Just want to verify Laplace equation in rectangular coordinates that:(adsbygoogle = window.adsbygoogle || []).push({});

[tex] \nabla ^2 \vec E = 0 [/tex]

[tex]\Rightarrow\; \nabla^2 \vec E = \left ( \frac {\partial^2}{\partial x^2} +\frac {\partial^2}{\partial y^2} +\frac {\partial^2}{\partial z^2} \right ) ( \hat x E_x +\hat y E_y + \hat z E_z) = 0 [/tex]

[tex]\hbox {(1)}\;\Rightarrow \;\frac {\partial^2 \vec E}{\partial x^2} = 0,\;\frac {\partial^2 \vec E}{\partial y^2} = 0 \;\hbox { and } \frac {\partial^2 \vec E}{\partial z^2} = 0 [/tex]

And

[tex]\hbox {(2)}\; \nabla ^2 \vec E = \nabla^2_{xy}\vec E + \frac {\partial^2 \vec E}{\partial z^2} = 0 \;\hbox { where }\; \nabla^2_{xy}\vec E = \left ( \frac {\partial^2}{\partial x^2} +\frac {\partial^2}{\partial y^2} \right ) ( \hat x E_x +\hat y E_y + \hat z E_z) [/tex]

**Physics Forums | Science Articles, Homework Help, Discussion**

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Verify Laplace equation in rectangular coordinates.

**Physics Forums | Science Articles, Homework Help, Discussion**