# Electrostatic Boundary Conditions

(Difference between revisions)
 Revision as of 10:12, 8 October 2009 (view source)JMora (Talk | contribs) (New page: Boundary conditions for electrostatic fields at the interface between two different media are: ::[itex]\left . \hat n \times (\vec{E}_1-\vec{E}_2) \right |_{\Gamma_{1 \to 2}} = \left . \l...) Revision as of 10:12, 8 October 2009 (view source)JMora (Talk | contribs) Newer edit → Line 33: Line 33: − == 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: Theory]]

## Revision as of 10:12, 8 October 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. 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-): $\left . \frac{\partial V}{\partial r} \right |_{\Gamma_{\infty}} \approx - \frac{V}{r}$