Solution Found!
(a) Write an expression for the volume charge density ?(r)
Chapter 1, Problem 47P(choose chapter or problem)
(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)