E&M simple polarizability question

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SUMMARY

The discussion centers on calculating the atomic polarizability of a model atom, as described in Griffiths' textbook. The model consists of a point nucleus surrounded by a uniformly charged spherical cloud of radius "a". The key equations involved include the dipole moment equation, $$\vec{p}=a \vec{E}$$, and the electric field produced by the electron cloud, $$E_e=\frac{1}{4\pi \epsilon_0}\frac{qd}{a^3}$$. The transition from the electric field equation $$E_e=\frac{1}{4\pi \epsilon_0}\frac{q}{a^2}$$ to the dipole field expression is a critical step in understanding the polarizability of the atom.

PREREQUISITES
  • Understanding of atomic models and polarizability concepts
  • Familiarity with Griffiths' "Introduction to Electrodynamics"
  • Knowledge of electric fields produced by charge distributions
  • Basic grasp of dipole moments and their calculations
NEXT STEPS
  • Study Griffiths' example problems on atomic polarizability
  • Learn about dipole fields and their mathematical derivations
  • Explore the implications of electric field equations in atomic models
  • Investigate advanced topics in quantum mechanics related to polarizability
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Students studying electromagnetism, physicists interested in atomic models, and educators looking for examples of polarizability calculations.

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this is a homework problem i realized after posting it. so could a moderator please move this question to the homework section? thanks

one of Griffiths' example:

A primitive model for an atom consists of a point nucleus surrounded by a uniform charged spherical cloud of radius "a". Find the atomic polarizability of such an atom.

(reference equation):

$$\vec{p}=a \vec{E}$$
-------------------

First step:

the field (produced by the electron cloud) at distance d from the center of a uniformly charged sphere is

$$E_e=\frac{1}{4\pi \epsilon_0}\frac{qd}{a^3}$$

---------------so why is that the field produced by the shifted electron cloud?

ie, how does one go from

$$E_e=\frac{1}{4\pi \epsilon_0}\frac{q}{a^2}$$

to..

$$E_e=\frac{1}{4\pi \epsilon_0}\frac{qd}{a^3}$$

(where "d" and "a" are not equal)?
 
Last edited:
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It's a dipole field.
 

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