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Homework Help: Guass's Law over the x axis

  1. Feb 19, 2013 #1
    1. The problem statement, all variables and given/known data
    Charge is uniformly distributed along the x axis with density ß. Use Gauss' Law to find the electric field it produces, and use this to calculate the work done on a charge Q that moves along the y axis from y = a to y = b.

    2. Relevant equations


    [itex]\phi[/itex]= [itex]\frac{Q}{\epsilon}[/itex]
    3. The attempt at a solution

    I used a cylinder for my surface since the normal vector will always align with the electrical field. So the first part, the equation ends up

    (r is the radius from the axis to the edge of the cylinder and h is the length of the cylinder.)

    and if I remember right, Q is the density times the are of enclosure.
    so Q = β(2∏rh)
    I set the two [itex]\phi[/itex] equations equal to each other and get

    I don't think that's right though. What did I do wrong?
    Last edited: Feb 19, 2013
  2. jcsd
  3. Feb 19, 2013 #2
    Since the charge is along the x-axis, then β is a linear charge density.
    So, to get the charge enclosed, you multiply β by the length h, and not the volume.
  4. Feb 19, 2013 #3


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    Hi Colts! :smile:
    No, "density" here means the line density (in coulombs per metre, not per metre3)

    So Q = βh. :wink:

    (of course, sometimes "density" means surface density, and occasionally it actually means density! :rolleyes:)

    EDIT: ap123 beat me to it! :biggrin:
  5. Feb 19, 2013 #4
    So the electrical field is

    E = [itex]\frac{β}{2πrε}[/itex]
    Last edited: Feb 19, 2013
  6. Feb 19, 2013 #5
    Is the last question asking me to integrate E from a to b?
  7. Feb 19, 2013 #6


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    Integrate the force, FExt, that would need to be exerted on a charge, Q, to move the charge from a to b . (Actually integrate the work the force does.)
  8. Feb 19, 2013 #7

    x is the distance

    does that look right? and the integral would be from a to b
  9. Feb 19, 2013 #8


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    Not correct.

    What is the force on a charge Q located on the y-axis , a distance y from the x-axis ?

    You (or some outside agent) must apply what force on Q to move it, at a constant rate, when the charge is located on the y-axis ?

    Added in Edit:

    Another way to do this is to find the potential difference from y = a to y = b .

    To do that, you do integrate -E .
    Last edited: Feb 19, 2013
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