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Solutions to laplace's equation & uniqueness thrm #2 (Griffiths)

  1. May 11, 2014 #1
    In griffith's intro to electrodynamics (4rth edition), ch. 3, pg. 121.

    here is the second uniqueness thrm for the solutions to laplace's equation:

    the only part i'm confused about is, in the beginning where he says "in a volume V surrounded by conductors and containing a specified charge density ρ"

    Q: is the charge density ρ referring to that belonging to the region of space whose potential we're trying to determine? or is it referring to that of the conductor/insulator?

  2. jcsd
  3. May 11, 2014 #2


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    It is referring to that belonging to the volume V in which we are solving for the electric field.
  4. May 11, 2014 #3
    thought so!

    but then this leads to another confusion. I thought both uniqueness theorems were meant for the solutions to the laplace equation. The laplace equation however does not deal with charges inside the region.

    so then, i guess, uniqueness thrm 1 is for both the laplace & the poisson equations while uniqueness thrm 2 is for just the poisson eqn?

    please confirm this for me
  5. May 11, 2014 #4


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    Uniqueness theorem 2 is for Poisson's and uniqueness theorem 1 is for Laplace's.
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