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(a) Write an expression for the volume charge density ?(r)

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

Solution for problem 47P Chapter 1

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 47P

Problem 47P

(a) Write an expression for the volume charge density ρ(r) of a point charge q at r ′. Make sure that the volume integral of ρ equals q.

(b) What is the volume charge density of an electric dipole, consisting of a point charge −q at the origin and a point charge +q at a?

(c) What is the volume charge density (in spherical coordinates) of a uniform, infinitesimally thin spherical shell of radius R and total charge Q, centered at the origin? [Beware: the integral over all space must equal Q.]

Step-by-Step Solution:

a.)

Step 1 of 3

We have to write an expression for the volume charge density ρ(r) of a point charge q at r ′.

The volume charge density ρ(r) of a point charge q at r ′ is given by the expression,

                                     

Making sure that the volume integral of   equals .

                        

Using Dirac delta function

         

 If contains                       

                                          if does not contain

Hence,

                    

Therefore, the volume integral of   equals .



b.)

Step 2 of 3

Chapter 1, Problem 47P is Solved
Step 3 of 3

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

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(a) Write an expression for the volume charge density ?(r)