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: Electromagnetism: Gauss's Law

  1. Sep 28, 2011 #1
    Not sure if this is advanced. Highly doubt it but oh well

    1. The problem statement, all variables and given/known data
    Consider an infinitely long charged cylinder of radius R, carrying a charge whose density varies with radius as ρ(r) = ρo r. Derive expressions for the electric field (a) inside the cylinder (i.e. r<R), and (b) outside the cylinder (i.e. r>R).

    2. Relevant equations
    Gauss's Law
    q=ρ δτ

    3. The attempt at a solution
    (a) E inside cylinder
    I sketched a Gaussian surface inside of the cylinder.
    I believe that E is parallel to ds ( E⃗ ||ds⃗ )
    So, gauss's law becomes E∮ds = q/ϵ for the side

    I believe the integral of ds is 2π r L (L being the length of the cylinder even though it is infinite.
    And q = ρo r π r2 L
    derived from q=ρ δτ

    So we have E (2π r L) = ρo r π r2 L /ϵ
    Simplifying to E = ρo r2/ 2ϵ

    Is this correct for (a)?
    And for (b) would it be the same idea but with a gaussian surface outside of R?

  2. jcsd
  3. Sep 29, 2011 #2

    Doc Al

    User Avatar

    Staff: Mentor

    It's a bit difficult to read your notation. Consider using Latex for your equations.

    (For example: [itex]q = \int \rho dv[/itex].)

    Show again how you integrated to find the total charge within your gaussian surface.
  4. Sep 30, 2011 #3


    User Avatar
    Homework Helper
    Gold Member

    So close! :cry: But as Doc Al says, it's kind of hard to understand your notation. By "r2" do you mean r2? If so, try the final simplification once more. I think you forgot to cancel something out.
    Yes. The trick is to just be careful about determining q. When outside the cylinder, is the total charge q within the Gaussian surface a function of r or a function of R?
  5. Sep 30, 2011 #4
    Yes I meant r squared. The thing is when i reposted this problem the pasting messed up a couple of things.
  6. Sep 30, 2011 #5


    User Avatar
    Homework Helper
    Gold Member

    Right. I think I figured that out when I looked at the other thread. Check that thread. I left a hint for you there.
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook