Capacitance of two tangential spheres

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Discussion Overview

The discussion revolves around the capacitance of two tangential conducting spheres, exploring the implications of their configuration on charge distribution and potential. Participants consider theoretical aspects and practical implications of capacitance in this specific arrangement.

Discussion Character

  • Exploratory
  • Technical explanation
  • Debate/contested
  • Mathematical reasoning

Main Points Raised

  • One participant questions how to calculate the capacitance of two tangential spheres, considering charge distribution and potential.
  • Another participant asserts that if the spheres are touching, they do not form a capacitor.
  • A subsequent reply suggests that the spheres should be considered as being infinitesimally close rather than touching, raising concerns about potential behavior at the tangential point.
  • One participant proposes that the combined surface of the two spheres can be treated as one plate of a capacitor, with the other plate at infinity, equating it to the capacitance of a single isolated metallic sphere.
  • There is uncertainty expressed regarding whether the problem has a closed form solution, with acknowledgment of the complexity involved.
  • A later reply discusses the uniformity of potential for a single sphere and questions how to handle non-uniform potential in the case of two spheres, suggesting the need for integration over the surface.

Areas of Agreement / Disagreement

Participants do not reach a consensus on the nature of the capacitance of the two spheres, with multiple competing views on whether they can be treated as forming a capacitor and how to approach the calculation of capacitance.

Contextual Notes

There are limitations regarding assumptions about the proximity of the spheres, the behavior of potential at the tangential point, and the complexity of deriving a closed form expression for capacitance in this configuration.

Ans426
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Hi,

Question:
Consider two conducting spheres with radius R, which are tangential each other (i.e. they touch right at one point)
If C = Q/V, where V is the potential at the surface, find the capacitance of this configuration.
--------------------------------------------------------------------------------------------

I've came along this question in some sort of old physics exam...
I've been giving it some thought for a while but haven't really came up with anything..
Anyone can shed some light on how to do this?
(For instance what charge distribution should it have? +ve on one, and -ve on the other?
And then integrate for all the charges on the surface?)

Thanks.
 
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If they are touching each other then they do not form a capacitor.
 
Thanks for the reply.

True...I guess that part was confusing me..
The question says that they are tangent to each other, so I guess we'll have to assume that they have infinitesimally close to each other but not touching?

But in that case, wouldn't the potential blow up at the point where they are tangent to each other?
 
Anyone, Please? :smile:
 
No, it is meant that the combined surface of the two spheres forms one plate of a capacitor, the other being at infinity. Think of it as just one isolated metalic sphere having a capacitance C = 4 \, \pi \, \varepsilon_0 \, R.

Your problem is really hard. I don't know if it has an answer in a closed form expression.
 
Dickfore said:
No, it is meant that the combined surface of the two spheres forms one plate of a capacitor, the other being at infinity. Think of it as just one isolated metalic sphere having a capacitance C = 4 \, \pi \, \varepsilon_0 \, R.

Your problem is really hard. I don't know if it has an answer in a closed form expression.
Thanks a lot, I wasn't aware that a single sphere could have capacitance too.
And yes, the question comes from an advanced level exam..

For a single sphere, it seems that C = Q/V makes sense only because V is uniform over the surface...
How about for a non-uniform potential in this case? Would you need to integrate over the surface?
Any input is appreciated! :smile:
 
Last edited:

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