Capacitance of three concentric spherical shells?

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SUMMARY

The capacitance of three concentric spherical shells can be calculated using the formula C = Q/V, where V is derived from the electric field E = -gradV. For two shells, the capacitance is given by C = (4πε) / ((1/a) - (1/b)), where a and b are the radii of the inner and outer shells, respectively. To find the total capacitance of three shells, one must first calculate the voltage between the inner shells and then between the outer shells, adding the voltages as they are in series. This method effectively combines the capacitance contributions of each shell.

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  • Understanding of electrostatics and capacitance
  • Familiarity with electric field concepts and gradient operations
  • Knowledge of spherical coordinates and geometry
  • Proficiency in applying formulas for capacitance in series
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  • Study the derivation of capacitance for concentric spherical shells
  • Learn about the application of Gauss's Law in electrostatics
  • Explore the concept of electric potential and its relation to capacitance
  • Investigate the effects of dielectric materials on capacitance
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Students in physics or electrical engineering, educators teaching electrostatics, and anyone interested in understanding the principles of capacitance in spherical geometries.

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Homework Statement



I do not have a specific question, I am just wondering how one would go about finding the capacitance of three concentric spherical shells. Suppose the outer radius of the each shell is a, b, and c from the center outwards.

Homework Equations



E= -gradV
C = Q/ V, which for two shells = (4∏ε)/ ((1/a)-(1/b)) ... this is the voltage between the two shells.

The Attempt at a Solution



If we found the voltage between the two inner shells and then the to outer shells, perhaps we could add them? What do you you all think?
 
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You can add the voltages across series elements.

ehild
 

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