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I Dimensional Analysis Poisson Equation

  1. Feb 18, 2017 #1
    Suppose I am given some charge density profile ρ(x). Poisson's equation in 1D reads

    d2φ/dx2 = ρ(x)/ε

    Is there a simple way to see what the order of magnitude of the electrostatic potential should be from a dimensional analysis?
     
  2. jcsd
  3. Feb 19, 2017 #2

    Orodruin

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    The potential is arbitrary. You can shift it by a constant and still satisfy the Poisson equation.
     
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