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Potential of a uniformyl charged sphere

  1. Apr 2, 2013 #1
    1. The problem statement, all variables and given/known data

    The question asks to find the potential due to a uniformly charged sphere at r<R where R is the radius.


    2. Relevant equations

    Va-Vb= ∫ E dr from a → b

    3. The attempt at a solution

    My attempt was like this

    Va is to be a the point of interest r.. Vb to be R... We know Vb to be KQ/R... Now E inside the sphere is KQr/R^3 .. After integration with respect to r we get (R^2-r^2)*Kq/2R^3 ... Thus the net potential at Va is Vb + the integral which is KQ/R + (R^2-r^2)*Kq/2R^3 ... However, this isn't the answer given.. Where was my mistake??
    1. The problem statement, all variables and given/known data



    2. Relevant equations



    3. The attempt at a solution
     
  2. jcsd
  3. Apr 2, 2013 #2

    mfb

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    Staff: Mentor

    How does it differ from the answer given?
    Note that it is possible to simplify your expression.
     
  4. Apr 2, 2013 #3
    I am not able to simplify.. Can you help me?
     
  5. Apr 3, 2013 #4

    mfb

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    2016 Award

    Staff: Mentor

    Just use (a-b)/c = a/c - b/c for (R^2-r^2)*Kq/(2R^3).
     
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