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Homework Help: Integrating dq to find that q(r) = Q(1-e^(-r/R))

  1. Sep 16, 2009 #1
    1. The problem statement, all variables and given/known data
    provided with data that
    dq = rho(r) *4phi*r^2*dr
    rho(r) = [Q*e^(-r/R) / 4phi R *r^2)

    I have to show that the charge q(r) enclosed in a sphere of radius r is q(r) = Q(1-e^(-r/R)) by using appropriate integral. how the integral should be?

    2. Relevant equations

    3. The attempt at a solution
    I've tried to integrate dq = ... but I can't find the final answer that q(r) = Q(1-e^(-r/R))
  2. jcsd
  3. Sep 16, 2009 #2


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    Homework Helper
    Gold Member

    It is a pretty straightforward integration. Why not post what you've tried so we can see where you are going wrong?
  4. Sep 17, 2009 #3
    never mind
  5. Sep 17, 2009 #4
    The easiest way is to integrate the charge density in a fitted coordinate system!

    Cause you need
    [tex] Q(r) = \int \limits_{\mathcal{V}} \, d^3r \, \rho(r) [/tex]​
    of a sphere, the most suitable one is the spherical coordinate system. So you need the volume element
    [tex]d^3r = \rm{?} [/tex]​
    and perform the integration!

    In the statement
    [tex]dq = 4\pi \, r^2 \,\rho(r) \cdot dr[/tex]​
    two integrations are already perfomed, so the best way to undestand it completley is to do it like i've said above!
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