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## Homework Statement

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)

## Homework Equations

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) ?