# Poisson's Equation in Electrostatics

(Difference between revisions)
 Revision as of 10:13, 8 October 2009 (view source)JMora (Talk | contribs)← Older edit Latest revision as of 09:06, 4 November 2009 (view source)JMora (Talk | contribs) (→References) (One intermediate revision by one user not shown) Line 20: Line 20: [[Category: Electrostatic Application]] [[Category: Electrostatic Application]] − [[Category: Theory]] + [[Category: Poisson's Equation]] + [[Category: Electrostatic Theory]]

## Latest revision as of 09:06, 4 November 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:

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