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Homework Help: Calculate the total charge on a sphere

  1. Feb 6, 2012 #1
    1. The problem statement, all variables and given/known data
    Using integration calculate the total charge on the sphere

    radius R
    Volume charge density at the surface of the sphere p0

    p = p0r/R



    I started with dq = 4*pi*r^2*dr*(p0r/R)

    but i am not sure how to integrate (in terms of what variable I would assume r=0 to r=R) but i am not sure i set up the question right
     
    Last edited: Feb 6, 2012
  2. jcsd
  3. Feb 6, 2012 #2

    SammyS

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    I presume that you mean ρ = ρ0(r/R) is the volume charge density for a sphere of radius, R, where ρ0 is the volume charge density at the surface of the sphere.

    The volume element is dV = 4πr2dr.

    So that dq = 4πr2(ρ)dr = 4πr20/R)r dr .

    4, π, ρ0, and R are all constants.

    Integrate that over the entire sphere. → r goes from 0 to R .
     
  4. Feb 7, 2012 #3
    That makes sense so if I was asked to find the E field using gauss's law for r<=R would I just use E=q/(area*epsilon) but how would I know what q enclosed is???
     
  5. Feb 7, 2012 #4

    SammyS

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    To find the charge enclosed in a sphere of radius, r, integrate from 0 to r .
     
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