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 \Rightarrow x=1,y=3, z=5

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

                              \fn_cm =tan^{-1}(\frac{3}{1})

                                \fn_cm =75^{o}

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

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

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

                        \fn_cm r= \sqrt{1^{2}+3^{2}+5^{2}}

                      \fn_cm r= \sqrt{35}

                    \fn_cm r=5.91

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

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

\fn_cm \theta =32.31^{o}

\fn_cm \phi =tan^{-1}(\frac{y}{x})

\fn_cm \phi =tan^{-1}(\frac{3}{1})

\fn_cm \phi = 75^{o}

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



Author: Lakshmi Prasanna Ponnala

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