Potential Energy of 2 Spherical Shells

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SUMMARY

The discussion focuses on calculating the energy required to assemble two uniform hollow spheres of charge q, with inner radius a, outer radius b, and separated by a distance c. The relevant equations include the incremental charge dQ defined as 4πroh-vR dR², and the total charge Q of one sphere calculated as roh-vπR³. The user expresses uncertainty about how the separation distance c affects the potential energy calculation for the two-sphere configuration, specifically whether to double the energy of one sphere and then adjust for the interaction between the two spheres.

PREREQUISITES
  • Understanding of electrostatics and potential energy concepts
  • Familiarity with spherical coordinates and volume charge density
  • Knowledge of calculus, particularly integration techniques
  • Experience with energy calculations in electrostatic systems
NEXT STEPS
  • Study the derivation of potential energy for multiple charged spheres
  • Learn about the effects of distance on electric potential energy in electrostatics
  • Explore the concept of superposition in electric fields and potentials
  • Review integration techniques for calculating energy from charge distributions
USEFUL FOR

Students in physics or engineering, particularly those studying electrostatics, as well as educators looking for examples of energy calculations involving multiple charged objects.

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Homework Statement



Find the energy required to assemble two uniform hollow spheres of charge q between radii a and b with a volume charge density roh-v. The shells are separated by a distance c.

*description of picture* - two identical spherical shells with inner radius a and outer radius b separated by a distance c

Homework Equations



dQ = 4*pi*roh-v*R dR^2 <--- "add incremental rings of charge dQ in order to assemble a hollow sphere of charge"

Q of one sphere = roh-v*pi*R^3

dW = V dQ

The Attempt at a Solution



I know how to do this problem with one solid sphere. I am unsure of how the second sphere and the distance c changes the problem.

Do I find the potential to assemble one sphere and then double it (for the second sphere) and then multiply it by the potential of the two sphere configuration?

[/B]
 
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