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Find the average potential over a spherical surface of

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

Solution for problem 1P Chapter 3

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 1P

Problem 1P

Find the average potential over a spherical surface of radius R due to a point charge q located inside (same as above, in other words, only with z < R). (In this case, of course, Laplace’s equation does not hold within the sphere.) Show that, in general,

where Vcenter is the potential at the center due to all the external charges, and Qenc is the total enclosed charge.

Step-by-Step Solution:

Step 1 of 2

We have to find the average potential over a spherical surface of radius due to a point charge located inside with .

Let us calculate  the average potential over a spherical surface of radius  due to a single point charge  located outside the sphere with . We will center the sphere at the origin and choose coordinates so that  lies on the z-axis as shown in the figure below.

The potential at a point on the surface of the sphere is,

                       

Where,

               

So,

Since,  ,  

Hence,

                                      

Therefore, the  the average potential over a spherical surface of radius due to a point charge located inside with  is

Step 2 of 2

Chapter 3, Problem 1P is Solved
Textbook: Introduction to Electrodynamics
Edition: 4
Author: David J. Griffiths
ISBN: 9780321856562

Since the solution to 1P from 3 chapter was answered, more than 1239 students have viewed the full step-by-step answer. Introduction to Electrodynamics was written by and is associated to the ISBN: 9780321856562. The full step-by-step solution to problem: 1P from chapter: 3 was answered by , our top Physics solution expert on 07/18/17, 05:41AM. This textbook survival guide was created for the textbook: Introduction to Electrodynamics , edition: 4. This full solution covers the following key subjects: center, potential, due, Charge, inside. This expansive textbook survival guide covers 12 chapters, and 550 solutions. The answer to “Find the average potential over a spherical surface of radius R due to a point charge q located inside (same as above, in other words, only with z < R). (In this case, of course, Laplace’s equation does not hold within the sphere.) Show that, in general, where Vcenter is the potential at the center due to all the external charges, and Qenc is the total enclosed charge.” is broken down into a number of easy to follow steps, and 68 words.

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Find the average potential over a spherical surface of