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Homework Help: Is this all you have to do for this problem

  1. Sep 5, 2011 #1
    1. The problem statement, all variables and given/known data
    A nonconducting solid sphere of radius R has a volume charge density that is proportional to the distance from the center. That is rho=Ar for r is less than/equal to , A is a constant. Find the total charge on the sphere.


    2. Relevant equations


    3. The attempt at a solution
    rho=Ar=Q/V
    Q=Ar(4/3)*pi*R^3

    Is that it?
     
  2. jcsd
  3. Sep 5, 2011 #2

    SammyS

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    No.

    Integrate the charge density over the volume of the sphere.
     
  4. Sep 5, 2011 #3
    would've that just be the integral of (Ar dV) which equals Ar*V?
     
  5. Sep 6, 2011 #4

    SammyS

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    Use dV = 4πr2dr .

    Integrate (A)r , with respect to r, from r = 0 to r = R .
     
  6. Sep 6, 2011 #5
    I went in for help on this one and my TA told me that I could do a triple integral for this one or with the integral you provided, but I chose to do the triple integral.

    What I did was take the triple integral of Ar*r^2 * sin(theta) in this order: dr,dtheta,dphi
    with limits of integration: 0 to R, 0 to pi, 0 to 2pi, respectively
    For the answer I got AR^4 * pi

    Can you explain how you get the dV = 4πr2dr
     
  7. Sep 7, 2011 #6

    SammyS

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    The surface area of a sphere of radius r, is 4πr2.

    So the volume of a spherical shell of thickness dr is given by multiplying the thickness by the surface area.

    dV = 4πr2 dr.

    What's the integral of 4πr2 dr, from 0 to R ?
     
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