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I have three point charges with the cartesian coordinates:

$q_1(a,0,0) \: \: \: q_2(0,a,0) \: \: \: q_3(0,0,a) $,

I want to convert these into both cylindrical and spherical coordinates.

The cartesian coordinates are written like this: $(x,y,z)$

The cylindrical coordinates are written like this: $(r,\theta,z)$

The spheircal coordinates are written like this: $(\rho,\theta,\phi)$

From https://en.wikipedia.org/wiki/List_of_common_coordinate_transformations I found these conversion formulas going form cartesian to cylindrical:

$r=\sqrt{x^2+y^2}$

$\theta=\arctan(\frac{x}{y})$

$z=z$

My Problem

Now, I want to convert the cartesian coordinates $(a,0,0)$ into cylindrical. We go like this $$r=\sqrt{a^2+0^2}=a $$ $$\theta=\arctan(\frac{a}{0})=??? $$ $$z=z $$

My problem is that I don't how to handle the $\theta$ calculation when the y-coordinate is $0$. Can somebody help me here, or maybe I'm using a wrong formula?

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You need to use the arctan2 function, which takes all 4 quadrants into account.

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  • $\begingroup$ Thank you for your answer. But what do I do for the point $(0,0,a)$? The arctan2 function is not defined when $x = 0$ and $y = 0$. Is the cylindrical coordinates then just $(0,0,a)$? $\endgroup$
    – Carl
    Sep 13, 2020 at 8:17
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    $\begingroup$ @Carl You mean when $r = 0$? In that case, you can choose any angle $\theta$. $\endgroup$
    – user76284
    Sep 13, 2020 at 18:25

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