What Is the Correct Sign for the Capacitance of a Spherical Capacitor?

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SUMMARY

The capacitance of a spherical capacitor, specifically one with a radius of 1 and a charge of -Q inside a larger spherical conductor with a radius of 2 and a charge of +Q at the inside surface, is calculated using Gauss' law. The resulting capacitance is determined to be 8πE₀, where E₀ is the permittivity of free space. Capacitance is always a positive value, confirming that the final result should be positive despite the presence of negative charges in the system.

PREREQUISITES
  • Understanding of Gauss' Law
  • Familiarity with electric fields and potential difference
  • Knowledge of capacitance and its mathematical representation
  • Basic concepts of electrostatics
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Physics students, electrical engineers, and anyone studying electrostatics and capacitor design will benefit from this discussion.

schattenjaeger
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Say you have a spherical conductor with radius 1 with charge -Q inside of another larger spherical conductor(with radius 2 to the inside edge of the conductor)with a charge +Q at the inside surface, what's the capacitance?

I used Gauss' law to find E in between the two conductors, then integrated with respect to r to find the change in potential, and did Q/that=C

I'm pretty sure I got the right actual answer, it was like 8*pi*Eo...and maybe something else(Eo is that constant), I don't remember off hand(this was on a test I took this morning)but my question...should it be positive or negative? That really confused me and I had all kinds of negatives floating around and finally fixed it up so that C came out positive, and it looked like it made sense
 
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Capacitance is always a positive value. Is that what you mean?
 
it is? Good then, that's what I figured at the time, but I got to thinking afterwards
 

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