show that the E outside an infinitely long rod of radius R with a uniform charge density p is E = pR^2/2r(e_0)
gauss' law EA=q/e_0
The Attempt at a Solution
I know how to solve this and get the correct answer but I don't totally understand it. Why is the height the same value on both sides of the gauss' law equation when the radii are different values?
ie, shouldnt there be a h and an H since theres a r and a R? obviously the answer is no since the heights cancel each other out, but why arent they different values?
why isnt the final answer E = pHR^2/2rh(e_0) instead of E = pR^2/2r(e_0) ?