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Spherically Symmetric charge distribution

  1. Jun 10, 2012 #1
    I am currently doing a past paper question for my electromagnetism exam and I can't seem to figure out this problem, it is probably quite simple but I can't see a solution


    1. The problem statement, all variables and given/known data

    Consider a spherically symmetric charge distribution:

    ρ(r) = ρ0(r/r0)-n for r>r0

    ρ(r) = ρ0 for r≤r0

    where ρ0, r0 and n are constants and r = |r|

    i) For which values of n is the total charge Q finite? compute the total charge for these values


    2. Relevant equations

    As above in the question


    3. The attempt at a solution

    I have no idea how to start
     
  2. jcsd
  3. Jun 10, 2012 #2
    The total charge is finite if the charge for r>r0 is finite.

    That charge is given by Q(r>r0) = ∫ρ(r) dV = 4π∫ρ(r)r2 dr = 4πρ0r0n∫r2/rn dr

    Now you need to know for which values of n does the integral ∫1/rn-2 dr converges. (The integral being taken from r0 to infinity, obviously).
     
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