Concentric Spheres Capacitance Question- How to use area

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SUMMARY

The discussion revolves around calculating the capacitance of three concentric metal shells treated as two capacitors in series. The user initially attempts to apply the formula C = ε₀ * area / distance, which is valid for parallel-plate capacitors, but is incorrect for spherical capacitors. The correct approach requires using the specific formula for spherical capacitors, which can be found in standard textbooks. This distinction is crucial for accurately determining capacitance in this scenario.

PREREQUISITES
  • Understanding of capacitance formulas, specifically for spherical capacitors.
  • Familiarity with the concept of series capacitors.
  • Knowledge of the permittivity constant (ε₀) in electrostatics.
  • Basic principles of electric charge and voltage relationships (C = Q/ΔV).
NEXT STEPS
  • Research the formula for capacitance of spherical capacitors.
  • Study the derivation of capacitance in series configurations.
  • Explore the relationship between charge distribution and capacitance in concentric shells.
  • Review relevant sections in textbooks on electrostatics and capacitance.
USEFUL FOR

Students studying electromagnetism, electrical engineering students, and anyone involved in capacitor design or analysis.

swooshfactory
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Homework Statement



I am trying to solve a question where I have three concentric metal shells at different radii. I am treating them as two capacitors in series. I would like to use the formula C= enot*area/distance between capacitors, but I have a few questions.



Homework Equations



(in next section)

The Attempt at a Solution



1. Which area would I use when computing the capacitance for between shells? I assume the smaller one, because I assume that if you put a small electrode over a larger electrode, the capacitor would only exist in the area between, making the smaller area the area to use.
2. Does this equation assume equal charge? No charge is used in the formula. However, the other formula I know for capacitance, C=Q/deltaV, would assume equal charge over both. Is this relevant for this problem?


Thanks for any help.
 
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HI swooshfactory,

swooshfactory said:

Homework Statement



I am trying to solve a question where I have three concentric metal shells at different radii. I am treating them as two capacitors in series. I would like to use the formula C= enot*area/distance between capacitors

This is the capacitance formula for a parallel-plate capacitor; a spherical capacitor would have a different formula. Once you find that formula (it should be in your textbook) you'll be able to answer your questions.
 

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