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2
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2answers
146 views

Why do electric field lines start and end at 90 degree at the surface of a conductor? [duplicate]

There is one property of electric lines of forces which states that: Electric field lines start and end at 90 degree at the surface of the conductor. But why is that so? Is there any proof for ...
2
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0answers
35 views

Newton's law of cooling for the heat equation boundary condition

Newton's law of cooling says the temperature of an object satisfies $$ \frac{dT}{dt} = -k(T(t) - T_0),\tag{1} $$ where $T_0$ is the surrounding temperature. See these HTML notes for example. Now if ...
5
votes
0answers
45 views

Is there a physical interpretation of Neumann boundary conditions for the free Schrodinger equation on a domain?

Let $\Omega$ be a domain in $\mathbb{R}^n$. Consider the time-independent free Schrodinger equation $\Delta \psi = E\psi$. Solutions subject to Dirichlet boundary conditions can be physically ...
3
votes
2answers
59 views

Why do we not require higher derivatives to match at boundary when solving the Schrödinger equation in a given potential?

When solving the time independent Schrödinger equation for a given potential in 1D, the main part of the solving involves matching boundary conditions. Usually, we require the value and the first ...
1
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0answers
24 views

Integrating entropy on an arbitrary boundary [migrated]

Entropy, denoted as H, is: $$ H = -\int_a^b p\ln(p) dx $$ where the range a to b is some arbitrary boundary and where p is given by the classic: $$ p(x) = ...
1
vote
1answer
27 views

How do i mathematically represent reflection in a (diffusion) Problem?

I am trying to formulate boundary conditions and it occurred to me that I never had to implement a reflective boundary before. The example is a one dimensional diffusion, where at $x=0$ the ...
0
votes
1answer
34 views

Fourier series for a wave on an infinite string?

From "Vibrations and Waves" by A.P. French I know that any wave on a string length $L$ can be represented by: $$y(x,t)=\Sigma^\infty_0 A_n \sin(\frac{n\pi x}{L})\cos(\omega_nt-\delta_n)$$ But can we ...
0
votes
2answers
62 views

When does $\mathbf n\times(\nabla V_2-\nabla V_1)=0$ imply $V_1=V_2$

I was reading a paper on electrohydrodynamics which has the following sentence (in my own words): At the interface/boundary, the requirement of continuity of the tangential component of the ...
1
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0answers
15 views

Phase change by reflection [duplicate]

Let's consider a light ray falling on a cuboid made of glass at the angle $\alpha$. Then there will be a reflected ray $A$. The ray will also refract. Let the refracted ray be $B$. Ray $B$ will be ...
2
votes
1answer
21 views

Could you give boundary conditions to the gravitational potential given the density distribution?

We´re doing a project that's all about solving differential equations with separation of variables. We´re trying to find the gravitational potential given the density distribution (that has azimuthal ...
0
votes
0answers
20 views

Electromagnetic boundary conditions for modelling symmetrical geometry

I stumbled upon this article: http://www.comsol.com/blogs/exploiting-symmetry-simplify-magnetic-field-modeling/ Since the article does not contain any mathematical formulations, I was wondering how ...
1
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0answers
18 views

How to specify boundary conditions as function of curvature in dynamic elastic beam pde?

In this article (already mentioned in this question) the dynamics of a planar elastic beam with "cantilever constrains" (one clamped end and one free end) is modeled. Using the Euler-Bernoulli Beam ...
1
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0answers
28 views

Neumann Green's function inside semi-infinite conductor [closed]

Consider a semi-infinite conductor with uniform conductivity $s$ occupying the space $z>0$. What is the Green's function with Dirichlet and Neumann boundary conditions inside the region $z>0$? ...
2
votes
1answer
37 views

How come a current sheet of $J_s = J_0 \hat{x}$ produces plane wave solution?

Given in the picture. There is a current sheet $J_s = J_0 \hat{x}$. Supposedly Jo is not oscillating. So, how does this thing create a plane waves propagating away from the current sheet? Shouldn't ...
0
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0answers
11 views

Solution for elastic wave on plane of ideal contact between two half spaces of elastic, homogeneous, isotropic, linear solids

Please give the solution for elastic wave of arbitrary polarization incident at arbitrary angle on plane of ideal contact (meaning no slip, homothermal, nondissipative, and no transfer of material ...
0
votes
0answers
7 views

Zero stress boundary conditions for the acoustic wave function

When is it appropriate to use zero normal stress boundary conditions when solving the acoustic wave equation. That is when the pressure is equal to zero.
3
votes
2answers
96 views

Idea behind Compactified Boson

On p. 167 of his Conformal Field Theory, Di Francesco introduces "Compactified Boson". He says: The invariance of the free-boson Lagrangian [...] with respect to translations $\varphi(x) ...
1
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0answers
32 views

Faraday's law in free space explaining away the constant vector?

Let's say that I have a plane electromagnetic wave travailing in free space, and I know the electric field part to be $\vec E$. If I am using Faraday's law to get the magnetic field part I will get ...
1
vote
1answer
126 views

Eigenvalues of the radial Schrödinger equation on a finite integration interval

There are numerous ways to estimate the eigenvalues of a radial Schrödinger equation, see http://arxiv.org/abs/math-ph/0703040 as an example. Anyhow, the formulas only cover the Schrödinger equations ...
2
votes
1answer
64 views

Question on boundary condition for Maxwell's Equations and Coulomb's law

When deriving Coulomb's law using the differential forms of Maxwell's equation, the boundary condition that $\phi = 0 $ at infinity is also used. From $\nabla × E = 0, E = \nabla \phi$ for some ...
0
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0answers
43 views

Terminal conditions and boundary terms in Lagrangian formulations: what do different choices mean?

For the sake of having compact expressions: $$ \left\langle f,g\right\rangle=\int^T_0 f(t)g(t)\,\text{d}t $$ Given some functional: $$ F=\frac{1}{2}m\!\left\langle ...
1
vote
1answer
54 views

Hamilton-Jacobi theory and initial value problem?

Having read through some recent posts regarding the Lagrangian formulation being interpreted into an initial value problem rather than the familiar boundary condition problem we are familiar with, I ...
0
votes
1answer
44 views

Meaning of boundary conditions in solid mechanics

The Question is: A uniform horizontal beam OA, of length $a$ and weight $w$ per unit length is clamped horizontally at O and freely supported at A. The transverse displacement $y$ of the beam is ...
0
votes
1answer
51 views

Losing a term for 3D radial schrodinger equation

I am trying to solve the Schrodinger equation For a potential $V(r)$ defined for $ 0<r<R$ as $$V(r)=-V_0 $$ and zero everywhere else. For wavefunction $u$ I can easily get to $$ u'' =-k^2u,$$ ...
1
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0answers
37 views

Deriving general boundary conditions from first principles for elastodynamic scattering

It seems that most of the relevant books only give the linear case and the rest say something along the lines of "here are common examples of boundary conditions." What are the most general boundary ...
0
votes
1answer
79 views

Lagrangian mechanics and initial conditions vs boundary conditions

It bothers me that many basic books on the classical mechanics don't discuss the following difference between "Newton's laws" and the "Principle of stationary action". Newton's laws can predict the ...
3
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0answers
78 views

Physical intuition for the solutions of the wave equation

I have been studying the wave equation in $\mathbb{R}^n$ for the cases $n=1,2$ and $3$. In the three cases, working all over $\mathbb{R}^n$. That is: $u_{tt}(x,t)=c^2 u(x,t)$ for $x \in ...
0
votes
1answer
63 views

Solving inhomogeneous differential equation with Green function

I'm not sure if this question is for physics forum, but my book's title is "Green's Functions in Quantum Physics", so I ask here. The book says that the Green's function defined as $$ (z-L( ...
8
votes
1answer
165 views

Why do we require quantum fields to vanish at infinity?

Classical fields, like the electrical field must vanish at infinity, because otherwise their energy would be infinite. This can be used in computations to exclude certain solutions. In quantum ...
1
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0answers
19 views

QM scattering in a finite-sized box

Background Consider a non-relativistic particle in a one-dimensional box of length $L$ with (for definiteness) an attractive delta function at the origin: $H = \frac{P^2}{2m} -|c|\delta(x), \qquad ...
0
votes
0answers
49 views

General boundary condition for 1D heat equation

I'm studying from Numerical Solution of Partial Differential Equations by K.W.Morton and D.F.Mayers (Amazon link). I'm confused with general boundary conditions. Could someone give me a clue? For ...
0
votes
2answers
57 views

Phase change on reflection only 0 and $\pi$ allowed

We know that when a wave on a string is reflected from a hard boundary, the phase change is $\pi$, and from a soft boundary, the change is 0. My question is: this two conditions (hard and soft ...
1
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0answers
21 views

Lagrangian with a boundary contribution, external work and interaction

I am considering a linear second order partial differential equation of the form \begin{align} F(q,p)&=-a\,q-\nabla\cdot p=0\\ p(q,\nabla q)&=b\cdot\nabla q \end{align} with $a$ scalar and $b$ ...
0
votes
1answer
34 views

How does one show specific thickness and wavelength determine full transmission of electromagnetic waves?

How does one show that thickness and wavelength determine the full transmission between two different dielectric media if the boundary condition equations between two dielectric media are independent ...
0
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0answers
198 views

Is the principle of least action fully equivalent to the Euler-Lagrange equations?

I am citing from Landau and Lifschitz, this statement that will seem to you well-known, trivial, etc: "Between these positions, (i.e. $q_1$ and $q_2$) the system moves then in such a way that the ...
0
votes
1answer
29 views

Wave guide boundary conditions

Why only the normal component of Electric field and the parallel component of Magnetic field exist at the surface of a wave guide or any conductor?
0
votes
1answer
54 views

Concentration distribution in a phase separated mixture. Can't get the correct ODEs and boundary conditions

I wish to compute the equilibrium concentration distribution of a binary mixture that has phase separated. I start with writing the free energy as a functional depending of the concentration. I use ...
0
votes
2answers
85 views

Solution of one dimensional wave equation by variable separation method

When solving the One dimensional wave equation by variable separable method, we equate left-hand side and right-hand side to a constant which is negative in nature. Why has the constant be only ...
0
votes
0answers
63 views

Boundary conditions of stream function

I have to do an problem about solving numerically the flow that goes under an airfoil. The airfoil has a flap deployed downwards and I need to solve the mesh that it's under the airfoil. I have drawn ...
1
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0answers
18 views

Heat Transfer in Cylindrical Coordinates

Lets say one has an infinitely long cylinder with some boundary heat terms on $r=r_0$ of the form $T(r=r_0, \phi,z)=T_0(\phi,z)$. What is the general solution for this type of equation? The general ...
2
votes
0answers
51 views

What is “above” and what is “below” the surface of a sphere?

When studying Electromagnetism using D.J. Griffith's Introduction to Electrodynamics, the boundary conditions for the electric potential across a surface charge density are expressed using the normal ...
2
votes
2answers
160 views

Are solutions coordinate invariant?

In the case of electromagnetism, we can solve the sorceless wave equation in Cartesian coordinates ($x$,$y$,$z$) getting plane waves as solutions: $$ u(x) = A(x-ct) + B(x+ct) $$ and actually I am not ...
1
vote
2answers
45 views

What are the end points in the action integral of field theory?

In the mechanics of particles when we apply the principle of the least action the two end points are two spatial coordinates. Therefore, if we consider the variation of the action with respect to the ...
1
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3answers
551 views

Does light change phase on refraction?

I have seen a lot about when light undergoes a phase change when it is reflected. But does it undergo a phase change when refracted and if so why and if not why not?
0
votes
0answers
23 views

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 ...
2
votes
3answers
335 views

Rigorously prove that electric field is zero in a perfect conductor

I have ran into a problem while trying to prove that the electric field is zero in a perfect conductor My argument went something like this: We know that: $$\vec J = \sigma \vec E$$ In a ...
0
votes
2answers
72 views

Why does $\hat n \times (\vec E_1 - \vec E_2) =0 $ imply that the tangential electric field components are equal?

On page 8: http://local.eleceng.uct.ac.za/courses/EEE3055F/lecture_notes/2011_old/eee3055f_Ch4_2up.pdfele I don't understand why $E_{t1} = E_{t2}$ is equivalent to $\hat n \times (\vec E_1 - \vec ...
1
vote
1answer
89 views

Large rotation Euler-Bernoulli beam boundary condition

Is given in Wikipedia as $$EI\frac{d^4u}{dx^4}-\frac{3}{2}EA\left(\frac{du}{dx}\right)^2\frac{d^2u}{dx^2} = q(x) ,$$ where $q(x)$ is the transverse load (assuming uniform cross-section and no axial ...
4
votes
1answer
102 views

Total derivative in action of the field theory

Consider a classical field theory. When applying the least action I see that a term is considered total derivative. We say that $$\int \partial_\mu (\frac {\partial L}{\partial(\partial_\mu ...
2
votes
1answer
91 views

Usage of Poisson's equation?

I revisited electrostatics and I am now wondering what the big fuzz about Poisson's equation $$\nabla^2 \phi = -\frac{\rho}{\varepsilon_0}$$ is. Wiki says One of the cornerstones of electrostatics ...