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Suppose the electric field in some region is found to be

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

Solution for problem 9P Chapter 2

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 9P

Suppose the electric field in some region is found to be  in spherical coordinates (k is some constant).

(a) Find the charge density ρ.

(b) Find the total charge contained in a sphere of radius R, centered at the origin. (Do it two different ways.)

Step-by-Step Solution:

Solution 9P

Step 1 of 8</p>

 Given, the electric field in spherical coordinates  is where k is constant

(a)

Step 2 of 8</p>

 To find the charge density of the sphere of radius ‘r’

 

  The charge density is given by the equation,

                                                                                          ….(1)    

From eq(1)  = (

  ) = =                   ….(2)

Step 3 of 8</p>

 Using Eq(2) we have,

 =  =                                          ….(3)

Therefore, substituting Eq(3) in Eq(1)

Hence the charge density is given by,

                                                                ….(4)

(b)   

Step 4 of 8 </p>

To find the total charge in the sphere of radius ‘R’ at the origin

First Method: Using Gauss’ law

The Gauss’ equation is given by

                                                                                                     ….(5)  

Where is the electric flux

Step 5 of 8

Chapter 2, Problem 9P is Solved
Step 6 of 8

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

The full step-by-step solution to problem: 9P from chapter: 2 was answered by , our top Physics solution expert on 07/18/17, 05:41AM. The answer to “Suppose the electric field in some region is found to be in spherical coordinates (k is some constant).(a) Find the charge density ?.(b) Find the total charge contained in a sphere of radius R, centered at the origin. (Do it two different ways.)” is broken down into a number of easy to follow steps, and 43 words. Since the solution to 9P from 2 chapter was answered, more than 239 students have viewed the full step-by-step answer. This full solution covers the following key subjects: Charge, some, Find, found, coordinates. This expansive textbook survival guide covers 12 chapters, and 550 solutions. This textbook survival guide was created for the textbook: Introduction to Electrodynamics , edition: 4. Introduction to Electrodynamics was written by and is associated to the ISBN: 9780321856562.

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