Poisson's Equation in Electrostatics

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(New page: A detailed form of the Poisson's Equation[9] in Electrostatics is: ::<math>\frac{\partial}{\partial x}\cdot \left( \varepsilon_{x} \cdot \frac{\partial V(x,y,z)}{\partial x}\right) +...)
 
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A detailed form of the [[Poisson's Equation]][9] in Electrostatics is:
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A detailed form of the [[Poisson's Equation]][1] in Electrostatics is:
  
  
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== 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}


References

  1. Poisson's Equation
  2. Electrostatics Summary
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