Re: [Phys-L] Charge division on Spheres.

[Carl Mungan <mungan@usna.edu>]

I’m not sure I exactly understand the geometry of how the can sits inside the steel container (a sketch would help), but if they are concentric we might model them as a cylindrical capacitor so that:

C = 2 pi epsilon0 LENGTH / ln(0.23/DIAM)

This gives a result that is in relatively good linear agreement with your measured values except it is too small by a factor of 2. We might try to improve it by adding the two end caps (assuming the cap is closed all around) in parallel modeled as parallel-plate capacitors:

C = 2 pi epsilon0 LENGTH / ln(0.23/DIAM) + pi epsilon0 DIAM^2 / d

where d = length of steel container - LENGTH. It can’t be that length of steel container = 0.132 m because that is smaller than your biggest LENGTH value. So I probably have the geometry wrong.

Anyhow, you might improve on what I’ve done or make the geometry more nearly concentric cylinders. -Carl

> On May 4, 2017, at 2:57 PM, brian whatcott <betwys1@sbcglobal.net> wrote:
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> 	On 5/2/2017 8:41 PM, Carl Mungan wrote:
> > For an isolated sphere, C = R/k. /snip/  -Carl
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> This is the story of my quick check on the capacitance of cans
> in a steel container.
>
> It is amusing on two counts:
> 1) it begins by supposing in the great physics tradition of spherical
> cows, that cans can represent spheres.
> 2) It appears to show that surface area of a can is a better fit to
> its capacitance than its equivalent spherical diameter - with graphs
> shown below.
>
> It is possibly instructive to see how this setup gives counterfactual
> evidence for a surface area relation, rather than the known spherical
> radius linear relation.
>
>
> I took the following measurements of four containers of canned goods
> (right cylinders)  in meters.
> LABELED
> CONTENT      LENGTH   DIAM       VOLUME     S. AREA      EQUIV SPH DIAM
> A    1.4kg    0.177    0.105    0.001533    0.07569    	0.143
> B    0.411    0.113    0.074    0.000486    0.0349    	0.0976
> C    0.198    0.070    0.066    0.000239    0.02136    	0.07707
> D    0.085    0.040    0.062    0.000121    0.0138    	0.0613
>
> I placed each in turn in a steel container Height = 0.132,  Diam =
> 0.23:  closed with a lid Height 0.05, on a ring of expanded polystyrene 0.02 tall X
> 0.07 Diam,  with their axis of symmetry horizontal and measured their capacitance
> after taring the unconnected spring clip.
>
> Here are the measured capacitance values:
> A    28 pF
> B    10.8
> C    6.9
> D    3.2
>
>
>
> Graph of Capacitance versus Diameter of equivalent Sphere.
> <http://s880.photobucket.com/user/betwys/media/Capacity%20of%20%20Right%20Cylinders/cap-quiv.jpg.html>
>
> Graph of Capacitance versus Surface Area of Can
> <http://s880.photobucket.com/user/betwys/media/Capacity%20of%20%20Right%20Cylinders/cap-surf.jpg.html>
>
>
> Brian W
>
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-----
Carl E. Mungan, Professor of Physics  410-293-6680 (O) -3729 (F)
Naval Academy Stop 9c, 572C Holloway Rd, Annapolis MD 21402-1363 
mailto:mungan@usna.edu     http://usna.edu/Users/physics/mungan/