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## Homework Statement

Find the electric field a distance z above the center of a square loop carrying a uniform line charge Q.

## Homework Equations

## The Attempt at a Solution

So we want the electric field generated by the charges that lie on the boundary of the "square loop" - it's just a square or a rhombus with equal lengths.

I attempted to solve this by splitting up the integral into 4 line integrals (each side of the square loop being an integral). Since the charge is uniform, I pull that out of the integral.

Furthermore, all the horizontal components of the electric fields cancels out so we need to integrate the vertical components, i.e. [tex]cos(\theta) = \frac{z}{\sqrt( (x-x_{0})^{2} + (y-y_{0})^{2} + z^{2})}[/tex]

Am I correct to assume that one of my integrals will look like this:

[tex]\frac{Qz}{4\pi\epsilon_{0}}\int_{0}^{a}\frac{dx}{((x-x_{0})^{2} +(y-y_{0})^{2} + z^{2})^{3/2}}[/tex]

Since [tex]R^{2} = (x-x_{0})^{2} + (y-y_{0})^{2} + z^{2}[/tex], i.e. assume the points on the square's boundary are (x, y, 0) and the point above the center of the square loop as coordinates [tex](x_{0}, y_{0}, z)[\tex]

z is a fixed number!

My questions are:

1) Would this be a correct expression for one of the line integrals?

2) How exactly do I integrate such an expression? Am I not seeing the antiderivative?

Sorry if I'm not being clear or concise, this is my first attempt at learning electromagnetism (I'm learning out of Griffiths and I am having a little trouble with all the notation and what not).

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