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Intermediate E&M. Electric Field above a square

  1. Sep 4, 2010 #1
    1. The problem statement, all variables and given/known data

    Imagine a square in the xy plane with each side of length a. It has a uniform charger per unit area (σ). The center of that square is at the origin. Determine the electric field at a distance z above the center.


    2. Relevant equations

    E=k integral{(sigma/r^2) * r * dA}


    3. The attempt at a solution
    I realize that all components should cancel except for that in the Z direction. I also tried to use the equation above and integrate from -a/2 to a/2. However as I proceeded, I started to get a bit confused with the integral. I am not even sure if I started it correctly, much less the integral. Thanks in advance.
     
  2. jcsd
  3. Sep 4, 2010 #2
    dont forget that you only want the component in the z direction
     
  4. Sep 4, 2010 #3
    Right, so I have to factor in a cos component?
     
  5. Sep 5, 2010 #4
    you dont know the angle. you only know the slope
     
  6. Sep 5, 2010 #5
    Wouldn't the slope be Z/X? Also would you use the value of r = sqrt(z^2 + x^2)?

    This is where I think I am having the most trouble.
     
  7. Sep 5, 2010 #6
    yes slope is Z/X
    I havent though it all out but I dont think you even need to know r
    you just need to know what you need to multiply r by to get z

    is this homework?
     
  8. Sep 5, 2010 #7
    That's why I was wondering about the cos(theta). I know we don't have the angle, but couldn't it also be equal to R/Z?

    And kind of. It's a problem that isn't necessarily graded, but one that we should do.
     
  9. Sep 5, 2010 #8
    Ok I am not making much progress on this. I have been working on it, but to no avail. Any help would be greatly appreciated.
     
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