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Finding the electric flux through a sphere

  1. Feb 11, 2012 #1
    1. The problem statement, all variables and given/known data
    A sphere of radius R is placed in a uniform electric field of E=233 N/C i. Find the electric flux into and out of the sphere.


    2. Relevant equations
    I understand that Gauss's Law is shown as...
    ∫E dot dA = Q/epsilon not


    3. The attempt at a solution

    Well, since we're dealing with a sphere with E being constant, I figured you could pull the E out of the integral and be left with E∫dA where dA is =4pi*r^2. So you'd be left with E(4pi*R). But this doesn't look right to me. Keep in mind, there is no charge in or out of the sphere. And the field lines are perfectly horizontal through the sphere.
     
  2. jcsd
  3. Feb 11, 2012 #2

    Doc Al

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    Staff: Mentor

    You forgot about the dot product. You need the component of surface area in the direction of the field. (Or vice versa.)
     
  4. Feb 11, 2012 #3
    I'm confused about what you're asking for. Are you saying there should be a dot somewhere in my flux=E(4pi*R) equation. I understand what the dot product is (I use it a lot in my Calc 3 class) I'm confused as to what you mean by "the component of the surface area". I understand that the field lines only have an x-component or i, so they're horizontal through the sphere.
     
  5. Feb 11, 2012 #4

    Doc Al

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    What do you think E*dA means? What's the significance of the dot product?

    (You were treating E*dA as if it were the same as EdA.)
     
  6. Feb 11, 2012 #5
    Oops. I see. So, I should be left with E*(4piR) R=radius. But what I'm now stumped on is the component of the surface area. As I said before. I understand the E has an i-component. But how do I find the components of the surface area?
     
  7. Feb 11, 2012 #6

    Doc Al

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    Well, you can do it the hard way. (By setting up the integral.) Or you can think about it a bit and maybe it'll dawn on you. Imagine a hemisphere with its axis along the x-axis. What will be the x-component of its surface area?

    This might be an even better way to visualize it. What flux of E field will be intercepted by the sphere? (Who cares about the shape of the surface?)
     
  8. Feb 11, 2012 #7
    Wouldn't the total flux through the hemisphere be zero? Thus, meaning the flux through a sphere would be zero as well? I'm talking about total flux meaning the sum of the positive and negative flux.
     
  9. Feb 11, 2012 #8

    Doc Al

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    Staff: Mentor

    The total flux through the sphere will be zero*. (Since whatever goes into it must go out of it.) But not through the hemisphere.

    *That should be clear from Gauss's law.
     
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