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Find the general solution to Laplace’s equation in

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

Solution for problem 3P 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 3P

Problem 3P

Find the general solution to Laplace’s equation in spherical coordinates, for the case where V depends only on r . Do the same for cylindrical coordinates, assuming V depends only on s.

Step-by-Step Solution:

Step 1 of 2

We have to find the general solution to Laplace’s equation in spherical coordinates assuming only depends  on .

Laplace’s equation is given as,

                                                 

where, is the electric potential

Now,  operator in spherical coordinates can be written as,

                                 

So,          

                                       

                   

                       

                         

               

                             

Therefore, the general solution to Laplace’s equation in spherical coordinates is

Step 2 of 2

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

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Find the general solution to Laplace’s equation in