Find the general solution to Laplace’s equation in

Chapter 3, Problem 3P

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QUESTION:

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.

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QUESTION:

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.

ANSWER:

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

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