# Questions tagged [boundary-conditions]

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### 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 ...
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### 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 $b$ ...
524 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 ...
403 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 ...
91 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?
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### 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 ...
607 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 ...
509 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 ...
67 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 ...
95 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 ...
3k views

### Question on open organ pipe

Although open organ pipe is open on both ends, how standing waves are produced in a open organ pipe. Can someone explain with more clarity?
205 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 ...
136 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 ...
39k 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?
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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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### 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 ...
604 views

### Challenging Magnetostatics Problem - the “blind spot” of a magnetic dipole

I'm reviewing for an electromag exam and I stumbled upon a problem that's really hard to figure out. Here it is: A small magnetic dipole with moment $\vec m = m_o \hat z$ is in a region with uniform ...
1k views

### What is the phase shift incurred by a sound wave as a result of reflection?

While studying waves I read the fact that a sound wave gets shifted by $\pi$ as a result of reflection against a surface. But I am unable to prove that fact. Assuming the interface to be a node I can ...