Electric Flux and Gauss's Law for Non-Uniform Charge Density in a Solid Cylinder

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SUMMARY

The discussion focuses on calculating the electric field (E-field) for a long non-conducting solid cylinder with a non-uniform charge density defined by ρ(r) = Ar², where A is a constant and r is the radial distance from the axis. Using Gauss's Law, the E-field is derived for two regions: inside the cylinder (r < R) and outside the cylinder (r > R). The results confirm that the E-field behaves differently in these regions due to the varying charge density, demonstrating the application of Gauss's Law in electrostatics.

PREREQUISITES
  • Understanding of Gauss's Law in electrostatics
  • Familiarity with electric field concepts
  • Knowledge of charge density functions
  • Basic calculus for integration
NEXT STEPS
  • Study the derivation of electric fields using Gauss's Law
  • Explore charge density variations in different geometries
  • Learn about the implications of non-uniform charge distributions
  • Investigate applications of electric fields in real-world scenarios
USEFUL FOR

Students of physics, electrical engineers, and anyone interested in advanced electrostatics and the application of Gauss's Law in non-uniform charge distributions.

johafmorsha
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Problem
A long non conducting solid cylinder of radius R has a non-uniform change density rho or (p) that is a function of the radical distance r from the axis of the cylinder. given by rho or p(r)=Ar^2 Find the E-field at regions r<R and r>R?
 
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you need to show your attempt.
 
Ah Gauss's Law, this brings meback...

Draw a picture.
 

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