Q 11. - Calculus

Question

To convert from cylindrical to spherical coordinates:

$\rho =----, \theta =----, \varphi =----$

Step-by-Step Solution

Answer

$\rho =\sqrt{r^2+z^2}, \theta =\theta , \varphi ={\tan }^{-1}\frac{r}{z}$

Step 1: Given Information

Given $\left(\rho ,\theta ,\varphi \right)$ are spherical coordinates and $(r,\theta ,z)$ are cylindrical coordinates.

Step 2: Simplification

The relation between two is:

$\rho =\sqrt{r^2+z^2}, \theta =\theta , \tan \varphi =\frac{r}{z}$

Hence,

$\rho =\sqrt{r^2+z^2}$

$\theta =\theta$

and $\varphi ={\tan }^{-1}\frac{r}{z}$