1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Homework Help: 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


    User Avatar
    Science Advisor

    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


    User Avatar
    Science Advisor

    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!
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted