# Solved Example problems in Electro Magnetic Theory

1. Convert Points P(1,3,5)  from Cartesian to Cylindrical and Spherical Co-ordinate system.

Ans. Given P(1,3,5) $\fn_cm&space;\Rightarrow&space;x=1,y=3,&space;z=5$

Cylindrical :- $\fn_cm&space;\phi&space;=tan^{-1}(\frac{y}{x})$

$\fn_cm&space;=tan^{-1}(\frac{3}{1})$

$\fn_cm&space;=75^{o}$

Similarly $\fn_cm&space;\rho&space;=&space;\sqrt{x^{2}+&space;y^{2}}&space;\Rightarrow&space;\sqrt{1^{2}+&space;3^{2}}&space;=&space;\sqrt{10}=3.16$

$\fn_cm&space;P(\rho&space;,\phi&space;,z)=&space;P(3.16,71.5^{o},5)$

Spherical :- $\fn_cm&space;r=&space;\sqrt{x^{2}+y^{2}+z^{2}}$

$\fn_cm&space;r=&space;\sqrt{1^{2}+3^{2}+5^{2}}$

$\fn_cm&space;r=&space;\sqrt{35}$

$\fn_cm&space;r=5.91$

$\fn_cm&space;\theta&space;=tan^{-1}(\frac{\sqrt{x^{2}+y^{2}}}{z})$

$\fn_cm&space;\theta&space;=tan^{-1}(\frac{\sqrt{1^{2}+3^{2}}}{5})$

$\fn_cm&space;\theta&space;=32.31^{o}$

$\fn_cm&space;\phi&space;=tan^{-1}(\frac{y}{x})$

$\fn_cm&space;\phi&space;=tan^{-1}(\frac{3}{1})$

$\fn_cm&space;\phi&space;=&space;75^{o}$

$\fn_cm&space;P(r,\theta&space;,\phi&space;)&space;=&space;P(5.91,32.31^{o},71.5^{o})$

## Author: vikramarka

Completed M.Tech in Digital Electronics and Communication Systems and currently working as a faculty.