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Electric field of a sheet of charge

  1. Apr 4, 2009 #1
    1. The problem statement, all variables and given/known data

    (This is a truncated question.)

    The electric field of a circular sheet of charge of radius a and surface charge density sigma and distance x away from the centre of the sheet is

    [tex]E = \frac{\sigma}{2 \epsilon_0} [1 - \frac{x}{\sqrt{x^2 + a^2}}][/tex]

    Prove that for x > 0

    [tex]E = \frac{\sigma}{2\epsilon_0}[/tex] when x << a
    [tex]E = \frac{Q}{4\pi \epsilon_0 x^2}[/tex] when x >> a

    The sheet resembles an infinite sheet and a point charge in each case and I'm required to prove this mathematically.

    3. The attempt at a solution

    For the first case, I note that for x << a, x/a approaches 0. I factor out x from the square roots to get the answer required.

    However, for the second case, I try the same thing, x >> a, now a/x approaches 0, but in this case the expression of E becomes E = 0. I've tried several methods and obtained the same thing. Someone help...
     
  2. jcsd
  3. Apr 4, 2009 #2

    rl.bhat

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    Homework Helper

    You can write E = sigma/2epsilon(not)[sqrt(x^2+a^2) - x]/sqrt(x^2+a^2)]
    Multiply and dived [sqrt(x^2+a^2) + x] and simplify. Neglect the term a/x.
     
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