What is the Electric Field in a Non-Uniformly Charged Spherical Volume?

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SUMMARY

The discussion revolves around calculating the electric field within a non-uniformly charged spherical volume, specifically where the charge density is defined as ρ(r) = (5.5 × 10-15) * r2.3. Participants express frustration over the complexity of the problem, particularly regarding the integration required to derive the electric field from the given charge density. The challenge lies in understanding how to apply integral calculus to solve for the electric field in this context, as the charge distribution is not uniform.

PREREQUISITES
  • Understanding of electrostatics principles
  • Familiarity with electric field calculations
  • Knowledge of integral calculus
  • Experience with spherical coordinates
NEXT STEPS
  • Study the derivation of electric fields from non-uniform charge distributions
  • Learn about Gauss's Law and its applications in electrostatics
  • Practice solving integrals involving variable charge densities
  • Explore examples of electric fields in spherical coordinates
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Students in electromagnetism courses, physics educators, and anyone preparing for exams involving electric fields and charge distributions.

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I have an exam on Monday in my E&M class. I've been doing the homework, etc etc. My prof. even has a link on his website that has old exams that we can use to study from. The exam I am practicing off of has the questions, a (sketchy) calculation, and an answer. This question has been driving me and my classmates NUTS! Nobody can solve it! I can't make sense of his calculations, can somebody please tell me I am not crazy…or, better yet…show me what I am not seeing. Thanks.

ScreenShot2011-09-17at114319PM.png


That weird looking thing at the top that looks like R**(2.3) is supposed to be the radius to the power of 2.3. Yeah, I don't get it either, but that's what my prof. told me.

The answer is in parenthesis.

Is there something wrong with the calculations?

Why can't I figure this out??
 
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Rewriting this, in case you don't understand it: you have a spherical volume filled with distributed static charge. It's not uniformly distributed, it gets more dense the farther you move away from the centre. The charge density in the sphere is a function of distance from the centre=(5.5*10-15)*r2.3

I've forgotten how to solve these. :redface: I guess it's going to involve an integral.
 

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