What is the charge density and electric field inside a polarized hydrogen atom?

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SUMMARY

The discussion focuses on calculating the charge density and electric field within a polarized hydrogen atom, modeled as a uniformly charged sphere representing the electron cloud. The charge density is determined by dividing the total charge of the electron by the volume of the sphere, while the electric field inside the cloud can be derived using Gauss' Law, particularly for points where the radius vector r exceeds the sphere's radius a. The importance of including the nucleus in the calculations is emphasized for accuracy.

PREREQUISITES
  • Understanding of charge density calculations
  • Familiarity with Gauss' Law
  • Basic knowledge of atomic structure and electron orbitals
  • Concept of electric fields in electrostatics
NEXT STEPS
  • Study the derivation of charge density in spherical coordinates
  • Learn about the applications of Gauss' Law in electrostatics
  • Explore the concept of polarization in atoms and molecules
  • Investigate the electric field calculations for different charge distributions
USEFUL FOR

Students studying electromagnetism, physicists interested in atomic models, and educators teaching concepts of charge density and electric fields.

yango_17
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Homework Statement


We have a crude model for the polarization of a hydrogen atom, by approximating its 1s orbital with a uniformly charged ball of radius a. What is the (negative) charge density of the electron cloud? What is the electric field inside the cloud, at the point with radius vector r (drawn from the center of the cloud)?

Homework Equations


Equation for charge density
Gauss' Law

The Attempt at a Solution


I was confused as to how to go about setting up the problem. For the charge density I was thinking simply dividing the total charge by the volume of the charged ball. For finding the electric field inside the cloud, I was considering using Gauss' law when a < r.
 
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Your thinking is on track. Go for it! (Don't forget the nucleus.)
 

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