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Find charge density rho of a uniform shpere with radius R

  1. Feb 21, 2015 #1
    1. The problem statement, all variables and given/known data
    Find the potential V(r) inside and outside of a uniformly charged sphere with radius R and total charge q.
    A) Fix first the charge density ρ(r) in the two regions 1: r>R and 2: 0<r<R the results should only be in terms of q and R

    2. Relevant equations
    ρ= qtot/Vtot
    dq= ρ*Venc

    3. The attempt at a solution
    ρ= qtot/(4/3)piR^3
    dq = [(qtot/(4/3)piR^3)*(4/3)pir^3]dr⇒(q*r^3/R^3)
    ∫dq = ∫q*(r^3/R^3)dr⇒ q*(¼r^4/R^3)

    not sure if this is the correct approach to the problem
  2. jcsd
  3. Feb 22, 2015 #2


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    2017 Award

    Staff: Mentor

    Don't forget brackets: ρ= qtot/((4/3)piR^3) or ##\rho = \frac{3q}{4\pi R^3}##. Also, is this the charge density everywhere?
    I don't understand what you are trying to do in the two lines below. You found the charge density, what does the integral mean and why do you integrate over a charge?
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