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Derive Electric Field of Cylinder Via Gauss' Law

  1. Sep 4, 2010 #1
    1. An infinitely long cylinder of radius R contains a uniform charge density Rho. Calculate the electric field using Gauss' law for r> R and R>r

    3. I attached a pdf with my attempt at r>R. My answer doesn't agree with those given http://hyperphysics.phy-astr.gsu.edu/hbase/electric/elecyl.html#c3". I noticed that length canceled but I'm not sure if my set up was done correctly. I solved the same problem using direct integration of Coulombs law and there I took the limit of L as it approached infinity. Any suggestions would be great. Thank you :]
    1. The problem statement, all variables and given/known data

    2. Relevant equations

    3. The attempt at a solution

    Attached Files:

    Last edited by a moderator: Apr 25, 2017
  2. jcsd
  3. Sep 5, 2010 #2


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    You just dropped the factor of r on the LHS of the second to last line. Other than this algebra error, your answer is correct.
  4. Sep 5, 2010 #3
    Alright thanks for catching me there. So this is a correct way for setting up a problem for an infinite cylinder? I couldn't wrap my mind around how you could use gauss' law for an infinite surface or volume.
  5. Sep 5, 2010 #4


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    Yeah, your approach is correct.

    If it helps, try to think about it this way: Apply Gauss's law to a finite cylinder, and then take the limit as the length go to infinity. (Since L cancels, you'll get the same answer.)

    Of course you have to ignore edge effects on the field with this approach but since you plan on taking the L going to infinity limit anyway, this doesn't matter.
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