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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 ...

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, ...

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 ...

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 ...

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 ...

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 ...

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. ...

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 $(m+1)... View answer Accepted answer 2 votes Really, photons are the wave. What makes a wave in the classical sense is a large number of photons all averaging together. Your question is an obvious guess to make -- other wave phenomenon is a ... View answer Accepted answer 2 votes It's not just about total speed, it's about the speed in each direction -- i.e. the velocity vector. If I'm driving east at 60kph, and I turn left using a turn of some radius, but maintain the same ... View answer 1 votes "Components in fixed direction" just means that the coordinate system basis vectors don't vary in space. For example$\mathbf{\hat{x}}$is the same for all$x,y,z$while$\mathbf{\hat{r}}$depends on ... View answer 1 votes Your mistake is using$x$for both the location of the point charge and the observation of the potential. Instead, introduce a third coordinate, say$x_0$, for the location of the point charge. Then ... View answer Accepted answer 1 votes Short answer:$\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$for this case. We ... View answer 1 votes They can't constructively or destructively interfere because the two sinusoids go in and out of phase with each other. First of all, it has more to do with frequency than wavelength. Obviously, ... View answer Accepted answer 1 votes When we talk of radiation patterns, we're assuming the limit as$r \rightarrow \infty$. After a cursory read of chapters 28 and 29, I didn't find where Feynman explicitly states that, but I'm sure he ... View answer Accepted answer 1 votes I wrote this out using Einstein notation, except since it's an orthogonal space, I ignored upper indices. Anywhere you see a double index, there's an implied summation. Here,$x_i$are the ... View answer 1 votes Calcite's structure is what makes calcite's structure so special. The lattice configuration in this specific material makes it anisotropic. A lot of dielectric materials (most?) are isotropic, or ... View answer Accepted answer 1 votes Displacement and position are just two words for the same thing, at least in this context. Displacement is a change in position, but position (or "location" or "coordinates", etc.) is just a change in ... View answer 1 votes I prefer to understand this question in terms of the electric fields. Basically, Snell's law falls out of forcing phase matching at the interface. First of all, when you talk of a light ray, I'll ... View answer 1 votes I think it's common to try to think of transmission lines like hoses carrying water, and the impedance corresponds to something like the radius of the hose, so the bigger the hose the easier it is for ... View answer 0 votes Your initial assumption that you can simply sum intensity (power) is incorrect. The law of superposition of Maxwell's equations says that you can sum electric fields and magnetic fields -- or ... View answer 0 votes I think you can accomplish this with a singular-value decomposition. I'll start by writing$\mathbf{E}$in the following form$\mathbf{E} = E_x \mathbf{\hat{x}} + E_y \mathbf{\hat{y}} = E_u \mathbf{\...
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 ...