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Homework Help: Help with linear charge density and flux

  1. Oct 30, 2011 #1
    1. The problem statement, all variables and given/known data
    The y-axis carries a uniform linear charge density of -2 nC/m, and there is a 8 nC point charge
    at the point (3 cm, 0 cm, 0 cm) as well as a -4 nC point charge at the point (-8 cm, 0 cm, 0 cm).
    What is the electric flux through a closed spherical surface of radius 4 cm centered at the origin?

    2. Relevant equations
    I know that flux is 4πkQin or Qin0, i dont understand where the linear charge density comes in. I know that the 8nC charge would be inside the sphere.

    3. The attempt at a solution
    I tried adding the linear charge density and the 8nC charge and putting it through that formula but i dont understand how the -4nC charge affects the flux, or how to factor it in.

    Any help would be greatly appreciated
    Last edited: Oct 30, 2011
  2. jcsd
  3. Oct 30, 2011 #2
    The charge outside the sphere doesnt affect the flux, correct? when adding the charges inside the sphere, -2 and 8, which gives 6nC, and putting it through the formula, 4πkQin, i get 678.58, but the correct answer is 886Nm2/C
  4. Oct 30, 2011 #3
    You are correct that the charge outside the sphere has no influence.
    You have made a mistake in determining the charges inside. While there is one charge of 8nC, the 2nC/m is a charge density, not a charge itself.
    You need to calculate the amount of charge within the sphere given this charge density, and the radius of the sphere. How might that be accomplished?
  5. Oct 30, 2011 #4
    well i have the equation E = 2kλ/r. E = k8nC/(.08)2?? but how does that help??
  6. Oct 30, 2011 #5
    Just think about the charge on the y-axis for a moment.
    It has a charge density -2nC/m. The sphere is radius 0.04m, so what is the total charge (on the y-axis) inside the sphere?

    Add this to the 8nC charge, and you have your Qin.
  7. Oct 30, 2011 #6
    im not sure. i dont see how its related at all, i mean besides a volume-density relation
  8. Oct 30, 2011 #7
    The charge density means that for every metre on the y-axis, there are -2nC of charge present. There is 0.08m of the y-axis within the sphere.
    Since charge density = charge/length, you can rearrange this equation to give the charge on the y-axis contained within the sphere.
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