# Poisson's Equation in Electrostatics

(Difference between revisions)
 Revision as of 10:12, 8 October 2009 (view source)JMora (Talk | contribs) (New page: A detailed form of the Poisson's Equation[9] in Electrostatics is: ::[itex]\frac{\partial}{\partial x}\cdot \left( \varepsilon_{x} \cdot \frac{\partial V(x,y,z)}{\partial x}\right) +...) Revision as of 10:13, 8 October 2009 (view source)JMora (Talk | contribs) Newer edit → Line 1: Line 1: − A detailed form of the [[Poisson's Equation]][9] in Electrostatics is: + A detailed form of the [[Poisson's Equation]][1] in Electrostatics is: Line 16: Line 16: == References == == References == − # [http://www.answers.com/topic/electrostatics Sci-Tech Encyclopedia: Electrostatics] − # [http://en.wikipedia.org/wiki/Electrostatics wikipedia Electrostatics] − # [http://en.wikipedia.org/wiki/Static_electricity wikipedia Static electricity] − # [http://en.wikipedia.org/wiki/Electric_charge wikipedia Electric charge] − # [http://en.wikipedia.org/wiki/Electric_force Electric force] − # [http://www.colorado.edu/physics/2000/waves_particles/wavpart2.html Electric force animation] − # [http://en.wikipedia.org/wiki/Electric_flux Electric flux] − # [http://en.wikipedia.org/wiki/Electric_displacement_field Electric displacement field] # [http://en.wikipedia.org/wiki/Poisson%27s_equation Poisson's Equation] # [http://en.wikipedia.org/wiki/Poisson%27s_equation Poisson's Equation] # [http://electron6.phys.utk.edu/phys594/Tools/e&m/summary/electrostatics/electrostatics.html Electrostatics Summary] # [http://electron6.phys.utk.edu/phys594/Tools/e&m/summary/electrostatics/electrostatics.html Electrostatics Summary]

## Revision as of 10:13, 8 October 2009

A detailed form of the Poisson's Equation[1] in Electrostatics is:

$\frac{\partial}{\partial x}\cdot \left( \varepsilon_{x} \cdot \frac{\partial V(x,y,z)}{\partial x}\right) + \frac{\partial}{\partial y}\cdot \left(\varepsilon_{y} \cdot \frac{\partial V(x,y,z)}{\partial y} \right) + \frac{\partial}{\partial z}\cdot \left(\varepsilon_{z} \cdot \frac{\partial V(x,y,z)}{\partial z} \right) + \rho_v(x,y,z)=0$

with:

$D_x = -\varepsilon_{x} \frac{\partial V(x,y,z)}{\partial x} \quad D_y = -\varepsilon_{y} \frac{\partial V(x,y,z)}{\partial y} \quad D_z = -\varepsilon_{z} \frac{\partial V(x,y,z)}{\partial z}$
$E_x = -\frac{\partial V(x,y,z)}{\partial x} \qquad E_y = -\frac{\partial V(x,y,z)}{\partial y} \qquad E_z = -\frac{\partial V(x,y,z)}{\partial z}$