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Strangely aligned capacitor plates

  1. May 18, 2012 #1
    Working along step-by-step with a text and I'm stumped as to how they reached a conclusion. In the first picture you see two plates aligned at an unspecified angle, theta. One plate is at a potential V and the other is grounded. The distance between the plates at one end is d, and at the other end d+a. You can see in the second picture how they've set it up with respect to a two dimensional coordinate system. Maybe it's late and I'm braindead or maybe not in any even I can't see how they've formed the relationship between b,d and a to determine the distance between the actual origin and the intersection of the plates (dotted lines in picture three). Can anybody enlighten me?

    Thanks.

    ScreenShot2012-05-18at11434AM.png

    ScreenShot2012-05-18at11722AM.png

    ScreenShot2012-05-18at11714AM.png
     
  2. jcsd
  3. May 18, 2012 #2
    P.S. the whole point is to find the potential, but this is where I'm hung up.
     
  4. May 18, 2012 #3

    robphy

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    In the triangle (in x<0) with base OO' and the height d, you have
    tan(theta_0)=d/(OO').

    In the trapezoid (in x>0), draw the horizontal at height d to form a similar triangle,
    with base b and height a. Thus
    tan(theta_0)=a/b.
     
  5. May 18, 2012 #4
    Truly geometry is my weakest link. Thank you.
     
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