PDE Problem - (really just an integral)
This problem isn't too bad in theory. I understand it, I'm just having great difficulty expressing the answer, so I'm wondering if anyone has some method, or insight how to "see" or express the answer.
Find from the formula:
If in the solid sphere and outside. ...
The "..." just represents the other part of the question that I'm not interested in.
As an example if we set:
The integral would drop to:
This makes sense, that as long as we integrate below R we get our integral back. But when we get above R then the integral returns 0. My question is this I guess...
Is there an easy way to setup all these equalities and integrals? Because I am getting lost when I try to do it. The only time it really makes sense is when I plug in numbers and force my way through it. I'm just curious what a better way to accomplish this task of setting up cases is. Thanks in advance.