Intermediate E&M. Electric Field above a square

[maherelharake]

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.

 

[granpa]

dont forget that you only want the component in the z direction

 

[maherelharake]

Right, so I have to factor in a cos component?

 

[granpa]

you don't know the angle. you only know the slope

 

[maherelharake]

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.

 

[granpa]

yes slope is Z/X
I haven't though it all out but I don't 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?

 

[maherelharake]

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.

 

[maherelharake]

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.