Spherical capacitor energy problem

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SUMMARY

The energy associated with a conducting sphere of radius R and charge Q in a vacuum is defined by the formula U = k*Q^2 / (2R). This formula derives from the work required to assemble the charge Q from an infinite separation to the sphere's surface. The key concept involves calculating the work done in contracting an infinitely large sphere of charge to a smaller radius, which is essential for understanding electrostatic energy in spherical capacitors.

PREREQUISITES
  • Understanding of electrostatics and electric fields
  • Familiarity with the concept of electric potential energy
  • Knowledge of the formula for work done in electrostatics
  • Basic grasp of spherical geometry and charge distribution
NEXT STEPS
  • Study the derivation of the electric potential energy formula for spherical capacitors
  • Learn about the concept of electric field strength around charged spheres
  • Explore the implications of charge distribution on energy calculations
  • Investigate the role of vacuum in electrostatic problems
USEFUL FOR

Students and professionals in physics, electrical engineering, and anyone interested in understanding the principles of electrostatics and energy calculations related to spherical capacitors.

AgPIper
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Show that the energy associated with a conducting sphere of radius R and charge Q surrounded by a vacuum is

U = k*Q^2 / (2R)

:smile: thanks
 
Last edited:
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Where are you having difficulty with the problem?
 
Consider how much work you would have to do to bring all of the charge together from an infinite separation. In other words, how much work does it take to contract an infinitely large sphere of charge Q down to a small sphere of radius R?
 

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