Is There an Error in the r+-r- Expression?

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The discussion centers on the expression r+-r- and its approximation as Lx/z0. The original equation involves square roots that account for the positions along the x and y axes, leading to confusion about the lack of y dependence in the final expression. The participant questions how the teacher derived the simplified form and highlights the asymmetry along the x-axis as a key factor in understanding the expression. Ultimately, the resolution involves recognizing the influence of the x-axis on the approximation while noting the absence of y's impact. This analysis clarifies the relationship between the variables in the context of the problem.
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Greeetings, yesterday I had to do the attached assignment but I ran into a problem. It is not so much about how to solve the exercise but rather about how to approximate the term:
r+-r-
My solutions notes writes this as:
r+-r- = Lx/z0
Is it just me or is there something wrong with this expression: How did my teacher arrive at that from:
r+-r- = √((x-L/2)2+y2+z02) - √((x+L/2)2+y2+z02)
 

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Divide everything by Zo then use the linear approximation of the square root.
 
hmm okay I think I got it. I just find it weird that there is no dependence on y while there is a dependence of x? Why is that intuitively?
 
Intuitively that is because of the asymmetry along the x-axis.
 

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