New answers tagged boundary-conditions
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votes
Physical interpretation of the Green's function approach to Laplace equation
I will set $\epsilon_0 = 1$ in the following. Recall that to solve the Poisson equation using Green's functions, you compute:
$$
u(x) = \int G(x,y)\rho(y)d^3y
$$
Staring hard at Kirchhoff integral ...
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When a boundary value problem for geodesics equation has a unique solution (is well posed)?
It is possible to prove the following result of (pesudo)Riemannian geometry.
If $(M,g)$ is a smooth (pseudo)Riemannian manifold, then there is a topological basis made of convex normal neighborhoods.
...
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Clarification on electric fields and potentials inside conductors
Due to the spherical symmetry, it is convenient to use Gauss' law in integral form with spherical closed surfaces.
For $0 \lt r \lt a$ the total charge enclosed by the sphere of radius $r$ is $q$, so ...
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vote
Clarification on electric fields and potentials inside conductors
The answer to your question can be obtained by using the Gaussian law. It states that the integral of the electric field $\mathbf{E}$ over a surface $\mathbf{A}=A\mathbf{n}$ is proprtional to the ...
- 56
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Potential at the center of a cubical box
The answer is very close to $V_0/5.5$ rather than $V_0/6$. The difference is because the potential at the center must equal the average of the potential around it. Typically, you must have the same ...
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Wave Propagation Free Space: Boundary Conditions
Perhaps this discussion could help: Wave function boundary condition in scattering problem
In scattering problems one usually assumes a form of an outgoing/incoming wave. These are also often ...
- 65k
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Wave Propagation Free Space: Boundary Conditions
The boundary condition is plane waves fill all space. The initial condition is they have existed from the infinite past.
In practice, this usually means plane waves extend far enough that you don't ...
- 45.7k
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Independence of Hamiltonian formulation from Lagrangian formulation
I want to comment on how you phrased the question.
Path-of-construction and independent-versus-dependent are distinct properties.
While it is possible to construct the Hamiltonian formalism without ...
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Independence of Hamiltonian formulation from Lagrangian formulation
Hamiltonian and (variational) Lagrangian formulations are intimately related, cf. this Phys.SE post, so even if one starts with the Hamiltonian formulation, there is implicitly also a (variational) ...
- 213k
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