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Get Full Access to Introduction To Electrodynamics - 4 Edition - Chapter 1 - Problem 47p
Get Full Access to Introduction To Electrodynamics - 4 Edition - Chapter 1 - Problem 47p

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# (a) Write an expression for the volume charge density ?(r) ISBN: 9780321856562 45

## Solution for problem 47P Chapter 1

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

Step 3 of 3

##### ISBN: 9780321856562

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