Finding the capacitance of two separated hemispheres

[jiajie]

Homework Statement

an interesting problem to discuss

Relevant Equations

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?

 

[Orodruin]

What is the definition of capacitance?

 

[Gordianus]

The assumption of uniformly distributed charge doesn't lead to equipotential hemispheres. In this case, calculating the capacitance isn't an easy task.

 

[Keith_McClary]

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.

 

[jiajie]

can we assume the electrical field is horizontally paralleled to simply it

 

[Gordianus]

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.