Electrostatic problem with vectors

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SUMMARY

The discussion focuses on calculating the electric field inside a spherical hole within a uniformly charged sphere centered at the origin (0,0,0) with the hole's center at (d,0,0). The method of superposition is employed to determine the electric field contributions. It is confirmed that the direction of the electric field vector E_x is indeed adjusted to account for the hole's position, specifically expressed as x-d. This adjustment is crucial for accurate vector representation in electrostatics.

PREREQUISITES
  • Understanding of electrostatics principles
  • Familiarity with vector calculus
  • Knowledge of superposition principle in electric fields
  • Basic concepts of electric field and charge distributions
NEXT STEPS
  • Study the superposition principle in electrostatics
  • Learn about electric field calculations for non-uniform charge distributions
  • Explore vector representation of electric fields in three dimensions
  • Investigate the effects of spherical symmetry on electric fields
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Students and professionals in physics, particularly those studying electrostatics, as well as educators looking for examples of electric field calculations involving charge distributions.

Niles
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Homework Statement


Hi all.

A uniformly charged sphere centeren at (0,0,0) has a spherical hole inside and the hole has it's center at (d,0,0). Find the electric field inside the hole.

The Attempt at a Solution


I use superposition. The electric field from the sphere itself is trivial.

Now to find the electric field from the hole. This is also trivial, but the direction of E_x is not just x, but x-d. Am I correct about that?
 
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