Answer by hyportnex for How does light know the destination?
The propagation of light waves satisfies Maxwell's equations and in the high frequency limit, that is when the permittivity and permeability changes slowly over the free-space wavelength $c/\omega$,...
View ArticleAnswer by hyportnex for Energy and Non-conservative forces
The quote at best is a badly phrased sentence, at worst is a fundamental misunderstanding. Instead of being unrecoverable the entropy generated by friction and other irreversible processes are in fact...
View ArticleAnswer by hyportnex for Can you have diffraction without a slit, simply by...
All objects diffract and diffraction is light's interaction with obstacles, specifically with their edges. The reason we see the effect more pronounced with smaller slits/openings is because the amount...
View ArticleAnswer by hyportnex for Is fuel cell efficiency limited by thermodynamics?
The efficiency with which chemical potential energy can be converted to work is no different from any other efficiency with which potential energy is convertible to work: potential energy does not...
View ArticleComment by hyportnex on Heat as a path dependent integral
there is nothing suspicious about this: every point in the path represents a certain amount of entropy transported at some temperature, even if the "heat" in question is latent: Latent heat is the...
View ArticleWhy is Sellmeier's equation an even function of $\lambda$?
According to Sellmeier's formula, the dispersion formula of a transparent material can be written as$$n^2(\lambda) = 1 +\sum_i\frac{B_i \lambda^2}{\lambda^2 - C_i},$$ where $B_i$ and $C_i$ are...
View ArticleAnswer by hyportnex for Wave dispersion relation as a differntial equation
Write this in coordinates.Let $$\left[\nabla \mathbf k\right]_{ij} = \frac{\partial k_j}{\partial x_i}$$then$$\left[\mathbf v \cdot \nabla \mathbf k\right]_j = \sum_i v_i \frac{\partial k_j}{\partial...
View ArticleAnswer by hyportnex for Is there no sense of 'absolute' in the universe?
Yes, there is a sense of absolute. The "potential" that has an absolute zero point is the thermal potential, that is the absolute temperature. In an irreversible process the dissipated work $q$ can be...
View ArticleAnswer by hyportnex for Clausius Inequality and Thermodynamic Potentials
The easiest way to think of this is as follows. In the formula $\frac{\delta q}{T_0}$ source of the heat $\delta q$ at temperature $T_0$ is actually transporting along with said heat an amount of...
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Answer by hyportnex for Understanding radiation mechanism of inset fed...
There are two apertures (you called them slots) radiating, these are fed approximately $\lambda_g/2$ apart therefore the charges on the metal that induce the electric fields parallel with the aperture...
View ArticleAnswer by hyportnex for Is the Huygens' principle consistent for intersecting...
It is true that in the optical (high frequency) limit the rays are orthogonal to the constant phase surfaces, the wavefronts, and the optical path length along these rays between any two wavefronts is...
View ArticleWhy Onsager's formulation of thermoelectricity is better than Bridgman's?
General comment: despite the longish historical introduction this question is not about the history of physics but rather about a specific conceptual problem in physics.Following Bridgman in the famous...
View ArticleAnswer by hyportnex for How did the scientist measure the dielectric...
dc or low frequency permittivity measurements are usually capacitance measurements in a bridge, see. At a higher frequency, microwaves and beyond, it is usually done in some form of cavity for its...
View ArticleWhat does the Jacobi identity *mean* statistically?
Given that the commutator of a pair of operators shows up explicitly in the lower bound of the Robertson-Schrodinger inequality, I am wondering what, if any, statistical meaning/significance one can...
View ArticleWhat is the topology of a phase diagram?
Looking at various two-variable phase diagrams I was struck by that on every one I have seen so far all the phases formed simple connected regions; see, for example the phase diagrams of $H_2O$ or of...
View ArticleAnswer by hyportnex for How to determine the light rays difference according...
You have $[MR]=2a\tan\phi$ because the ray $\vec{NQ}$ is at a critical angle, such that it suffers total reflection, in other words its $\mathbf {\text{incident angle = reflected angle}}$ and,...
View ArticleComment by hyportnex on Diffraction proof
@garyp the shape differs not at $x=\pi$ but at $x=\pm\frac{\pi}{2}$
View ArticleCarroll's interpretation of 1-forms
Carroll writes in his Spacetime and Geometry book on page 68 that"[...] in fact, however, we could just as well have begun with an intrinsic definition of one-forms and used that to define vectors as...
View ArticleAnswer by hyportnex for Integral Quantity Interpretation
Apply the standard expansion of the vector identity, see$$\nabla (\mathbf a \cdot \mathbf b) = (\mathbf a \cdot \nabla)\mathbf b + \mathbf a \times (\nabla \times \mathbf b) + (\mathbf b \cdot...
View ArticleAnswer by hyportnex for Phasors and propagating modes in a waveguide
In a homogeneous waveguide, both propagating TE and TM waves, modes, can be derived from the scalar Helmholtz equation. Let $\partial \mathcal B =0$ denote the metal boundary of the cross section....
View ArticleComment by hyportnex on I don't understand intuitively why the instantaneous...
@Dale Thank you for your comment. I was tempted and started to write out why the FM demodulator needs a slow (adiabatic for the physicists among us) FM to work and show how it differs from the...
View ArticleAnswer by hyportnex for Applying Fermat's principle in Fraunhofer's diffraction
If measured from the source you take the constant phase surfaces of the propagating wave, these are the wavefronts, then Fermat's principle holds between any to points that lie on the same orthogonal...
View ArticleAnswer by hyportnex for Brownian noise variance
In the problem statement for the stochastic differential equation $mx''+fx'=\mathbf F(t)$ it is specified that the power spectral density of the process $\mathbf F$ be $S_F(\omega)=2kTf$ where $f$ is...
View ArticleAnswer by hyportnex for White noise fluctuation amplitude
From the Wiener-Khinchin theorem you know that the Fourier transform of the auto-covariance function is the power spectrum density: $S(u)=\int_{-\infty}^{\infty}K(\tau)e^{-\mathfrak j2\pi u}du.$Here...
View ArticleComment by hyportnex on Can a region of electromagnetic waves alone be...
(1) yes, the black body radiation in a volume $V$ has internal energy density $u=aT^4$, has entropy density $\tfrac{4}{3}aT^3$, and pressure $p=\tfrac{u}{3}$, and satisfies the Gibbs equation:...
View ArticleComment by hyportnex on Why is potential continuous at dielectric conjunction?
@my2cts I was careful to assume no free charges only as a sufficient condition and avoided the issue of necessity. Otherwise, the question of moveable charges may come up and then it gets complicated...
View ArticleAnswer by hyportnex for Physics of microwave oven
How exactly is food heated? Do microwaves penetrate all the way inside or do they heat only the surface layer?This is a complex problem because the penetration depth, intensity to drop by 1/e, depends...
View ArticleAnswer by hyportnex for Entropy of dielectric in Capacitor?
This is called the electrocaloric effect and para- and ferro- magnetic materials also show similar behavior. It can be shown that, see Eq (5) and the references therein, with $\mathbf D=\epsilon_0...
View ArticleAnswer by hyportnex for Why equation 5.29 in Schroeder's Thermal Physics is...
This confusion is caused by the schizophrenia of traditional thermodynamic teaching. On the one hand it says that "heat" is only energy transported in motion like work but it is not work, and tries to...
View ArticleComment by hyportnex on Why $VdP$ term omitted in isothermal Work?
you are right, just forgot to add the punchline but now I have, see above.
View ArticleComment by hyportnex on In thermoelectric effect is neutral temperature...
what is a "neutral" temperature?
View ArticleComment by hyportnex on Why isn't the original EM wave in a beam of light in...
this has nothing to do with photons propagating, see the Brillouin - Sommerfeld precursor theory in Jackson chapter 7.11 and also in Loudon
View ArticleComment by hyportnex on Is the spontaneous flow of heat to thermal...
the problem I have with your argument is that leaves out the case when there is no $q_{rev}$ connecting two equilibrium points, see, for example, ferromagnetic or plastic deformation hysteresis, a...
View ArticleComment by hyportnex on Using Ampere's law, what is the magnetic field of a...
all true iff you assume an axially symmetrical current distribution; in real life the internal current distribution can be surprisingly complex and contribute to the resistive losses in surprisingly...
View ArticleComment by hyportnex on Why doesn't gravity causing the adiabatic lapse rate...
all this movement is fueled by an external energy source, the Sun
View ArticleComment by hyportnex on Can heat transfer decrease with increasing diffusivity?
I’m voting to close this question because it is about a python application of a physics problem
View ArticleComment by hyportnex on Why do valence electrons not push each other away?
beautiful explanation, but with one thing is still to be explained: why would the electronic configuration of an atom seek the minimum energy, where is that to be found in the axioms of QM?
View ArticleComment by hyportnex on Babinet's principle, Arago point and Airy's disc
Not really. Arago's point develops as a result of diffraction at a finite distance from the diffracting object, here the opaque disc. Airy's pattern is what antenna designer's call the (Fraunhofer)...
View ArticleComment by hyportnex on Can anyone please give some explanation in terms of...
the Taylor expansion you have for $H(f)$ is a so-called asymptotic expansion, it is not valid for $f=0,$ instead it is true only asymptotically as $f\to \infty$. You can read about this very...
View ArticleComment by hyportnex on Why is entropy defined in the way it is?
Because "heat" is $TdS$. Every time you think of a quantity of heat you should have in my a certain amount of entropy at some temperature.
View ArticleComment by hyportnex on If Electrostatic Force dissipates Heat , then why is...
what example you have in mind when you are saying that an "Electrostatic Force dissipates Heat"?
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