Let $r=(x^2+y^2+z^2)^{1/2}$ be the radial distance from the origin expressed in cartesian coordinates.
I have been asked to express this in cylindrical coordinates.
Is $r=(x^2+y^2+z^2)^{1/2}$ the same as $r=x\hat{e}_x + y\hat{e}_y + z\hat{e}_z$
if yes then to convert to cartesian coordinate:
- $R=\sqrt{x^2+y^2}=R$
- $\theta=tan^{-1}(\frac{y}{x})=tan^{-1}===??$
- $z=z$
i dont' understand what values we have put in?
You have to use these $$\left\{\begin{aligned}x&=\rho \cos \varphi \\y&=\rho \sin \varphi \\z&=z\end{aligned}\right.$$ in order to convert from cartesian to cylindrical coordinates.
$r=(x^2+y^2+z^2)^{1/2}$ becomes $r=(\rho^2+z^2)^{1/2}$