Eletric field within a cavity of a cylinder.

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SUMMARY

The discussion focuses on calculating the electric field within a spherical cavity of radius R/2 located inside a uniformly charged cylinder of radius R and length D. The user contemplates using Gauss's Law to determine the electric field, suggesting that the field may be zero due to the uniform charge distribution. The problem's symmetry allows for simplification, indicating that the cavity's position at D/2 from one end of the cylinder is crucial for analysis.

PREREQUISITES
  • Understanding of Gauss's Law in electrostatics
  • Familiarity with electric field concepts and calculations
  • Knowledge of charge density and its implications
  • Basic geometry of cylindrical and spherical shapes
NEXT STEPS
  • Study the application of Gauss's Law in non-uniform charge distributions
  • Explore the concept of electric field inside cavities of charged objects
  • Investigate the effects of symmetry on electric field calculations
  • Review examples of electric fields in cylindrical coordinates
USEFUL FOR

This discussion is beneficial for physics students, educators, and anyone interested in electrostatics, particularly those studying electric fields in complex geometries.

PenKnight
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Homework Statement


Considering a cylinder of radius, R, and length D with uniform charge density p containing a spherical cavity of radius R/2. Find the field in the cavity.

The cavity sits on one side of the cylinder so that it's diameter spans from the concave face of the cylinder to the center.I'm not sure at what length the cavity is. Probably at D/2. I think that D > R as well.

The Attempt at a Solution


I'm not sure where to start. The only thing that is symmetrical about this problem is that you can cut the shape in half and have two mirror pieces.
 
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I'm thinking that you could use Gauss's Law somehow, but I'm not sure how to apply it. I'm guessing that the field should be zero, as the charge is distributed uniformly and the charge inside the cavity is equal to the charge outside the cavity.
 

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