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

Chapter 1, Problem 47P

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QUESTION:

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

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

(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.]

Questions & Answers

QUESTION:

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

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

(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.]

ANSWER:

a)

Step 1 of 3

We have to write an expression for the volume charge density  of a point charge  at .

The volume charge density  of a point charge  at  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)

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