Finding the capacitance of two separated hemispheres

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Calculating the capacitance of two adjacent hemispheres with radius R and distance d, each carrying a charge of ±Q, poses significant challenges due to the non-uniform distribution of charge. The assumption of uniformly distributed charge does not result in equipotential hemispheres, complicating capacitance calculations. The discussion highlights that these hemispheres cannot be treated as standard conductors, making it difficult to apply conventional capacitance definitions. Attempts to simplify the problem by assuming a horizontally parallel electric field are deemed insufficient. Overall, the complexity of the scenario suggests that established methods may not adequately address the capacitance of this configuration.
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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