How to Design a Charge Distribution for E Proportional to r^2?

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SUMMARY

The discussion focuses on designing a charge distribution that results in an electric field (E) proportional to the square of the distance (r^2). Participants suggest utilizing Maxwell's equations, specifically the relationship between electric fields and volume charge density, to derive the necessary charge distribution. This approach emphasizes the importance of understanding electrostatics and the mathematical relationships governing electric fields.

PREREQUISITES
  • Understanding of Maxwell's equations
  • Knowledge of electrostatics principles
  • Familiarity with electric field concepts
  • Basic calculus for deriving relationships
NEXT STEPS
  • Research the derivation of electric fields from charge distributions using Maxwell's equations
  • Study the concept of volume charge density and its applications
  • Explore examples of charge distributions that yield specific electric field patterns
  • Learn about the mathematical modeling of electrostatic systems
USEFUL FOR

Students in physics, electrical engineers, and anyone interested in electrostatics and electric field design principles.

SirPencil
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Homework Statement


Design a charge distribution so that the resulting E is proportional to r^2.

The Attempt at a Solution


This is not really a homework problem just something our professor told us to think about at the end of our lecture. It made me really curious as to how you would do this.

You guys have any ideas or something to get me started?

Thanks
 
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Isn't there a Maxwell equation relating the electric field to the volume charge density that might help you here?:wink:
 

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