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 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
