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Finding total charge from volume charge density

  1. Oct 16, 2011 #1
    Why do I have to integrate? Isn't it redundant?

    1. The problem statement, all variables and given/known data
    The volume charge density inside a solid sphere of radius a is given by ρ=ρnaught*r/a, where ρnaught is a constant. Find the total charge as a function of distance r from the center.


    2. Relevant equations
    Q=ρV


    3. The attempt at a solution
    Q=(ρnaught*r/a)*(4/3)(∏a^3)
    Q=(4/3)∏ρnaught*r*a^2

    but the solution manual says it's supposed to be Q=∏ρnaught*a^3
    It says that you have to integrate ρ with respect to V, and that's what confuses me. If you integrate, you're taking the charge of one tiny sphere and adding it the the charge of a concentric sphere a little bigger, so on and so forth, so doesn't that mean that each time you move up to a bigger sphere, you're being redundant? Why can't you multiply the total volume by the charge per volume to get charge?
     
    Last edited: Oct 16, 2011
  2. jcsd
  3. Oct 17, 2011 #2
    The charge density is zero at the center and gets larger with increasing r, as you wrote,

    ρ=ρnaught*r/a
     
  4. Oct 18, 2011 #3
    Thank you! I finally noticed that after way too long...
     
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