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Poissons Equation

  1. Apr 12, 2008 #1
    1. The problem statement, all variables and given/known data
    So poissons equation takes the for uxx + uyy = f(x,y)
    Laplace is where f(x,y). What does the f(x,y) physically represent?


    2. Relevant equations



    3. The attempt at a solution
     
  2. jcsd
  3. Apr 12, 2008 #2
    Laplace equation is when f(x,y)=0. f(x,y) can represent many things physically. the solution of this problem can represent many things for example u could be a steady state temperature of the cross section of a rod with an electrical current.
     
  4. Apr 12, 2008 #3

    quasar987

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    What you wrote does not make sense to me, but the question got throught nonetheless.

    In Maxwell's theory of electromagnetism, the electromagnetic field is governed by a set of 4 equations and one of them is Poisson's equation where u is the electric field in space-time (x,y,z,t) and f(x,y,z,t) is an expression taking into account the density of charge and the rate of change of the magnetic field at the point (x,y,z,t) in space-time.
     
  5. Apr 13, 2008 #4
    But what is f actually doing to this cross section?
     
  6. Apr 13, 2008 #5
    And when f = 0 ? What does it mean in this case?
     
  7. Apr 13, 2008 #6

    quasar987

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    Well it means that this particular Maxwell's equation ([tex]\nabla^2\vec{E}=0[/tex]) is describing the evolution of the electric field in a region where there are no electric charges and where the magnetic field is constant.
     
  8. Apr 13, 2008 #7
    So say one is concerned with the heat distribution among a metal plate, what would f mean and what would f = 0 mean?
     
  9. Apr 14, 2008 #8
    Maybe I should have written this in the undergraduate physics forum.
     
  10. Apr 14, 2008 #9

    quasar987

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    You can ask a mentor to move it.
     
  11. Apr 14, 2008 #10

    HallsofIvy

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    I hate to keep saying this but mathematics is not physics! Quantities in a mathematical equation do NOT have any "physical" meaning and do not "physically represent" anything until you apply them to a specific physics problem.

    (I guess I am like an ex-smoker. I started majoring in physics, then switched my major to mathematics, though staying in applied math (My doctoral disertation was on computing Clebsch-Gordon Coefficients in general SU(n)) but have steadily moved to more abstract mathematics since.)

    That said, if you have [itex]\nabla \phi= \kappa \partial \phi/\partial t+ f(x,y,t)[/itex] specifically applied to heat distribution on a plate, then f(x,y,z) might represent an external heat source applied to every point of the plate.
     
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