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Homework Help: The electric field at the center of a square

  1. Sep 5, 2011 #1
    http://helios.augustana.edu/~dr/203/probs/Set 1.pdf
    Scroll down to #11 for a picture.

    So I kind of understand the math. I am a little confuse though. So why is a divided by sqrt(2)?
    If this is a vector, then the center is really (a(sqrt(2)))/2 and the x component would be divided by sqrt(2) which makes the equation equal a/2. Can someone explain this? Is my math wrong?
  2. jcsd
  3. Sep 5, 2011 #2
    The diagonal distance from corner to corner is a*2^.5 and the distance from corner to the center is half of that,

    a*2^.5/2 = a/2^.5

  4. Sep 5, 2011 #3


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    The distance from the center to any corner is [itex]a/\sqrt{2}[/itex], that's why a is divided by sqrt(2).

    Taking the x-component is accounted for by the cos(45) in the expression.
  5. Sep 5, 2011 #4
    I'm not sure why it's a/sqrt(2). I do know that (a(sqrt(2))/2 is the exact same number. I don't know why.

    Basically, I found the length of the diagonal, a(sqrt(2)) and divided it by 2. It's the same as a/sqrt(2)
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