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Determining Charge from Charge Density

  1. Jun 14, 2017 #1
    1. The problem statement, all variables and given/known data
    A positively charged nonconducting solid sphere of radius R has a nonuniform volume charge density given by ρ0 for r≤R/2 and given by 2ρ0(1−r/R) for R/2 ≤r≤R, where r is the radial distance from the sphere center.


    Part A
    Determine the charge q on the sphere in terms of ρ0 and R.


    2. Relevant equations

    ∫ρ*dv = Q


    0R/2 ρ0 dVolume + R/2R ρ0 dVolume = Q from 0 to R/2 + Q from R/2 to R


    3. The attempt at a solution
    0R/2 ρ0 dVolume = 0R/2 ρ0 4πr2 dr
    = R3πρ0/2


    R/2R ρ0 dVolume = R/2R ρ0 4πr2 dr

    = (4R3- 3R4)*8πρ0/(12R)




    Is my math wrong or is my attempt at the solution wrong? If both is wrong could you help me more with the attempt at the solution?

    Thanks!!!

    Sun

    (ρ) Is rho btw.
     
  2. jcsd
  3. Jun 14, 2017 #2

    haruspex

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    What is ∫r2.dr?

    In the second integral, you left out the (1-r/R) factor.
     
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