LedHead
  • Member for 5 years
  • Last seen more than 1 year ago
  • Columbus, OH
Far away from a charged conductor, the field is like a point charge. Where's the point located?
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36 votes

Based on some of the back-and-forth I see, I think you're asking the wrong question. I think the question you want to ask is "Given a charge distribution $\rho(\mathbf{r})$, where should I place a ...

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Can you derive new theories in physics by only looking at the math?
8 votes

This is about theoretical physics and experimental physics working together. The purpose of physics is to create a set of laws that allow us to predict the behavior of physical systems. New, ...

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Explanation of $\sin(\theta) > 1$ for total internal reflection
5 votes

Look at it this way: We can express a plane wave as $$\mathcal{E}_z(x,y,t) = \cos(k_x x + k_y y - \omega t)$$ where I've assumed a $z$-polarized wave propagating in the $x$ and/or $y$-directions. In ...

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Why Legendre transform works?
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4 votes

The point of the Legendre transform is to switch out independent variables. You can't write $g(x,y,u)$, because $x$ and $u$ aren't independent from one another. Another way of looking at it is that ...

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Why is this "the" functional of Laplace's equation?
3 votes

The key is that the minimization of that functional yields the original BVP for the exact problem, and the FEM system of equations for the numerical problem. The chain of logic goes something like ...

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Actual classical time evolution in a closed Cavity
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2 votes

It's a perfect electrical conductor (PEC) at the endpoints. Assuming $u(x)$ represents a component of the electric field perpendicular to the $x$-axis, the boundary conditions are $u(0)=u(L)=0$, which ...

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What is the significance of different modes?
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2 votes

You're confused because there are two separate concepts here: the plane interface problem, and waveguide modes. The definition for what is TE or TM is completely different between the two cases. ...

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While solving 2D Poisson's equation, how to apply floating boundary at two edges, and Dirichlet at other two?
2 votes

You can't let the values at the top and bottom totally float. It will leave the matrix system under-determined. If you look at it from the discretized matrix perspective it's obvious: Total of $(m+1)...

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Electromagnetic waves and photons
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2 votes

Really, photons are the wave. What makes a wave in the classical sense is a large number of photons all averaging together. Your question is an obvious guess to make -- other wave phenomenon is a ...

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How can only the change in direction can be called acceleration?
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2 votes

It's not just about total speed, it's about the speed in each direction -- i.e. the velocity vector. If I'm driving east at 60kph, and I turn left using a turn of some radius, but maintain the same ...

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Direction of vector magnetic potential
1 votes

"Components in fixed direction" just means that the coordinate system basis vectors don't vary in space. For example $\mathbf{\hat{x}}$ is the same for all $x,y,z$ while $\mathbf{\hat{r}}$ depends on ...

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How to recover the potential field from Green's function and Poisson's equation for a point charge
1 votes

Your mistake is using $x$ for both the location of the point charge and the observation of the potential. Instead, introduce a third coordinate, say $x_0$, for the location of the point charge. Then ...

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Derivation of Electric Vector Potential
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1 votes

Short answer: $\nabla \cdot \mathbf{D}=0$ comes from taking the divergence of $\nabla \times \mathbf{H}_F = j \omega \epsilon \mathbf{E}_F$ since we have assumed that $\mathbf{J}=0$ for this case. We ...

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Can only two equal EM-wavelength interfere? If so why is that?
1 votes

They can't constructively or destructively interfere because the two sinusoids go in and out of phase with each other. First of all, it has more to do with frequency than wavelength. Obviously, ...

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The radiation pattern of six dipoles in phase and in series
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1 votes

When we talk of radiation patterns, we're assuming the limit as $r \rightarrow \infty$. After a cursory read of chapters 28 and 29, I didn't find where Feynman explicitly states that, but I'm sure he ...

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Different ways of expressing the Euler equations
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1 votes

I wrote this out using Einstein notation, except since it's an orthogonal space, I ignored upper indices. Anywhere you see a double index, there's an implied summation. Here, $x_i$ are the ...

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What is so special about calcite that it has double refraction?
1 votes

Calcite's structure is what makes calcite's structure so special. The lattice configuration in this specific material makes it anisotropic. A lot of dielectric materials (most?) are isotropic, or ...

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Derivative of position vs displacement with respect to time?
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1 votes

Displacement and position are just two words for the same thing, at least in this context. Displacement is a change in position, but position (or "location" or "coordinates", etc.) is just a change in ...

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Why does the angle of waves change in refraction instead of just altering the relative position of each component the medium?
1 votes

I prefer to understand this question in terms of the electric fields. Basically, Snell's law falls out of forcing phase matching at the interface. First of all, when you talk of a light ray, I'll ...

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On a transmission line, why is there a reflected wave when a voltage/current wave encounters a different impedance?
1 votes

I think it's common to try to think of transmission lines like hoses carrying water, and the impedance corresponds to something like the radius of the hose, so the bigger the hose the easier it is for ...

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How to explain the relationship between wave's amplitude and intensity?
0 votes

Your initial assumption that you can simply sum intensity (power) is incorrect. The law of superposition of Maxwell's equations says that you can sum electric fields and magnetic fields -- or ...

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How can I get the axes of the polarization ellipse from the Jones vector of the light?
0 votes

I think you can accomplish this with a singular-value decomposition. I'll start by writing $\mathbf{E}$ in the following form $\mathbf{E} = E_x \mathbf{\hat{x}} + E_y \mathbf{\hat{y}} = E_u \mathbf{\...

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Vector Potential and Zero Divergence
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0 votes

You're right that $\nabla \cdot \mathbf{A}$ could be anything, but the relationship between $\mathbf{A}$ and $\mathbf{B}$ you show is only true in the Coulomb gauge. It's straightforward to show ...

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