Electric field above a charged square loop

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Cocoleia
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Homework Statement


Diagram of a square loop of side a in blue, lying flat, with point P a distance z directly above its centre on a dashed vertical line; text asks for the electric field at P due to a uniform linear charge density lambda.


Homework Equations

The Attempt at a Solution


I have the complete solutions for this problem, I just don't understand them:
Handwritten derivation of the electric field from the bottom side of a square loop: a sketch of the square with axes, an integral for E with vectors r and r', the distance |r - r'| and charge element dl' = dx'.

This is the first part. I don't understand what r' is, or how we found it. Otherwise I understand the concept of the problem just not the details...
 
Cocoleia said:

Homework Statement


View attachment 113644

Homework Equations

The Attempt at a Solution


I have the complete solutions for this problem, I just don't understand them:
View attachment 113645
This is the first part. I don't understand what r' is, or how we found it. Otherwise I understand the concept of the problem just not the details...
r' is the position vector from selected origen to a charge element.
Hand-drawn sketch on grid paper: origin O with vector r' to a charge element dq on a curve, vector r to a point of interest, and vector r - r' joining dq to that point.
and to get the value of r' choose one point on the line and draw the vector to that point to see which are its components in x and y direction.
 
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