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Electrostatics -- the case of a charged cylinder

  1. Jan 3, 2016 #1
    • Missing template. Originally posted in technical forums.
    Hello , I post a message because I will need help with this exercise I would like to knowif my answer are
    good,

    I'm french :

    An infinite hollow cylinder charge is constituted of a sheath whose outer limits are R2 and R3. Wearing a uniform charge density ρ
    160103061028647147.jpg
    Question 2)calculate the total electric field E at any point M ( r ,θ, z) into space.
    3) Give the appearance of E according to the relevant variable .
    4 ) Calculate the electrostatic energy carried by a cylinder length L.
    And my answers are:
    2)There are 3 cases:
    The first r<R2
    Whe can say that :
    160103055129288919.jpg
    And Er(r)=0 because ρ=0.
    Second and third case:
    160103055118493319.jpg
    3) 160103055128956052.jpg
    I had a problem to place A and B because I do not know how far they must be put to the origin O ( 0,0,0) .
    I do not know either the distance required between R2 and R3 on the drawing or the shape of the curve.
    4) 160103060710389264.jpg
    and Ep=0 beacause ρ=0.

    Also the beginning of my reasoning is here(in french,but the only the formulas are important).
    160103055856887730.jpg
     
  2. jcsd
  3. Jan 3, 2016 #2

    TSny

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    In all three cases, you have not correctly calculated the charge enclosed in the Gaussian surface.

    In the region where r < R2, what is the charge density?

    For each of the other two cases, make sure you draw a picture showing your Gaussian surface.
     
  4. Jan 3, 2016 #3
    the load is 0 because there is no load , I wrote it above.
    And the other cases it's "rho" no?
     
  5. Jan 3, 2016 #4

    TSny

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    OK, I overlooked that. So, your answer for r < R2 is correct.
    For the second and third parts, make sure you are taking into account that ρ = 0 for the hollow region.
    Also, for the second part where R2 < r < R3, make sure you are finding the charge enclosed in your Gaussian surface. Thus, make sure you can draw and describe the dimensions of your Gaussian surface.
     
  6. Jan 3, 2016 #5
    Ah okay!

    I had not taken it into account between R2 and R3 actually , thank you very much.
    Hum for r>R3 it's 0,and for R2<r<R3 it varies between 0 and rho I think.
    I will think carefully before you answer in this case!
     
    Last edited: Jan 3, 2016
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