Charge Distribution on Two Neighboring Conductors

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SUMMARY

The charge distribution on two neighboring spherical conductors, each with a charge of +Q and radius r, is influenced by their proximity. When the distance d between their centers is much greater than r, the charge distribution remains uniform. However, as d approaches values slightly greater than 2r, the repulsion between like charges alters the distribution. This problem can be accurately solved using the method of image charges, which converges rapidly for d much larger than r.

PREREQUISITES
  • Understanding of electrostatics and Coulomb's law
  • Familiarity with spherical conductors and their properties
  • Knowledge of the method of image charges
  • Basic calculus for solving electrostatic problems
NEXT STEPS
  • Study the method of image charges in electrostatics
  • Explore the effects of charge distribution on conductors in close proximity
  • Investigate the mathematical derivation of charge distributions on spherical conductors
  • Learn about the implications of charge interactions in electrical engineering applications
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Physics students, electrical engineers, and anyone interested in electrostatics and charge distribution phenomena.

conquerer7
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Say you have two spherical conductors, of radius r, centers a distance d apart. Both have charges of +Q. What are the charge distributions on them?

My physics book more or less handwaves and says it'll be more or less unaffected, but is there a way to solve this exactly?
 
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I haven't solved an problems like that in many,many years...but I can provide a bit of an insight:

are these solid or hollow conductors...?

anyway, Say d is much, much greater than r...there should be a uniform distribution on each sphere...now bring them close together, say d is just a bit bigger than 2 r so they are close...like charges will repel somewhat at the closest point, less so further...so it sure
seems like the charge distribution WILL change...I disagree it would be "unaffected".
 
This problem can be solved with a sequence of image charges. It gets quite complicated, but for d>>a, the series converges fast.
 

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