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Question
why the electric field is same at all points of infinitely long charged rod?

Answer
I assume you mean, "why is it the same at all points equidistant from an infinitely long charged rod?"  The distance from the rod's center matters.  The distance from a charged plane does not matter, but the reasons for it are obvious.  No matter where you move long a charged rod, it looks the same if it is infinitely long.  Therefore, the field is the same.  No matter what point you start at, you can't do the integral over the charged parts any differently to determine the electric field.

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Dr. Stephen O. Nelson

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I can answer most basic physics questions, physics questions about science fiction and everyday observations of physics, etc. I'm also usually good for science fair advice (I'm the regional science fair director). I do not answer homework problems. I will occasionally point out where a homework solution went wrong, though. I'm usually good at explaining odd observations that seem counterintuitive, energy science, nuclear physics, nuclear astrophysics, and alternative theories of physics are my specialties.

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I was a physics professor at the University of Texas of the Permian Basin, research in nuclear technology and nuclear astrophysics. My travelling science show saw over 20,000 students of all ages. I taught physics, nuclear chemistry, radiation safety, vacuum technology, and answer tons of questions as I tour schools encouraging students to consider careers in science. I moved on to a non-academic job with more research just recently.

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Ph. D. from Duke University in physics, research in nuclear astrophysics reactions, gamma-ray astronomy technology, and advanced nuclear reactors.

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