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Electric field outside a long cylindrical shell

  1. Jan 26, 2012 #1
    1. The problem statement, all variables and given/known data

    A long cylindrical shell of radius R = 12.3 cm carries a uniform surface charge 4.60E-6 C/m2. Using Gauss's law find the electrical field at a point p2 = 16.5 from the center of the cylinder.

    2. Relevant equations


    3. The attempt at a solution
    This is what I thought would work but does not produce the answer. The area is arbitrary I believe so I just used a 1m strip of the cylinder, A=2*0.123m*1m=0.246,**2. Q is found by multiplying the area of the cylinder by the charge density, Q=2*pi*r*1*(density)=3.555*10**-6 C. Solve for E, E=Q/(A*epsilon0) =0.163*10**6 N/C which is not correct. Any help would be great, especially if its before 11pm EST tonight.
  2. jcsd
  3. Jan 26, 2012 #2


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    Hi MeMoses! :smile:

    Difficult to tell without seeing your intermediate steps …

    but did you use r = 16.5 ?
  4. Jan 26, 2012 #3
    i dont believe r=16.5 is needed, we just need to know that it is outside the cylinder, since it is an infintely long cylinder the feild should not be dramatically affected by distance. I think i just calculated area wrong
  5. Jan 26, 2012 #4


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    that works for an infinite flat plate, since the field lines can't get any further apart as they go away …

    but they do get further apart from a cylinder, don't they? :wink:
  6. Jan 26, 2012 #5
    Yup compare the lines for a plane, cylinder/wire and sphere to see how their spacing varies with distance from the object.
  7. Jan 26, 2012 #6
    Ok that makes sense now. I feel like an idiot for think that. However, just to clarify, would the equation I need simplify as such, E*A=Q/epsilon -> E(2*pi*r*h)=Q/epsilon, and Q=(2*pi*r*h)*charge density? and would every r here be the distance from the center, not the radius of the cylinder as I previously thought?
  8. Jan 26, 2012 #7
    Ok i got, thanks for the help
  9. Jan 26, 2012 #8
    Good job!
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