Finding the capacitance of two separated hemispheres

In summary, the conversation discusses the difficulty of calculating the capacitance of two adjacent hemispheres with a radius of R and distance of d, assuming a ±Q charge evenly distributed on each side. The assumption of uniformly distributed charge does not lead to equipotential hemispheres, making the calculation challenging. It is also noted that the hemispheres cannot be conductors, so there is no standard definition of capacitance. The possibility of simplifying the calculation by assuming a horizontally parallel electrical field is also discussed, but it is determined that this is not a feasible solution.
  • #1
jiajie
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0
New poster has been reminded to show their work on schoolwork problems
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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  • #2
What is the definition of capacitance?
 
  • #3
The assumption of uniformly distributed charge doesn't lead to equipotential hemispheres. In this case, calculating the capacitance isn't an easy task.
 
  • #4
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.
 
  • #5
can we assume the electrical field is horizontally paralleled to simply it
 
  • #6
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.
 

FAQ: Finding the capacitance of two separated hemispheres

What is capacitance?

Capacitance is a measure of an object's ability to store electrical charge. It is measured in units of farads (F).

How do you calculate the capacitance of two separated hemispheres?

The capacitance of two separated hemispheres can be calculated using the formula C = 4πε0(r1r2)/(r1+r2), where r1 and r2 are the radii of the two hemispheres and ε0 is the permittivity of free space.

What is the significance of finding the capacitance of two separated hemispheres?

Finding the capacitance of two separated hemispheres is important in understanding the behavior of capacitors and their ability to store charge. It can also be useful in designing electrical circuits and systems.

How does the distance between the two hemispheres affect the capacitance?

The capacitance is inversely proportional to the distance between the two hemispheres. This means that as the distance increases, the capacitance decreases.

Can the capacitance of two separated hemispheres be changed?

Yes, the capacitance of two separated hemispheres can be changed by altering the distance between them, the size of the hemispheres, or the material between them. It can also be changed by applying a voltage or charge to the hemispheres.

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