1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

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

    gabbagabbahey

    User Avatar
    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!



    PS:
    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!
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook




Similar Discussions: Integrating dq to find that q(r) = Q(1-e^(-r/R))
  1. Review Q #1 (Replies: 13)

  2. 1-D Kinematics (Q) (Replies: 2)

  3. 1 Q need help (Replies: 1)

Loading...