# Questions tagged [boundary-conditions]

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604 questions
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### Why is the total force at a free surface zero?

I am looking into waves on a free surface for which their are two main conditions: Kinematic condition: Particles on the surface remain on the surface. Dynamic condition: Forces acting on the surface ...
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### Laplace equation outside sphere

When solving the Laplace equation on sphere coordinates you get: $$u(r,\theta) = \sum_{n=0}^{\infty}\left( A_n\,r^n + \frac{B_n}{r^{n+1}} \right) P_n(\cos\theta)$$ And it is clear that if you have ...
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### Conducting cylinder by dielectric interface

To help me with a project I'm working on, I attempted to solve what I thought was an easy problem - There is an infinite, conducting cylinder of radius R at some potential V, located distance b from a ...
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### Deriving the Electrostatic boundary conditions

When deriving the electrostatic boundary conditions for any charge distribution (to my knowledge at least), Griffiths in his textbook references this illustration: So, when considering the boundary ...
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### Realistic vacuum boundary conditions in fluid mechanics?

What are some realistic boundary conditions between a fluid and vacuum? Is there an interface or does the fluid kind of spray out into the vacuum?
Consider $\Omega = \Omega_1 \cup \Omega_2$, where $\Omega _1$ and $\Omega_2$ are two different media with conductivity and permeability \sigma= \begin{cases} \sigma _1 & \text{in ...