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I Interaction between two charged surfaces in contact

  1. Feb 2, 2017 #1
    Dear all,

    I'm curious to know how to calculate an interaction.

    I'm a chemist and I'm not really used to practice Maxwell equations, so I don't have the complete background for that, but I think it may be trivial even for a physicist student.

    Let's say we have two surfaces, one has a total charge of q1 and the other has a total charge of q2. These two surfaces, of exactly the same area A, are in close contact, that is, there is no distance between them. How to calculate the potential energy difference between those surfaces infinitely separated, and in such close contact? I fail in finding relevant textbook references in which this is explained step by step.

    In principle, the potential energy should be favorable for oppositely charged surfaces while it should be unfavorable in the opposite case.

    The three geometries for which I really need such energy are planar layer (here, interaction energy between two planes), cylindrical layer (interaction energy between two cylinder layers) and spherical layers (interaction energy between two spherical layers. I really recall, there is no distance between both surfaces to which we study the interaction! They are sticked together. It seems simpler for me than the case where there is a definite surface, but all cases I find while browsing either google or facebook introduce some distance, which unavoidably results in an expression diverging to infinity :cry: when distance shrinks to zero...

    It would be a great help if you show me relevant equations, or orient me to relevant well explained and self contained theories regarding this problem which looks simple to me, but for which I lack relevant keywords.

    Best regards! :smile:
  2. jcsd
  3. Feb 2, 2017 #2


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    You can't have no distance between two real-life sheets. At best, they will be separated by some atomic distance, and probably quite a bit more. In reality, you have to also consider the thickness of the sheets, and if they are insulators or conductors.
  4. Feb 3, 2017 #3


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    Firstly welcome to PF.

    Your two surfaces form a capacitor with parallel, cylindrical or spherical plates.
    In all geometric cases, if the separation is zero then the capacitance will be infinite. There is no escaping that.

    Since capacitance is defined as the ratio of charge to voltage, c = q / v, the potential you want will be v = q / c.
    But by the definition of capacitance, if c is infinite, then v must be zero.

    Maybe more information about the model and it's application could resolve your tragic paradox.
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