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Charge Density

  1. Oct 9, 2009 #1
    1. The problem statement, all variables and given/known data
    In a sphere of radius R, the charge density varies as [tex]\rho[/tex](r) = BrN. There is no charge outside the sphere. B and N are constants.

    a.) Find the charge enclosed in a sphere of radius r<R.


    2. Relevant equations
    [tex]\rho[/tex]=dq/dv


    3. The attempt at a solution
    I integrated [tex]\rho[/tex](r)(4[tex]\pi[/tex]r2dr) and got q=(4[tex]\pi[/tex]BrN+3)/(N+3) + C. Is this right? If so, would it be correct to use the boundary condition; @ r=R, q=0 in order to solve for C? It doesn't sound right because there must be charge at the surface?
     
  2. jcsd
  3. Oct 9, 2009 #2

    rl.bhat

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    Homework Helper

    Hi YoGabbaGabba, welcome to PF,
    You are required to find the field at r<R. So you need not the condition r = R. Instead you can take the condition q = 0 at r = 0.
     
  4. Oct 10, 2009 #3
    Thanks for your time. So if asked to find the charge when r>R, is the charge simply zero or do we consider the boundary conditions r=R? Thanks.
     
  5. Oct 10, 2009 #4

    rl.bhat

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    Charge density cannot be zero between r = 0 to r = R. And asking to find the charge density when r > R is meaning less.
     
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