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Total volumetric charge distribution of the universe

  1. Aug 30, 2017 #1
    Greetings! I'm new here and I think about this place as soon as I see what the statement asks.

    1. The problem statement, all variables and given/known data
    Considering the volumetric density ρv=(e-2r/r2), figure the total charge (ℚ) of the universe.

    2. Relevant equations

    ρv=ΔQ/ΔV -> (ΔQ ∝ ΔV)
    ℚ=∫v ρv dxdydz

    3. The attempt at a solution
    I know you can figure it out ℚ when you've a pack of coordinates (bounds of the volume) in which you can calculate the total charge if you find some kind of symetry or not (i.e: cilindric, spherical coordinates and so on); but my mind just stacked overflow when the book asks the total charge of the universe... I wonder what system of coordinates and values should I use for the triple integral?

    I've read that the shape of the universe —or known one— is flat; but I'm pretty sure I haven't the proper knowledge and mathematical understanding to realize that; so I assume for early problems, the shape is spherical, so I would use the following:

    ℚ=∫vρv dv = ∫∫∫ρvr2Sin(Φ) drdΦdΘ

    Jacobian Determinant.

    I've found this problem at the second chapter of the book Electromagnetic Theory - Hayt. I'd appreciate some help with this problem. Thank you for your attention and keep this pantheon of physics alive! Congrats on this forum. :woot:
     
  2. jcsd
  3. Aug 30, 2017 #2

    phyzguy

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    Science Advisor

    I think you've set it up properly. Go ahead and put limits on the integrals and evaluate them.
     
  4. Aug 30, 2017 #3
    But buddy, how would you put the limits of a spherical-universe (some rate of change?) The book suggest 6.28[C] as a result.

    Ty for reply! :oldbiggrin:
     
  5. Aug 30, 2017 #4

    phyzguy

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    Well, r will go from 0 to ∞. What about θ and φ?
     
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