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According to Eq. 4.1, the induced dipole moment of an atom

Introduction to Electrodynamics | 4th Edition | ISBN: 9780321856562 | Authors: David J. Griffiths ISBN: 9780321856562 45

Solution for problem 3P Chapter 4

Introduction to Electrodynamics | 4th Edition

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Introduction to Electrodynamics | 4th Edition | ISBN: 9780321856562 | Authors: David J. Griffiths

Introduction to Electrodynamics | 4th Edition

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Problem 3P

Problem 3P

According to Eq. 4.1, the induced dipole moment of an atom is proportional to the external field. This is a “rule of thumb,” not a fundamental law, and it is easy to concoct exceptions—in theory. Suppose, for example, the charge density of the electron cloud were proportional to the distance from the center, out to a radius R. To what power of E would p be proportional in that case? Find the condition on ρ(r ) such that Eq. 4.1 will hold in the weak-field limit.

Reference equation 4.1

p = αE.

Step-by-Step Solution:

Solution 3P

Step 1:

We need to find out the relation between electric field and the induced dipole.

From gauss law, the is electric field,

The enclosed charge,  is,

And the charge density is,

 is the area                 

        

Comparing this equation with equation ,

                         

                         

Step 2 of 3

Chapter 4, Problem 3P is Solved
Step 3 of 3

Textbook: Introduction to Electrodynamics
Edition: 4
Author: David J. Griffiths
ISBN: 9780321856562

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According to Eq. 4.1, the induced dipole moment of an atom