Optimization of sphere and cyliners (Electrical physics)

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SUMMARY

The discussion focuses on the optimization techniques used in electrical physics for calculating electric fields around symmetrical insulating and conducting shapes, specifically spheres and cylindrical shells. The user highlights the application of treating these geometries as point charges and line charges, respectively, which yielded correct results. The mathematical foundation for this simplification is rooted in Gauss's Law, which applies to symmetrical charge distributions. The user seeks clarification on the theoretical justification for these optimization methods.

PREREQUISITES
  • Understanding of Gauss's Law in electrostatics
  • Familiarity with electric field calculations for symmetrical charge distributions
  • Knowledge of point charge and line charge concepts
  • Basic principles of electrostatics and charge density
NEXT STEPS
  • Study Gauss's Law and its applications in electrostatics
  • Research electric field calculations for various symmetrical geometries
  • Explore the mathematical derivation of electric fields from charge distributions
  • Investigate the limitations of optimization techniques in complex geometries
USEFUL FOR

Students and professionals in electrical engineering, physicists, and anyone interested in optimizing calculations for electric fields in symmetrical geometries.

jlee167
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I recently noticed that I have blindly used optimization in some problems that involve symmetrical insulating/conducting spheres and cylindrical shells.
For example, when calculating outer electric field caused by a spherical insulator/conductor, I just treated these as a simple point charge located at their center, and those ways rendered correct answers. Also, in a question involving an infinite cylindrical shell, (given charge density), I treated it as a simple line charge located at its center, and it also gave me a right answer. However, I am still not convinced how this works mathematically. Is it just a way of simplifying problem for faster calculation, or is there any theorem / definition that fully explain the validity of this simplification?
I would appreciate some help
 
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Look up Gausses Law.

You've noticed that the "optimization" only works for simple geometries, and only outside the objects in question.
 

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