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Gauss problem

  1. Jan 22, 2007 #1
    I can't figure out how to get started on this problem. Maybe you guys can help. A spherical ballon carries a total cahrge Q(1C) uniformly distributed over the surface. At t=0, r=r(sub 0), at t=30s, r=2r(sub 0). Find what is the electron field at 90 s at a distance of .5m from the ballon surface. I have to use Gaussean for this problem. I know that you have to get an expression for E(t), the electric field as a function of time. Can you guys help?
    thanks
    nertil
     
  2. jcsd
  3. Jan 22, 2007 #2

    Hootenanny

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    Welcome to the forums,

    For future reference, could you please post all homework questions in the appropriate forum, thanks.

    With respect to your current question, can you write down a mathematical expression of Guass' law? Can you also write an expression for the area A of the balloon at time t?
     
  4. Jan 22, 2007 #3
    Gausses law
    E=kQr/R^3, for a sphere where r is the radius of the imaginary Gauss sphere in the balloon and R is the radius of the ballon. The Surface area of the balloon as a function of t is SA(t) = 4(pi)r^2t. I don't know if thats correct or not. And sorry about the post location. I didn't realize.
    thanks
     
  5. Jan 22, 2007 #4

    Hootenanny

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    Ahh, you've skipped a few stages :approve:; now that we have the electric field of a sphere, all we need to consider now is how the radius changes with time.
     
  6. Jan 22, 2007 #5
    thats where im stuck. I don't know how to relate the two.
     
  7. Jan 23, 2007 #6

    Hootenanny

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    Okay, if we assume that the radius of the balloon increases linearly then we can say that r(t) = r0+ar0t = r0(1+at) , where a is some positive constant. From the conditions we have;

    [tex]r(30)=r_{0}\left(1+30a\right) = 2r_{0} \Rightarrow 1+30a = 2\Rightarrow a = \frac{1}{30}[/tex]

    [tex]\therefore r(t) = r_{0}\left(1+\frac{t}{30}\right)[/tex]

    Can you go from here?
     
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