the smaller toroid can be explained like 
this: For a given major diameter, the toroid with the larger chord will have 
a smaller inner diameter, meaning the curvature around the donut hole is 
tighter. For the smaller inner diameter of the toroid with the larger chord, 
there is greater repulsive force between the charges on the inside curve 
which reduces the effective capacitance until that inner diameter becomes 
large enough that the effect is negligible. The smaller the inner diam., the 
more distorted the charge distribution. A 14" outer diameter toroid with a 4" 
chord (6" id) actually has more of its surface at a greater distance from the 
center than one with a 6" chord and 14" outer diameter (2" id). 
The formula, as an approximation, also allows for negative inner diameters to 
be computed, which is of course, silly. 
Matt D.