1. Not finding help here? Sign up for a free 30min 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!

Laplace equation in rectangular geometry

  1. Nov 29, 2011 #1
    [/itex][/itex]1. The problem statement, all variables and given/known data

    A battery consists of a cube of side L filled with fluid of conductivity s. The electrodes in the battery consist of two plates on
    the base at y = 0, one grounded and one at potential V = 12 Volts. The other sides of the battery casing are not
    conductive. Find the potential f everywhere inside the battery.
    Hint: current density j(x, y) flows according to Ohn’s law, j = σ Ewhere E = -div ∅. For equilibrium current flow, div.j = 0 which
    implies σ (div)^2 f = 0. Therefore you must slove Laplace’s equation. Note that on nonconducting surfaces, j.n `
    = 0wheren `
    is normal
    to the surface, so such surfaces have a Neumann boundary condition.

    2. Relevant equations



    3. The attempt at a solution
    I think the boundary at y=L is a Neumann boundary, and the boundary at y=0 is a Dirichlet boundary, but i don't know what is the boundary condition for y=0 since half of it is 0V and half of it is 12 V.
     
  2. jcsd
  3. Dec 2, 2011 #2
    If it's a cube with lower left corner on origin then x=0 would be Dirichlet and x=L would be Neumann wouldn't they?

    Also, a cube is 3d but j is just a function of x and y suggesting you don't have to worry about z.

    It's been a while since I did this stuff though!
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook




Similar Discussions: Laplace equation in rectangular geometry
  1. Laplace's equation (Replies: 4)

  2. Laplace equation (Replies: 7)

  3. Laplace's equation (Replies: 6)

  4. Laplace's Equation (Replies: 1)

Loading...