Intermediate E&M. Electric Field above a square

  • #1

Homework Statement



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.


Homework Equations



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


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.
 

Answers and Replies

  • #2
2,257
7
dont forget that you only want the component in the z direction
 
  • #3
Right, so I have to factor in a cos component?
 
  • #4
2,257
7
you dont know the angle. you only know the slope
 
  • #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.
 
  • #6
2,257
7
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?
 
  • #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.
 
  • #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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