Finding the capacitance of two separated hemispheres

jiajie
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Homework Statement
an interesting problem to discuss
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How to calculate a pair of adjacent hemispheres capacitance?
like the picture, two adjacent hemispheres（radius R, distance d, assume the charge is ±Q of each side（assume evenly distributed）, can we calculate its capacitance?
 

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What is the definition of capacitance?
 
The assumption of uniformly distributed charge doesn't lead to equipotential hemispheres. In this case, calculating the capacitance isn't an easy task.
 
Gordianus said:
The assumption of uniformly distributed charge doesn't lead to equipotential hemispheres. In this case, calculating the capacitance isn't an easy task.
They can't be conductors, so I don't think there is any standard definition of capacitance.
 
can we assume the electrical field is horizontally paralleled to simply it
 
jiajie said:
can we assume the electrical field is horizontally paralleled to simply it
Unfortunately, it isn't that simple. I checked whether Smythe had addressed this case but I had no luck.
 

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