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The above is screen shot from my professor solving the problem of electric field above the center of a non uniform charged ring, where he is using cylindrical coordinates. My question is he says the vector to any point on the ring, i.e. the source vector, is $\vec{r'}=s'\hat s$. However for cylindrical coordinates I thought the source vector should be $\vec{r'}=s\prime\hat{s} + \varphi\prime\hat{\varphi}$, can some please explain why we do not need the extra term?

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  • $\begingroup$ FWIW, this is a question you could/should ask during the lecture. $\endgroup$
    – Kyle Kanos
    Aug 17 '17 at 10:01
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All that your Professor has done is to define a unit vector $\hat s$ which will be different for every position on the ring as shown in the diagram below.

enter image description here

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