Electrostatic Boundary Conditions

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(New page: Boundary conditions for electrostatic fields at the interface between two different media are: ::<math>\left . \hat n \times (\vec{E}_1-\vec{E}_2) \right |_{\Gamma_{1 \to 2}} = \left . \l...)
 
 
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== 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://electron6.phys.utk.edu/phys594/Tools/e&m/summary/electrostatics/electrostatics.html Electrostatics Summary]
 
  
 
[[Category: Electrostatic Application]]
 
[[Category: Electrostatic Application]]
[[Category: Theory]]
+
[[Category: Electrostatic Theory]]

Latest revision as of 09:06, 4 November 2009

Boundary conditions for electrostatic fields at the interface between two different media are:

\left . \hat n \times (\vec{E}_1-\vec{E}_2) \right |_{\Gamma_{1 \to 2}}
= \left . \left ( E_{t_1}-E_{t_2} \right ) \right |_{\Gamma_{1 \to 2}} = 0
\left . \hat n \cdot (\vec{D}_1-\vec{D}_2) \right |_{\Gamma_{1 \to 2}}
= \left . \left ( D_{n_1}-D_{n_2} \right ) \right |_{\Gamma_{1 \to 2}} = \rho_C


with \hat n \, the normal vector to the interface between the two media (see picture) and \rho_C \, the charge density in the boundary.


BoundaryCond.jpg


Dominio2D.jpg


For a domain {\Omega} \,, we should consider three different boundary conditions:

  • Dirichlet boundary condition:
\left . V - \bar V = 0 \right |_{\Gamma_{V}}
  • Neumann boundary condition:
\left . \hat n \vec{D} - \bar D_n = 0 \right |_{\Gamma_{q}}
  • Infinit condition (when no physical boundary are presents -free space-):
\left . \frac{\partial V}{\partial r} \right |_{\Gamma_{\infty}} \approx - \frac{V}{r}
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