Follow along with the video below to see how to install our site as a web app on your home screen.
Note: This feature may not be available in some browsers.
For Q2, the extra ρ is a normal part of doing volume integrals in cylindrical coordinates. You probably just forgot that fact.
Contrary to what you say in Q1, charge density is not in general constant over space or time. There are special cases where this might be true enough, but generally it is not true, and in this case, the problem is telling you that it is not true and explicitly tells you the distribution.
Was my answer correct? Please let me know.