Finding the capacitance of two separated hemispheres

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Homework Help Overview

The discussion revolves around calculating the capacitance of two adjacent hemispheres with a specified radius and distance between them, assuming a charge distribution. Participants are exploring the implications of these assumptions on the calculation of capacitance.

Discussion Character

  • Exploratory, Assumption checking

Approaches and Questions Raised

  • Participants question the definition of capacitance and the implications of assuming a uniformly distributed charge. There are discussions about whether the hemispheres can be treated as conductors and the challenges in calculating capacitance under these conditions.

Discussion Status

The discussion is ongoing, with participants raising questions about the assumptions made regarding charge distribution and the nature of the electric field. Some guidance has been offered regarding the complexity of the problem, but no consensus has been reached.

Contextual Notes

There are constraints regarding the assumptions of charge distribution and the nature of the hemispheres, as well as references to external sources that have not provided clarity on the topic.

jiajie
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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?
 

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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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