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Electric field calculation

  1. Oct 24, 2009 #1
    This is for a stat mech class which randomly has a hw question with an electric field calculation. It's been a while, so I've forgotten a lot :(

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

    We have a wire of radius [tex]r_0[/tex] that is coincident with the axis of a cylinder with radius [tex]R[/tex] and length [tex]L[/tex]. The wire is maintained at positive potential $V$ with respect to the cylinder. Find the electrostatic field that exists at [tex]r, r_0 < r < R[/tex].

    There is some thermodynamics stuff about the electrons forming a dilute gas, etc, but since we're given no information about the density and stuff I assume that they won't affect the electric field.

    2. Relevant equations

    Gauss's law: [tex]\Phi = \frac{Q}{\epsilon_0}[/tex]
    Definition of potential: [tex]\int_{r_0}^{R} E dr = V[/tex]

    3. The attempt at a solution

    The issue is pretty straight forward. I plan on picking a cylinder with radius [tex]r[/tex] around the wire as the Gaussian surface for Gauss's law. However, I can't seem to use the potential with Gauss's law.

    Thanks in advance.

    EDIT: issues with tex.
     
  2. jcsd
  3. Oct 24, 2009 #2
    Let [tex]\lambda[/tex] be the linear charge distribution in the wire.

    Use Gauss's Law to express the electric field in terms of [tex]r[/tex] and [tex]\lambda[/tex].

    Then use this:


    to determine the expression of [tex]\lambda[/tex] as a function of [tex]V[/tex].
     
  4. Oct 24, 2009 #3
    Gotcha gotcha, seems so obvious in hindsight, thanks.
     
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