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




On 5/2/2017 8:41 PM, Carl Mungan wrote:
For an isolated sphere, C = R/k. /snip/ -Carl









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