Solution Found!
Find the general solution to Laplace’s equation in
Chapter 3, Problem 3P(choose chapter or problem)
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.
Questions & Answers
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