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Math Help - Laplace equation and electrostatic potential

  1. #1
    Junior Member Pinsky's Avatar
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    Laplace equation and electrostatic potential

    Can someone please explain the connection between electrostatic potential and Laplace's equation? And what does that have to do with harmonic functions?
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  2. #2
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    Quote Originally Posted by Pinsky View Post
    Can someone please explain the connection between electrostatic potential and Laplace's equation? And what does that have to do with harmonic functions?
    This is a real broad brush question. A decent answer would take up several chapters of a book. I can say this with confidence because I have studied the chapters of such books.

    In my opinion you're best advised to consult any decent undergraduate textbook on electro-magnetism and study the salient chapters at your leisure.

    eg. Lorraine and Corson - Electromagnetic Fields and Waves, Jackson -Classical Electrodynamics.

    In a nutshell:

    1. In regions of space where there is no charge density the electrostatic potential satisfies Laplaces equation: \nabla^2 V = 0 where V is the electrostatic potential.

    2. Any real function with continuous second partial derivatives which satisfies Laplace's equation is called a harmonic function.

    Background knowledge, derivation, details and examples (and answers to the million and one questions the nutshell has prompted) are what constitute the above-mentioned chapters.

    Just curious by the way ...... how do you happen to be in the unfortunate circumstance of this question being urgent homework?
    Last edited by mr fantastic; January 20th 2008 at 02:22 AM.
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  3. #3
    Junior Member Pinsky's Avatar
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    O well, i'll try that then.

    It's one of my questions for math theory.

    "Appliance of harmonic functions on electrostatic potential"
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  4. #4
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    Quote Originally Posted by Pinsky View Post
    O well, i'll try that then.

    It's one of my questions for math theory.

    "Appliance of harmonic functions on electrostatic potential"
    So you have to write a paper or something?

    The nutshell says it all. What you should do:
    1. Summarise definitions of terms and concepts in the nutshell.
    2. Go from the nutshell to worked examples.
    Any decent textbook on electro-magnetism will have all you need.
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