I didn't know how to display a lot of the symbols, so I wrote the problem out in microsoft word, took a screenshot, uploaded it to photobucket, and linked it.
Basically, I have to find the charge density as a function of r given the electrostatic field in the image. Any constants are positive. Bold means it's a vector; ignore the green underline; the del function is upside down - sorry about that.
My questions are..
1: Is my work method correct? i.e. is this how you solve for charge density?
2. Is there a way to simplify it more?
3. Is E0 a constant or not? The problem doesn't really say and is ambiguous to me. If it's not, how should I approach it? Thanks.
In all cases... please don't tell me if my answer is right or wrong. YES/NO answers are very much appreciated.
Relevant equations I used in the image
The Attempt at a Solution
My attempt is in the image. ^_^