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Jackson Emag 1.

  1. Dec 7, 2016 #1
    Hey all,
    So the question in Jackson 1.4 is that I have 3 spheres that all have a total charge Q on them, but each sphere has different material properties. For instance, I have a conducting sphere, a sphere with a uniform charge distribution, and one with a charge distribution that has a charge distribution that varies as rn. It's the last one I am having trouble with, how can I get an r dependence in ρ without screwing up the units? I tried something like:

    ρ(r) ∝ ρo*(rn+1/rn)

    buuuuut that still leaves me some messed up units.

    Also, ρ0 = 3Q/(4πr3)

    Any ideas?
     
  2. jcsd
  3. Dec 7, 2016 #2

    phyzguy

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    You can have [itex] \rho(r) = \rho_0 \, r^n[/itex], but the units of [itex]\rho_0[/itex] will not be [itex] \rm \frac{Coulombs}{cm^3}[/itex], they will be [itex] \rm \frac{Coulombs}{cm^{3+n}}[/itex],. And then you have to determine [itex] \rho_0[/itex] by integrating the total charge over the sphere to give Q.
     
  4. Dec 7, 2016 #3
    Whoa whoa ρ can take on arbitrary units? Like Coulombs/cm3+n? The units just have to balance out in ∫ ρ dV = Q?....Also as an aside, are you using LaTex or something because I like the format in your response.
     
  5. Dec 7, 2016 #4

    phyzguy

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    Yes, [itex] \rho_0 [/itex] is just a constant in your equations that can have whatever units it needs to to make the units come out right. In that case it's not a charge density any more.

    This link shows you how to include latex in your posts.
     
  6. Dec 7, 2016 #5
    Interesting, learned something new. I just learned mathematica so I guess I will put LaTex on my to do list. Thanks!
     
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