E field calculations for continuous charge distributions

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SUMMARY

The discussion focuses on calculating electric fields for continuous charge distributions using three key tools: symmetry, charge density representation, and limit checks at large distances. The Giancoli textbook emphasizes that expressing the charge dq in terms of charge density lambda is crucial for accurate calculations. Additionally, verifying results at large distances (large r) ensures the correctness of the derived electric field equations, as they should approximate Coulomb's law for point charges in such scenarios.

PREREQUISITES
  • Understanding of electric fields and Coulomb's law
  • Familiarity with continuous charge distributions
  • Knowledge of charge density concepts
  • Basic calculus for limit evaluations
NEXT STEPS
  • Study the application of symmetry in electric field calculations
  • Learn about charge density lambda and its role in electric field equations
  • Explore limit evaluation techniques in physics
  • Investigate electric field calculations for various geometries like rings, discs, and spheres
USEFUL FOR

Students of physics, educators teaching electromagnetism, and anyone involved in advanced electric field calculations will benefit from this discussion.

kiwibird4
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so I was reviewing my textbook on calculating electric field when we can assume a continuous charge distribution and they said three useful tools are
(1) making use of symmetry
(2) expressing the charge dq in terms of charge density lambda
(3) and checking the answer at the limit of large r which serves as an indication of the correctness of the answer -- if result does not check at large r, your result has to be wrong (giancoli textbook).

Anyway, I understand the usefulness of 1 and 2 but do not fully understand what number 3 is talking about or how to check the answer in that way? Can anyone explain further what they are referring to or maybe give an example
 
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For example, if you're calculating the electric field around a ring or disc or sphere or something, then you should expect that for ##r## that are very far away, since the object will look essentially like a point, the electric field equation should look like coulomb's law for a point charge.
 

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