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Force between charged plates

  1. Sep 12, 2009 #1
    1. The problem statement, all variables and given/known data
    Two charged plates, plate 1 and plate 2, are separated by a distance s. Plate 1 has charge density [tex]\sigma_{1}[/tex] and plate 2 has charge density [tex]\sigma_{2}.[/tex] Assume that the electric field to the left of plate 1 is [tex]E_{1},[/tex] in between the 2 plates is [tex]E_{2},[/tex] and to the right of plate 2 is [tex]E_{3}.[/tex] Find the force per unit area of this configuration (I guess assume that somehow these two plates were connected).

    3. The attempt at a solution

    Assume Gaussian units:
    So would I do [tex]dF = \int Edq[/tex] and so assume that the plates have a width called say r, then for plate 1,
    [tex]F = \int E\sigma_{1}dr[/tex] from 0 to r
    and since by Gauss' Law, [tex]dE = 4\pi\sigma_{1}[/tex], so I have
    [tex]F = \int \frac{EdE}{4\pi}[/tex] evaluated from [tex]E_{1}to E_{2}.[/tex]
    Then I have [tex]F = \frac{E_{2}^{2}-E_{1}^{2}}{8\pi}.[/tex] BUt since I know that
    [tex]E_{2}-E_{1} = 4\pi\sigma_{1}[/tex] so this is [tex]\frac{(E_{1} + E_{2})\sigma_{1}}{2}?[/tex] And that would be the force. I would do the same thing for plate 2? Thanks.
     
    Last edited: Sep 12, 2009
  2. jcsd
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