Q stringlengths 18 13.7k | A stringlengths 1 16.1k | meta dict |
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How to find the direction of an eddy current? Suppose there is a magnetic field going from left to right. Suppose a thin sheet of metal conductor (e.g. a 1m*1m square) is dropped through the magnetic field such that the plane of the conductor is PERPENDICULAR to the magnetic field.
Now I know that by Faraday's Law, the... | as a thought
$$\nabla \times j = M$$
$$\nabla \times M = j$$
this current density has three manifestations shown in amperes material derviation:
$$ \nabla \times B = \mu_0(j_f + j_p + j_m) + \epsilon_0 \frac{\partial E}{\partial t}$$
Current due to change in polarisation
$$j_p = \frac{\partial P}{\partial t}$$
Current... | {
"language": "en",
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"timestamp": "2023-03-29T00:00:00",
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What is the curve that describes the Daytime line in a Day and Night World Map? A Day and Night World Map shows which parts of the Earth are in daylight and which are in night at a given instant.
At one side of the Daytime line they are in daylight and at the other side they are in twilight.
The shape of the day and ni... | Absent a small amount of distortion from the oblateness of the Earth, yes: it is a great circle. To generate the corresponding curve on a flat map, you have to use the map's projection rules to project the coordinates of the circle's circumference onto the map. That completely depends on the projection rules for the sp... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/214728",
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Why does a ray passing through optical centre remain undeviated? How can it be explained using the laws of refraction that a light through optical centre of a lens passes undeviated?
If we assume the portion of the lens in the middle to be made of even number of alternately place up and down prisms, then it's clear, b... | The middle part of the lens will just act as a rectangular glass slab. We may verify it by cutting the lens horizontally. Now we know that rectangular glass slab refract light in such a way that emergent is parallel to incident. Actually the same happens when the ray passes through optical centre. This can be observed ... | {
"language": "en",
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"timestamp": "2023-03-29T00:00:00",
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Are chemical bonds matter? So it recently blew my mind that chemical bonds have mass. And that a spring that's wound up similarly weights a little more.
But there is a distinction between mass and matter.
I believe that a chemical bond, even though it has mass, is not considered matter and is instead a form of energy... | Chemical bonds form when atomic orbitals of the nuclei to be bonded interact and form a molecular orbital.
The simplest case of bond formation is the formation of dihydrogen ($\mathrm{H_2}$) from 2 hydrogen atoms. The latter have (in the ground state) each one electron in a $1s$ atomic orbital and these orbitals then c... | {
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What it sounds like when I'm travelling at the speed of sound totally hypothetical here:
lets say a man is playing a song on a guitar and I begin travelling quickly away from the guitar, if I were to reach the speed of sound, what will I hear? (my assumption is that I will hear a single note humming in a constant stat... |
my assumption is that I will hear a single note humming in a constant state.
A sound wave is not a thing that you can hear. Assume for a moment that you are just standing in the coffee shop, enjoying the music. What you are hearing is not the waves. What you are hearing is the guitar.
The waves carry acoustic ener... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/215179",
"timestamp": "2023-03-29T00:00:00",
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What does the discovery of a pentaquark signify? at a particle collider a pentaquark was discovered. My question in short is what does the discovery of a pentaquark signify? Is there a theory that it supports or something like that?
| You're asking about the significance of the discovery of the Pentaquark. It would shed light on some mysteries surrounding the nuclear force, to begin with. It could perhaps lead to a change in what we understand about Neutron stars, too.
In terms of "some theory it supports or something like that", generally the stuff... | {
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Is it (practically) possible for a large building to be a Faraday cage? In my sophomore year of high school, my P.E. teachers kept on complaining about how phones didn't have a network connection in our gym, regardless of model, service provider, etc. A couple of feet outside the gym, cellular reception was crystal cle... | Just to add to what Floris has said. It is frequent (in the UK) that institutional settings would have toughened glass in windows, particularly in bathrooms, gyms etc. that would have the form of a wire mesh (of order 1cm grid) embedded in the glass. That would do a particularly good job of blocking phone signals that ... | {
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What is the smallest item for which gravity has been recorded or observed? What is the smallest item for which gravity has been recorded or observed? By this, I mean the smallest object whose gravitational effect upon another object has been detected. (Many thanks to Daniel Griscom for that excellent verbiage.)
In oth... | The classic gravitational measurement is the Cavendish Experiment, and the masses involved were a pair of 0.73 kg lead weights. So that forms an accessible reference. Other versions of the experiment may have used smaller weights, though.
| {
"language": "en",
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Why can't I push myself in a chair? If I am sitting in a chair with wheels and someone pushes on the back of my chair with sufficient force it will role along the ground. However, if I push on the back of the chair with the same force it will not move the chair. Why?
| If you sit on the chair and push with same force, it is not an external force. Newton's law of motion: if external force is not acted on a body it will remain same in state. So the chair will not move. Your acted force is an internal force.
| {
"language": "en",
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"source": "stackexchange",
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Why do tall buildings have low resonant frequencies? I know that tall buildings have low natural frequencies, hence they're more vulnerable to earthquakes, but why do they have low natural frequencies?
| Real pendulums are pendulums with non-point distribution of mass. For these, to calculate time period as a function of length, we can apply the regular formula for harmonic motion after considering the length of the oscillator to be the the distance between the pivot and the center of mass. A tall building would obviou... | {
"language": "en",
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Does quantum tunnelling drill holes in solid state drives? The solid state drive (SSD) consists of numerous data storage elements. Each element (NAND flash memory element) reminds me of a microscopic battery. An electron is supposed to enter the element through the oxide layer and remain inside. A transistor beneath th... | The electron does not deposit energy in the oxide layer. The oxide layer provides for a potential barrier, the electron moves though it despite the fact that in a classical picture the electron should have a negative kinetic energy there. You can consider a process where the electron is going to do some damage to the o... | {
"language": "en",
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What is the definition of linear momentum? Every where and book I search I get that the definition of linear momentum is the amount of speed (quantity of motion) contained in it or simply it is mass $\times$velocity? So, what is an appropriate definition of linear momentum? What did Newton think when he discovered it... | Newton (if I recall correctly) typically referred to the concept of inertia, which was an objects resistance to changes in velocity when subjected to external forces. You are right about him not thinking about it as just the speed of the object, because this is where the mass term comes in. Many people think of Newto... | {
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What prevents me to accelerate an object to near light speed in space? As far my limited knowledge go, things in space aren't slow down unless something interferes with them, so what prevents me to build a spaceship powered by nuclear power that will keep accelerating until we get to the limits of physics?
Like the voy... |
so what prevents me to build a spaceship powered by nuclear power that
will keep accelerating until we get to the limits of physics?
Now matter how long the spaceship is able to accelerate (as measured by an accelerometer attached to the spaceship), there is always an inertial reference frame in which the spaceship... | {
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Derivation of $E=pc$ for a massless particle? In classical mechanics, massless particles don't exist because for $m=0$, $p=0$.
The relativistic relation between energy, mass and spatial momentum is: $E^2= (pc)^2 + (mc^2)^2$ . So it is said that setting $m=0$ in the first equation you get $E=pc$.
How could setting $m=0$... | If one considers that the deBroglie relationship holds for photons we have $$p=\frac{h}{\lambda} = \frac{hf}{c} = \frac{E}{c}$$
which immediately gives us $$E=pc.$$
This is consistent with the Lorentz invariant energy four-vector magnitude which yields the mass of a particle: $$ mc^2=\sqrt{E^2-(pc)^2}=0.$$
| {
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Why do helium balloons rise and fall? I understand why a regular party balloon filled with helium falls over time due to leakage of the helium. However I've also noticed that recently filled helium balloons put outside rise and fall. At one point in the afternoon they were dropping but later in the evening it was fully... | The upthrust on the balloon is equal to the weight of air displaced, so we get:
$$ F = V_b \rho g \tag{1} $$
where $V_b$ is the volume of the balloon and $\rho$ is the density of the air. Assuming air is approximately an ideal gas it obeys the equation of state:
$$ PV = nRT $$
so the molar density is:
$$ \rho_M = \frac... | {
"language": "en",
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Hyperfine lifetime calculation: what is the spin eigenfunctions?
I'm trying to calculate the lifetime of the 21 cm line in hydrogen and have the following expression:
$$\frac{1}{\tau} = \frac{4\alpha}{3}\omega_{if}^3|\langle a_f|\vec{x}|a_i\rangle|^2.$$
The initial state is $a_i = a|{F=1, F_z=1}\rangle + b|F=1, F... | So the matrix element I tried to calculate is indeed zero for the dipole moment. In order to find the hyperfine splitting, one must calculate $|\langle a_f|\mu|a_i \rangle|^2$.
| {
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What experimental evidence shows that sound velocity is the same for all wavelengths? I'm studying sound waves with Halliday's book, and after reading the whole chapter, one of the questions suggested was:
What is the experimental evidence that allows the assumption that the sound wave velocity in air is the same for ... | The spectrum of various resonant tube arrangements (half-open, fully-open fully closed) is something that can be measured in a very basic laboratory and gives solid evidence that the claim is true over the kinds of frequencies that are accessible in such a lab. Say a few hundred to a few thousand hertz.
| {
"language": "en",
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Does turning a spoon in water raise the temperature? I read about Joule's experiment proving the transformation of mechanical work into heat. But say I have a bowl with some water, and I start turning a spoon in it very fast, thus doing work — the water won't get hotter! What am I missing?
I think maybe the work I put ... | One of the reasons that makes you not to believe that one cannot heat up water by stirring it, might be that we usually experience the opposite effect. Namely, one usually stirs a hot tea or soup to cool it down. Why a cup of hot tea or a bowl of warm soup cools down when one stirs it? The reason is that the liquid/air... | {
"language": "en",
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How does mass change with speed? While reading a textbook on Physics, I came across this :
Mass is a universal constant. It does not depend upon the position of the body on the Universe but it changes with speed of the body.
It's just two contrasting statements with no further explanation. Maybe the author left it to... | The textbook writer is referring to the concept of relativistic mass, which is the idea that accelerating a body tends to become harder and harder as its speed approaches the speed of light. This is sometimes thought of in terms of an increase in the object's mass as the speed increases.
However, you should think of t... | {
"language": "en",
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Why can we replace a cavity inside a sphere by a negative density? I have a sphere with radius $R$ and inside this sphere there is a smaller sphere with radius $\frac{R}{3}$. This small cavity has its center at $\frac{R}{2}$, it doesn't matter in which direction.
If I want to find the electric field at the point $(0.0.... | "I find lots of solutions on the internet that say you can replace the cavity with a negative density, why?"
Because they use a trick to calculate the potential easier. They assume that the empty hole is neutral, but composed of a positive charge density equal to that of the sphere plus a negative charge density of the... | {
"language": "en",
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Could gravity accelerate light? Gravity causes anything with energy to accelerate toward the source. Black holes, for example, have such strong gravity that they pull in light and don't let any escape. But can acceleration still apply to light? The speed of light is constant, of course, but why are photons affected by ... | I would suppose the short answer is no, but photons are affected by gravity.
What is happening is naturally quite relativ to the observer. Suppose you are sitting on the photon, travelling past the gravity source with the speed of light. As has been argued above you would experience the force of the gravitational pull... | {
"language": "en",
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"timestamp": "2023-03-29T00:00:00",
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Distortion of body in Schwarzschild black hole Suppose I toss a cloud of matter into a Schwarzschild black hole; for the sake of argument, have it be timelike dust. As we know, the dust is "spaghettified" by tidal forces: simultaneously compressed in the tangential and elongated in the radial directions relative to the... | The volume of your dust cloud will not change. The shape changes but the volume does not, so the density of the cloud remains constant.
The Schwarzschild solution is a vacuum solution and the Ricci tensor is everywhere zero. If you look at section 5.2 of this paper it shows that the change in volume of an infinitesimal... | {
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Visualising gas temperature and gas pressure Gas pressure is created when gas molecules collide with the wall of the container creating a force.
Gas temperature is a measure of how fast the molecules are moving / vibrating.
However, they both seem to be concerned by "kinetic energy" of the molecules, or in other words,... | An example of a difference where the pressure of a reasonably dilute gas depends on something else other than the kinetic energy of the particles is actually just the air on Earth. A classic exercise in statistical mechanics is to consider an ideal gas subject to gravity and find how the pressure varies with altitude.
... | {
"language": "en",
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The dual of a surface element in 4-space In reading the classic text, "The Classical Theory of Fields", Third Edition, by Landau and Lifschitz, I found an "obvious" statement not so obvious to me. It is on p.19, the statement of the normality of the dual of a surface element, $df^{*ik}=\frac{1}{2}e^{iklm}df_{lm}$ to t... | It is OK to use an explicit form in a local orthonormal coordinate system (in the Minkowski sense). The dual for each component would then be just a possible flip of signs (see, e.g., https://en.wikipedia.org/wiki/Hodge_star_operator#Four_dimensions). Raising the indices would amount to doing nothing in that coordinate... | {
"language": "en",
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FWHM increase with energy (gamma spectra) Below I have two plots from a gamma spectrum which I've been analyzing. The first plot is between a low energy range, the second between a significantly higher energy range. It is clear that the FWHMs (Full Width Half Maxima) of the peaks in the spectrum increase with energy. T... | This is something I never really understood, but Glen Knoll offers the following in pp. 116 of his book "Radiation Detection and Measurement":
The energy resolution of the detector is conventionally defined as the FWHM divided by the location of the peak centroid $H_0$. The energy resolution $R$ is thus a dimensionles... | {
"language": "en",
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Why can't I see the blue color scattered by the lower atmosphere of the earth? I understand that the blue colour of the sky is because of the scattering of blue light by molecules in earth's atmosphere. The scattering appears to be happening from molecules that are far above in the earth's atmosphere. What about the sc... | Two reasons:
The scattering separates red/orange and blue in different directions. At sunset you'll see the red parts that are missing from the blue skies by day. This isn't noticeable for objects close by, because those objects surround you. The blue from some objects mixes with the red from others.
Secondly, there i... | {
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"source": "stackexchange",
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A false proof of drag force being conservative Consider a particle moving along some trajectory in the $x$-$y$ plane, in a viscous medium.
Then its equation of motion is given by:
$$\mathbf{F}_d = - b \mathbf{v} .$$
it's well-known from the Gradient theorem(fundamental theorem of line integral) that if there exists a ... | The issue is that the formula that connects force and potential gets an extra term when the force depends on velocity ${\bf v}$. The formula reads (see e.g. Ref. 1)
$$\tag{1} {\bf F}~=~\frac{d}{dt} \frac{\partial U}{\partial {\bf v}} - \frac{\partial U}{\partial {\bf r}},$$
rather than just $$\tag{2}
{\bf F}~=~ - \fra... | {
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Equivariant cohomology formula I'm studying equivariant cohomology on three references:
*
*Szabo's review about equivariant localization (S);
*Libine's note on equivariant cohomology (L);
*Berline, Getzler, Vigne's book "Heat Kernels and Dirac Operators", Springer (BGV).
I'm deriving all formulas by myself. I fa... | The main issue seems to be that BGV uses a supercommutator notation
$$\tag{1} [a,b]~:=~ab-(-1)^{|a||b|}ba,$$
where $|a|$ and $|b|$ denote the $\mathbb{Z}_2$-grading of operators $a$ and $b$,
respectively. So if $a$ and $b$ have odd gradings, then $[a,b]$ is actually the anticommutator.
References:
[BGV] N. Berline, E.... | {
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Is Newton's second law tautologous? Newton's second law
$$\mathbf{F} = m\mathbf{a}$$
where $\mathbf{F}$ is the force, $m$ the mass, and $\mathbf{a}$ the acceleration, seems at first blush to be a simple tautology, since $\mathbf{F}$ and $m$ are not defined anywhere else in the formalism. Of course we can use the more g... |
F and m are not defined anywhere else in the formalism
The force F is generic. In each particular case it is replaced by a force that is defined. For example $F = kx$ or $F = KMm/r^2$.
$m = Weight/g$ and the weight is measurable with a balance.
So everything is defined.
What I know is that the Aristotelian view, bef... | {
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What depth should water be filled to in a cylinder flask to make it the most stable As said in title, a cylinder flask with a mass of 100g and radius of 3 has a center of balence 10cm above the base. Assuming negligible wall thickness, to what depth should water be added to this flask to make it the most stable.
The q... | The flask become most stable when its centre of gravity is at the smallest height. If you start pouring water, you will notice that the effective centre of gravity gets down to a lower postion. As you keep on filling, it would be at the lowest height for some level of water and rises again, afterwards. You will have to... | {
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How do we know that the rate at which a body loses heat is proportional to the difference between its temperature and that of its environment? Did someone do an experiment, or was that fact derived from other ideas we had about how the world works?
|
How do we know that the rate at which a body loses heat is proportional to the difference between its temperature and that of its environment?
In classical physics this is a law.
"Fourier's law
The law of heat conduction, also known as Fourier's law, states that the time rate of heat transfer through a material is... | {
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Does Newtonian physics work on a galactic scale? I'm currently working on a simulation that aims to use Newton's Law of Gravitation to simulate how a galaxy behaves gravitationally. While I haven't gotten the simulation finished yet, I have had a few people tell me that Newtonian Physics don't work on a galactic scale,... | Yes, Newtonian Physics works on a galactic scale.
Still, for long distance interactions on fast objects you might want to take into account the finite speed of gravity, but I don't think it is necessary for ordinary galaxies simulations.
Conversly a lot of phenomena occur that impact the galactic material: writting a... | {
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How does order of scalar $\phi$ interaction impact feynman diagrams? On page 60 of srednicki (72 for online version) for the $\phi^{3}$ interaction for scalar fields he defines
$Z_{1}(J) \propto exp\left[\frac{i}{6}Z_{g}g\int d^{4}x(\frac{1}{i}\frac{\delta}{\delta J})^{3}\right]Z_0(J)$
Where does this come from? I.e f... | Yes for the $\phi^{3}$ theory the vertex has 3-lines, whereas for the $\phi^{4}$ theory this becomes 4 lines meeting at the vertex. g just refers to the number of vertices in the diagrams, so for $g^{1}$, you're summing all diagrams with one vertex, for $g^{2}$, you're summing all diagrams with two vertices, and so on.... | {
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Special Relativity in water If there are 2 observers in water moving relative to each other as well as to water, they measure different speeds of light. So does time dilation occur for them? (since Time dilation is based on constancy of speed of light)
| The opening statement "If there are 2 observers in water moving relative to each other as well as to water, they measure different speeds of light" is false. Both observers will measure the same speed for light, and therefore, relativistic effects will occur.
Unlike sound, light does not require a medium through which ... | {
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The maximum distance for which Coulomb's law has been verified? We know that Coulomb's law, $F_{12} = \frac{kq_1q_2}{r^2}$, was experimentally verified for small distances by Coulomb himself at the and of the XVIII century.
The question is what is the maximum distance, experimentally confirmed, between two charges for ... | I might be erring something basic here, so downvotes are welcomed, but I would love if they include comments to correct this answer, or just erase it.
I do not believe the Coulomb law has been tested beyond the order of a few meters. Arguing that light remains unchanged across the universe should be irrelevant. The rea... | {
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"source": "stackexchange",
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Light and Gravity
The gravitational force does not affect the speed of light rather affects the frequency of light (hence light changes colors, red to blue and vice-versa).
I know this has been verified but I have 2 questions:
1.Why the speed of light is not accelerated due to gravity?
2.Why the frequency is affecte... | The laws of special relativity, of which the constant speed of zero mass particles in vacuum is a basic tenet , have been tested innumerable times with many experiments, particularly in particle physics. The Michelson Morley experiment has shown that there exists no luminiferous ether, i.e. there is no medium on which ... | {
"language": "en",
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When does normal force equal to $mg$? Can someone once and for all explain when does normal force equal to mg?
I know for sure that when there is no friction, normal force will be equal to mg.
But, i encountered some questions when there is some mass on an incline with friction, and then the normal force was the y comp... | Normal Force arises due to the Newton's Third law.
Normal Force will be always acting opposite to the force falling on the surface.
Normal Force is a reaction force. Remember
Normal force is equal to mg only when the object is placed horizontally, and the force is acting in the direction of the gravitational field.
No... | {
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Why aren't pictures of Pluto darker than those of other planets? Just as the intensity of the light from a candle decreases with distance, I would expect the light from the sun to illuminate the distant planets less than the closer ones. However, the pictures of Pluto from New Horizons don't seem any "darker" than thos... | This question has been asked and answered (by me) on Astronomy Stack Exchange:
It's brighter on Pluto than you think.
NASA developed a tool called Pluto time, which tells you when at your place the ambient light conditions are similar to the ones on Pluto. This occurs when the Sun is only 2° below the horizon! That'... | {
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Do a receiving antenna interfers with an emitting antenna? As I understand:
*
*Accelerating electrons generate electromagnetic waves.
*An emitting antenna have an alternating current (electrons are moving) which generates an electromagnetic waves.
*The electromagnetic waves reach the receiving antenna and makes th... | Yes they both operate to different frequencies.
Two-way radios can be designed as full-duplex systems, transmitting on one frequency and receiving on another, this is also called frequency-division duplex.
How is this not affecting the incoming wave?
Source : Wikipedia
A radio transmitter is an electronic circuit wh... | {
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Inconsistency with electrostatic energy formulas The energy of point charge configuration can be written as:
$$W = \frac{1}{2}\sum_{i=1}^{n}q_{i}V(r_{i}) \, ,$$
which can take both positive and negative values.
However, when we integrate the equation to get the energy of a continuous charge dustribution:
$$W = \frac{1}... | Your formula for the first energy is incorrect. Instead use:
$$W = \frac{1}{2}\sum_{i\neq j}q_{i}V_j(\vec r_{i}) \, .$$
Or even:
$$W = \frac{1}{2}\sum_{i\neq j}\frac{q_iq_j}{4\pi\epsilon_0|\vec r_i-\vec r_j|} \, .$$
And now you see right away that you are avoiding the energy of the point charges themselves. Because nai... | {
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Can light have zero wavelength? As you increase the energy of a photon it's wavelength shortens. Is it theoretically posible for light to not have a wavelength? Like a still pond?
| A still pond would be equivalent of infinite wavelength and the frequency of 0. The equivalent of 0 wavelength would be an infinitely tall tsunami wave in the pond. It is not possible to have wavelength at exactly 0, but you can get arbitrarily close to 0. Proof: any positive non-zero wavelength, no matter how small, c... | {
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What is the correct way of writing the antisymmetrized state of two identical fermions? I am just confused:
If I have 2 identical fermions, where one of them is in state A and the other one is in state b, and they are normalised and orthogonal, which statement is right:
1) $|\Psi\rangle=\frac{1}{\sqrt{2}}\left(|a_1\ran... | Your second option is correct.
Writing
$$ \lvert a_1\rangle\lvert b_2 \rangle - \lvert a_2 \rangle \lvert b_1\rangle$$
does not make sense. The notation $\lvert \psi_1\rangle\lvert\phi_2\rangle$ is shorthand for the state $\lvert\psi_1\rangle\otimes\lvert\phi_2\rangle$ in the tensor product $\mathcal{H}_1\otimes\mathca... | {
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Nature of Pressure Pressure is defined as force per unit area. Therefore, pressure = force divided by area. Since force and area are both vectors, how can we perform this division without violating the rule of vectors?
If pressure is a scalar quantity, how did this scalar nature came about from the vector nature of for... | The pressure is defined by:
$$ \text{d}\mathbf{F}_n = -P\text{d}\mathbf{A} $$
where $\text{d}\mathbf{F}_n$ is the normal force on a surface element $\text{d}\mathbf{A}$. The pressure $P$ is the (scalar) constant of proportionality linking the two. Since the two vectors are in the same direction we can rewrite the equat... | {
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Work done in moving a body out of Gravitational influence By "out of Gravitational influence ", I suppose it's meant that Gravity of a planet has no effect whatsoever on the body.
Am I correct?
Could we do it by making the object reach Escape Velocity by doing Work = GMm/2D? {assuming circular orbit}
(m, mass of obj... |
By "out of Gravitational influence ", I suppose it's meant that Gravity of a planet has no effect whatsoever on the body. Am I correct?
Yes, that's correct.
An object that is subjected to a central gravitational field has potential energy $U$, given by:
$$U(r)=-\frac{GMm}{r},$$
where $G$ is the universal constant of ... | {
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Combination of Simple Harmonic Motions Will the combination of 2 Simple Harmonic motions will be an SHM in itself?
For example for simple functions such as
$$\ f(t)=\sin\omega t-\cos\omega t$$ I can use trigonometry to show that it can be expressed as $$\ f(t)=\sqrt 2\sin(\omega t-\pi/4) $$.
But what about functions g... | Consider the superposition of two simple harmonic motions
\begin{equation}
x(t) = x_1(t) + x_2(t) = A_1 \cos \left( \omega_1 t + \phi_1 \right) + A_2 \cos \left( \omega_2 t + \phi_2 \right).
\end{equation}
The first motion $x_1(t)$ is periodic with period $T_1 = \frac{2\pi}{\omega_1}$ and the second motion $x_2(t)$ is ... | {
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Relativistic acceleration in sinusoidal electric field Consider a relativistic charge $q$ moving with an oscillating electric field $E_z$ with phase velocity $v_p=c$ in direction $\hat{z}$ (e.g. radially polarized laser coprogating with electron). What is the energy gain of this charge as a function of time?
I set thi... | The very first thing you should do is to Lorentz transform into the initial rest frame of the electron. This leads to a doppler shift in the electric field. If you really want to omit the magnetic field your equation of motions become 1 dimensional because the electron will only oscillate in the direction of the polari... | {
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Do liquids creep from cold to hot like gases? Consider the U-tube water experiment below with the left red block
at 10C and the right red block at 90C. I think the right level
will become about 3% higher than the left level simply because
hotter water is 3% less dense than colder water, but I'm
assuming negligible pre... | If there was a horizontal pressure gradient, this unbalanced force would begin to redistribute the fluid. So by assuming the fluid settles in a static equilibrium configuration, you've implied that there is no pressure change along the bottom.
Of course, in a realistic situation (with a tube that is not infinitesimal i... | {
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Velocity of a leak in a closed water tank Bernoulli's equation states
$P_1+{1\over2}\rho v_1^2+\rho g h_1 = P_2+{1\over2}\rho v_2^2+\rho g h_2$
In a classic "water tank with an open top and a leak" scenario, "point 1" is the surface water in the tank, and "point 2" is the leak. The equation could be rewritten for $v_2$... | For a tank that is either open at the top or has a (sufficiently large) venting hole in it above the fluid line, the outflow speed is indeed approximately:
$$v= \sqrt{2g\Delta h}$$
But with a closed tank pressure $p_0$ above the water and thus also hydrostatic pressure:
$$p=p_0+\rho g\Delta h,$$
drops and flow rate dro... | {
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Rolling Friction Problem The handbrake of a vehicle of mass $1.5\ \mathrm{tonnes}$ completely fails while it is parked on a $30^\circ$ slope. It rolls $20\ \mathrm{m}$ down the slope before colliding with, and locking on to, a parked vehicle of mass $0.9\ \mathrm{tonnes}$.
(a) estimate the velocity of the two vehicles ... | Rolling friction is neither static nor kinetic (sliding) friction. It's caused by inelastic forces between the wheels and the road. For example, compressing the tire may take a lot of force, which is pointed up and toward the back of the vehicle. But when the tire expands (as that part of the tire is leaving the roa... | {
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What does "the fabric of space and time" actually mean? I've heard the term "the fabric of space and time" in both physics and science fiction, and although I know it has something to do with general relativity, I don't understand what, specifically, they're referring to.
| In Einstein's theory space and time is single entity called spacetime. We treat spacetime as a smooth fabric which is distorted by presence of energy.Thus the term the fabric of space and time.The term fabric is used to help us visualize how spacetime works in GR.
| {
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How does one get the first few terms of the $S$-matrix expansion? According to a set of notes I'm reading
$$\langle p_f | S | p_i \rangle = \delta(p_f-p_i) + 2 \pi \delta(E_f-E_i) \bigg[\langle p_f | V | p_i \rangle + \cdots\bigg]. \tag{1.29}$$
I don't understand where the $2 \pi \delta$ factor comes from in the second... | The Hamiltonian is: $H=H_0+V$, where V is the interaction part. The scattering matrix (expansion form to the first order) is:
$$S=1-i\int_{-\infty}^{\infty}V(\tau)d\tau+...$$
where $V(\tau)=e^{iH_0\tau}Ve^{-iH_0\tau}$ (interacting formalism). So:
$$S^{(1)}_{fi}=-i\int_{-\infty}^{\infty}\langle\psi_f|e^{iH_0\tau}Ve^{-iH... | {
"language": "en",
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Can we speed up the evaporation of black holes manually by accelerating it? If we throw an object to pass near a black hole, to bypass it, it will change the speed of the black hole, just like gravitational assist for a space probe. Does an accelerating black hole evaporate faster because:
*
*When object accelerates... | Isn't this just like the twin paradox? The twin that undergoes acceleration is the one that ages the slowest. So if you want to speed up the evaporation of black holes (from your viewpoint), you should accelerate yourself.
Maybe black holes work differently, but offhand I don't see why they should.
| {
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Question regarding gravity and time I and my friend (Age 15) were discussing about light and speed of light when we thought of a question. Imagine you are travelling in a spaceship at the speed of 2.9*10^8 m/s circling the earth. According to our calculations, 1 second on the spaceship is 30 seconds on earth. Lets take... | Start in the Earth frame i.e. the frame of an observer standing on the Earth watching the orbiting spaceship. In this frame the acceleration is given by the usual expression for circular motion:
$$ a = \frac{v^2}{r} $$
where $v$ is the speed of the spaceship and $r$ is its distance from the centre of the Earth.
This is... | {
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Does 'focal length' mean something different with lenses and pinhole cameras? Sometimes different but related things have the same name by some tradition or accident, causing a lot of headache to newcomers to a field.
I would like to come to clear terms with this: does the expression 'focal length' mean something disti... | Have a look to the beginning of this video https://www.youtube.com/watch?v=ecuDGXZjyl0 The presenter is trying to make links between the people comming from computer vision and optics and explicitely discuss this.
| {
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"source": "stackexchange",
"question_score": "13",
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Does the Entropy of the Visible Universe Decrease? My understanding is that the entropy in a closed system increases. However, I would also assume that the number of particles in the open system of a visible universe decreases because of accelerated expansion.
(1) What would be the entropy of the visible universe when ... | *
*With one particle, it would be nearly impossible to convert energy into work. So the entropy would be significantly higher than the entropy of our current universe, in which energy to work conversion is possible.
*Overall, the entropy of our universe increases in accordance to the second law of thermodynamics. The... | {
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What is the energy source if a tall water tank is used to transfer floating objects upwards instead of cables with motors? Suppose I want to transport some logs from the ground to the roof of a tower. Originally I can use a lift, or some cables, or even move the logs upwards manually; then the energy is converted to th... | When you put the log inside (from the side) you need to place the water from the log position somewhere else. The relevant "somewhere" is at the surface of the tank, so you have to lift the water there (it takes a lot of energy to get a log-equal volume of water to the roof level). The surface is now higher than before... | {
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Can you compress pure carbon into diamonds? I'm doing a science project, and we're wondering if it is possible to compress pure carbon (C) to the point where it becomes diamonds? What would the process have to be and how much energy would this take? Has this been done and is this feasible?
| Theoretically yes but those diamonds would be industrial, not worth much and wouldn't have the exterior of natural diamonds. Like what was said in a previous answer, these diamonds can be made in an explosion too! I think there's a myth busters episode on it if I'm not wrong!
| {
"language": "en",
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Simple quadrupole field not yet in Lorenz gauge? I'm having trouble reproducing some of the results regarding gravitational waves in the Wald's General Relativity.
In section 4.4 of gravitational radiation, eq.4.4.49 shows the far-field generated by a variable mass quadrupole:
$$ \gamma_{i j}(t,r)=\frac{2}{3R} \frac{d^... | I think the issue here is that you are simply forgetting the $\gamma_{0\mu}$ components of the metric. As mentioned in Wald, these are to be obtained using the (Lorenz) gauge condition, and are given explicitly in terms of the spatial components of the metric in eq. (4.4.45).
When those components are included in your... | {
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Electrostatic induction, induced charges Is it true that if a conducting object is not grounded, the nearby charge will induce equal and opposite charges in the conducting object?
It is mentioned on Wikipedia (electrostatic induction) but it is also mentioned that charges will appear such that the total electric field... | What happens is that for a conductor limited in real space and not grounded the net charge can't change (if is 0 it has to remain 0), so on the face towards the external charge it accumulates a charge to balance the electric field inside the conductor, but on the other face it accumulates a charge opposite in sign, to ... | {
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Is it possible that a person with myopia will see a blurry picture as normal? I am trying to process an image in good quality to appear blurred to a normal person and good to a person suffering from myopia
as seen in this source.
Is it possible that a picture that is blurry will appear normal to a person suffering from... | A quick footnote to Nathaniel's answer:
If an image looks blurred to you it's because you are viewing it in a plane that isn't the focal plane.
If you put a screen where I've drawn the red dotted line then the image on the screen will look blurred.
If you measure the light in the red dotted plane then at every point i... | {
"language": "en",
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How do I figure out the totally airborne height for a given machine? Technically "airborne" can just mean to move through the air, but I would like to know how high you have to be before you are entirely supported by air in a helicopter-like machine, as opposed to benefiting from the reaction from the earth (or whateve... | The effect is never zero, unless you happen to stop producing lift.
Lift is produced by air being continuously pushed downwards. This downward motion continues for several minutes, but is dissipated eventually. But in all cases the motion produces a pressure increase on the ground underneath. This is clearly audible fo... | {
"language": "en",
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Symmetry factor for Feynman diagrams in $\phi^4$-theory for $n$-points Green function I'm working with two theories.
Theory A: $H_{int} =\int d^3x \frac{Mg}{2}\phi\varphi^2$
Theory B: $\phi^4$-interaction: $H_{int} = \int d^3 x \frac{\lambda}{4!}\phi(x)^4$
Where $M$ is the mass associated to the field $\phi$.
I have ... | The symmetry factor should be 1 in both theories.
First a few remarks. If you are computing amputated diagrams the external propagators are removed from the evaluation of the amplitude, however it is unnatural (to me) to remove them from the count when considering symmetry factors. In Theory A I would say that $\#\Delt... | {
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Origin of radio waves In the same way as the origin of X rays is the excitation of electrons, what is the origin of radio and infrared radiations in this respect?
| There are a number of ways of generating radio waves.
The simple acceleration of electrons in a transmitting dipole will generate radio waves. I guess as you might have been using wi-fi to write your question, you knew this and are more concerned with "natural" sources of radio waves?
Basically, electromagnetic radiati... | {
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Hot Object In a Cooler Space How would you calculate the heat given by an object that is hotter than its surroundings? I know there's Newton's Cooling Law, but what about any heat given off by radiation? Are these additive quantities?
| Just use Newton's cooling Law to calculate heat transfer:
$$\frac{dQ}{dt}=hA(T-T_0)$$
where:
*
*$\frac{dQ}{dt}$ is the heat transferred from the glass to the room.
*$A$ is the total surface area of the glass.
*$T$ and $T_0$ are the temperatures of the glass and the room respectively.
$h$ is the overall heat tran... | {
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How can I convert Right Ascension and declination to distances? I am calculating galaxy rotation curves for various galaxies in the Ursa Major cluster and I want the distance of those galaxies from the center of the Cluster. The values referred to as coordinated are RA and dec and I don't know anything about these coor... | If the centre of your cluster has coordinates $\alpha, \delta$, the right ascension and declination in radians$^{1}$, and you have a galaxy's coordinates $\alpha_g, \delta_g$ in radians, then the following formula gives the angular distance $\theta$ in radians.
$$ \cos \theta = \sin \delta \sin \delta_g + \cos \delta \... | {
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We say Light is Red-Shifted or Blue-shifted from faraway stars and galaxies We say Light is Red-Shifted or Blue-shifted from faraway stars and galaxies. Can we find out the distance at which it changed its frequency.
So in another solar system, it might seem to be Green shifted or something similar. (Assuming that thos... | It is my understanding that virtually all galaxies are moving away from us, and so red shifted, except for a few galaxies (including dwarfs) in the local group, like Andromeda, which would be blue shifted. So, most galaxies are red shifted, and the further away they are, the more red shifted they are. So the the chan... | {
"language": "en",
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What is difference between polarization and polarizability and how do we define it? The book of physics that I have, uses the word "polarization" sometimes and sometimes uses the term "polarizability" and I am getting confused. And I even checked the dictionary for the term "polarizability" and it is not even a word in... | In short, polarization (the noun) is the displacement of positive charges relative to negative charges in a system (i.e. an atom's nucleus vs its electrons). Polarizability refers to the difficulty with which such a displacement can be achieved.
As discussed in Griffiths Introduction to Electrodynamics 4E, we can imagi... | {
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Why didn't the glass break? In the figure below, a needle has been placed in each end of a broomstick, the tips of the needles resting on the edges of filled wine glasses. The experimenter strikes the broomstick a swift and sturdy blow with a stout rod. The broomstick breaks and falls to the floor but the wine glasses ... | Well, the fact is that the needle lies atop the edge of the glass, and aas a rod stikes at the middle of the broom, a vertical component of force, acts on the needle, mind you, there is no horizontal vector, the needle produces a normal force, so in the end, no force is actually transmitted to the glasses. However a th... | {
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What is the trajectory of a photon moving through a vacuum? Since electromagnetic energy is carried by photons and moves in forms of waves, does it mean that a single photon when propagating through space doesn't follow the straight path but instead always moves up and down, up and down like a wave. If so another quest... | Your confusion comes from combining two different concepts (although they are related). Photon is a discrete particle. A wave is a continuous. You can look at light as a discrete particle or a wave, but if you think of them the way you are thinking of them, things get confusing.
*
*A photon does not travel among th... | {
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How can I prove that for a Killing vector $\nabla^a \nabla_a \xi^\mu = -R^b_a \xi^a$? I'm taking a course on General Relativity and I'm trying to prove that for a Killing vector field $\xi^\mu$ the following equation holds:
$$\nabla^a \nabla_a \xi^\mu = -R^\mu_a \xi^a$$
Where $R_ab$ is the Ricci tensor. To prove this I... | Let us look at $-g^{ac} \nabla_a \nabla_b \xi_c$. Because the part symmetric in $(bc)$ vanishes, we have $$-g^{ac} \nabla_a \nabla_b \xi_c = -\frac{1}{2} g^{ac} (\nabla_a \nabla_b \xi_c - \nabla_a \nabla_c \xi_b).$$
Now by the definition of the Riemann tensor, $\nabla_a\nabla_b \xi_c = \nabla_b\nabla_a \xi_c + R_{abc}{... | {
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Is there any physical interpretation for $\nabla\cdot(\nabla \times F)=0$? It is well known that the divergence of the curl is always 0. Mathematically I understand why this happens ($d^2=0$ where $d$ is the exterior derivative) but today I was wondering what is the physical meaning of this.
The divergence represents t... | First I should say that it is a mathematical definition and does not carry any physical meaning necessarily. But as an example it relates the Maxwell equations:
$$\nabla\times E=-\frac{\partial B}{\partial t}$$
and
$$\nabla \cdot B=0$$
$$\Longrightarrow \nabla\cdot(\nabla\times E)=-\frac{\partial \nabla\cdot B}{\partia... | {
"language": "en",
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How exactly can a speaker produce the huge number of frequencies in musi at he same time? I know the basics of how a speaker works, but when I think about the fact that just one sound from an instrument has many frequencies happening at once and there are other sounds such as the guitar pick, echo in he chambers, etc. ... | Adding on to the above answer, let's think of how the speaker's motion would then be generated. If a waveform has a time varying amplitude x(t), a voltage $V$ is applied so that at any time t, the integral of that voltage's action on the speaker membrane yields an amplitude of x(t). Thus, the desired waveform is rea... | {
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I do not understand this comparison? It is frequently discussed that to find solutions having some sort of supersymmetry is easier than solving Einstein’s equations of motion.
I do not understand this discussion though. Specifically, why are Einstein's equations difficult to solve? Is it because they are second order ... | The problem with the Einstein equations is that they are non-linear partial differential equations and, as you know, there are no general algorithms to solve them. Sometimes you can impose some symmetries - make an ansatz (guess) such that the Einstein equations becomes ODE and then solve them (that is how the Schwarzs... | {
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Why do we only feel the centrifugal force? After spending some time researching about the centrifugal force, I now understand that it is needed in a non-inertial reference frame for Newton's Laws to hold true. However, I don't understand why we only feel the centrifugal force when moving in a circular path. For example... | Suppose you have your feet pointing outwards and your head pointing towards the centre of rotation:
Now ask your self what direction the force you feel is pointing. Well, the force is pushing upwards on your feet, so the force points from your feet towards your head. In other words the force you feel is pointing inwar... | {
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Liouville's theorem for systems with dissipation described by a single hamiltonian Following this link, one can treat dissipation by using a factor $e^{\frac{t \beta}{ m}}$ in addition to the Lagrangian $L_0$ of a system without disspation:
$$
L[q, \dot{q}, t] = e^{\frac{t \beta}{ m}} L_0[q, \dot{q}] \, ,
\quad \text{w... | In my opinion, we should define the Lagrangian only when the force is conservative. Eventhough the force is not conservative, we can write down the Lagrangian which is mathmatically correct. However, the Lagrangian and the Hamiltonian do not contain correct nature inside it. Only mathmatically, those work. So, the dive... | {
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LCD's working principle
In the image's information it says ''Liquid crystal device windows are in the group of electrically activated smart windows in which normal "off" condition of the glazing is a translucent milky white. When an electric current is applied, it turns clear.''
Shouldn't it be the reverse?
| The diagram you reproduce shows that the liquid crystal elements align in the presence of a potential difference - and when they do, they no longer scatter the light. This makes the window "clear".
Note that this is different than the situation in a monochrome LCD, where the liquid crystal elements are placed between c... | {
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Motion of an object in rotating frame Yesterday I was looking at an old sloan video that describes motion in inertial and non-inertial frame. An experiment was actually like this. Two persons are sitting on the opposite side of a table fixed to a turning platform. The platform is rotating in uniform circular motion. N... | The motion for viewer inside rotating frame will be a straight line while for inertial frame observer or outside person it will be circular as motion is relative to the frame.
| {
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Why does moving air have low pressure? According to Wikipedia lift in an aircraft is due to an area of low pressure formed above the wings of an aircraft due to the fast moving air there. So why exactly is an area of low pressure created due to fast moving air?
| Moving air can have any pressure. However if air is moving away from a surface without enough new air flowing in to replace it, then the pressure at that surface drops. For a wing with lift the cause is inertia / momentum conservation. Since the air collides at higher rate with other parts of the wing there is a net fo... | {
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Is spin-orbit coupling really necessary for topological insulators I have heard that for an insulator to be non-trivial, large spin-orbit coupling is necessary.
However, I have read the definition of $Z_2$ topological invariant and chern number. In no way can I recognize what role spin-orbit coupling plays in topologic... | I guess no. Su-Schrieffer-Heeger (SSH) chain is one of the simplest topological insulators and has no spin-orbit coupling.
| {
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Is causality a total order? I've read that it is physically not possible to violate causality defined as a total order on the spacetime graph. So I was wondering if at least causality can be broked down to a partial order and if phenomenon in the universe exist that induce such an order.
Meaning if we have a set of eve... | Partial orders are permitted in Causal Set Theory (Raphael Sorkin) and it does make predictions, which relate to an information universe at least, and these might be regarded as physical. That said, at present such predictions are rather limited. Separately, violation of Bell's inequality, in which the result of an exp... | {
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How the LHC bump can be a mere coincidence? Speaking of http://www.nature.com/news/lhc-sees-hint-of-boson-heavier-than-higgs-1.19036.
I understand that such a bump can be a statistical fluctuation.
What troubles me is that the bump has been seen in two completely disconnected and independent experiments. How can this... | I rolled two sixes in a row when I sat down once and rolled a six sided die five times. Same thing happened to my friend once! Instead of asking how that can be, you can just ask about the chance of that happening.
When the chance gets too small you are starting to get good evidence that something is going on. When the... | {
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Orbifold actions and twist operators A twist operator $\sigma$ is the operator that acts on the untwisted vacuum $|0\rangle$ to create a twisted vacuum $\sigma|0\rangle$. States belonging to the twisted sector of an orbifold are built on such twisted vacua (which are also in 1-1 correspondence with the fixed points of ... | For a toroidal orbifold, suppose you know the boundary condition in the k-twisted sector and the spin structure $\alpha, \beta \in \lbrace 0,1/2\rbrace $. In light cone gauge you have:
$\psi^{j}(\sigma^0, \sigma^1+2\pi)=- e^{2\pi i \alpha }e^{2\pi i k v_j }\psi^{j}(\sigma^0, \sigma^1)$
where:
$v_j=a_j/N$
in which $a_j$... | {
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Is polarization a stable state? Do a polarized light beam stays polarized over large distance or does it kind of relax and eventually become unpolarized?
| It depends on the material the light beam is traveling through.
If the light is traveling through some media - vacuum, glass, etc. - then its polarization state will remain the same. However, if it is traveling through certain birefringent materials, then its polarization state may change.
Mathematically, this differen... | {
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Physics after a Theory of Everything There is a lot of controversy over the existence of a Theory of Everything (ToE), and as far as I know, we are a long way from having a possible candidate. But what interests me is, what after that? If a Theory of Everything is truly found, will there be anything left for physics to... | It's a question of definition what really is a physics, where the engineering and applied sciences begin etc. In this point of view:
$A)$ There is really lot of uncertainties and blank spaces when it comes to human senses and cognitive sciences and their connections to "objective" physics.
$B)$ There is much of cases ... | {
"language": "en",
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How does calblock (water softener) work? This "calblock" device claims to prevent limescale accumulation on water heaters in a washing machine. It sits between the water faucet and the washing machine; the water passes through it.
I cannot imagine how it could work. This video, made by a supplier, describes its functio... |
How do the magnets convert calcium bicarbonate to aragonite?
They can't.
I cannot imagine how can a chemical transformation be caused by magnets. Also, why 2 magnets?
If one magnet would do it, then wouldn't two be even better?
How are they arranged?
The magnets are arranged in such a way to separate your money ... | {
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Effect of Particle Mass on Thermal Conductivity Fouriers law of thermal conductivity is
$$ \vec{q} = -k\nabla T $$
where $q$ is the heat flux, $k$ is the thermal conductivity.
Mass does not seem to appear in the equation. So I'm wondering what if keeping all else constant, but if we change the particle mass (i.e. incr... | The thermal conductivity contains the cross-section for particle collisions.
The cross-section itself contains the mass of the particles that are carrying the thermal energy (as well as the mass of the "thing" the particle is colliding with). Sometimes one of these masses can be ignored.
The exact dependence of the cr... | {
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Conservation of angular momentum while sitting on a spinning chair Today my friend was sitting on a spinning char. By moving his top part of the body left to right and his bottom part of the body the opposite he managed to spin. As I understand Conservation of angular momentum if he was just sitting still he should not... | You do not say, but I assume his feet were in the air and not on the floor which is why you are wondering about conservation of angular momentum.
I suspect the spin axis of the chair was not exactly vertical and the plane of all possible positions was tilted from the horizontal, one side of this plane is actually lower... | {
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Biot-Savart law from Ampère's with multivariate calculus Let us assume the validity of Ampère's circuital law $$\oint_{\gamma}\mathbf{B}\cdot d\mathbf{x}=\mu_0 I_{\text{linked}}$$where $\mathbf{B}$ is the magnetic field, $\gamma$ a closed path linking the current of intensity $I_{\text{linked}}$.
Can the Biot-Savart la... | I really like the proof contained in the paper Derivation of the Biot-Savart Law from Ampere's Law Using the Displacement Current from Robert Buschauer (2013)
It's simple and it fulfills the role of convincing the reader.
Basically the author works with one point charge $q$ situated in origin of Z azis $(0,0,0)$. He s... | {
"language": "en",
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Missile-like trajectory calculation First of all I want to let you know that I'm not a Physicist, I am a Video Game Developer. I can simulate physical and mathematical equations and can also use some built in physics.
For example I can move an object through parametric equation of projectile
$$x = vt\cos\theta$$
$$y ... | One of the pieces that you need is called the range equation (assuming that you are firing from the ground):
$$
R=\frac{v^2_0\sin(2\alpha)}{g}\tag{1}
$$
So if you start with knowing $v_0,\,\alpha$, you can figure out how far it will go. But you are starting with $R$ and trying to see what pairs of $v_0,\,\alpha$ would ... | {
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Why do the conserved charges in the case of SSB of a global symmetry not exist? Reading "From Linear SUSY to Constrained Superfields" by Komargodski and Seiberg, I got a bit confused regarding the existence of the conserved charges in a theory with spontaneous symmetry breaking (SSB) of a global symmetry:
More precisel... | This is called the Fabri-Picasso theorem. Their argument requires both the vacuum and the charge $Q$ to be translationally invariant: $P |0\rangle = 0$, and $[P, Q] = 0$.
The argument goes as follows: Since the charge originates from a symmetry, then according to Noether's theorem:
$$Q = \int d^3x j_0(x)$$
Consider th... | {
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What does singularity mean in the context of black holes? Non-rotating big stars can be subject to a gravitational collapse increasing their density. When the density is so high that the mass volume shrinks below the event horizon, a black hole is formed.
Is such an "initial" black hole already considered as a singular... | A singularity is defined as a point of infinite density and they are believed to reside at the center of a black hole .
The "when does the singularity form" question, is answered concisely here.
| {
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What does the Dirac delta function physically do while deriving Gauss Law form Coulomb's law? While doing this derivation, the the source coordinates are mentioned as "$s$" and the coordinate of the point at which field is to be calculated is mentioned as "$r$". Kindly follow this Wikipedia link and click on the "Outli... | I think I have found the answer.
Let us consider the case of a uniformly charged sphere of radius $R$ and charge density $\rho$. The field inside this sphere is
$E_{in}=\frac{\rho\times r}{3\epsilon_0}$.
Here $r$ is the distance from the centre and $r < R$.
If we calculate the divergence of $E_{in}$ then
$$\nabla.E... | {
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Isn't LIGO basically measuring the luminiferous aether? I am bit confused about this one. I am not very acknowledgeable about gravitational waves and LIGO. But if it is basically a Michelson interferometer and can detect shifts in vacuum, doesn't this means that we detected the luminiferous aether and if not, why? Is t... | You are right, spacetime is the luminiferous aether (that kind of aether that Einstein abhorred) and gravitational waves are ripples in that aether. But, the Michelson-Morley experiment showed us in 1887 that there is no luminiferous aether, therefore gravitational waves do not exist or they cannot be detected by means... | {
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What size particle would be attracted to this 340 ton sculpture's gravitational field? I know that gravity is a weak force, but this rock has mass, so it has gravity. The Levitated Mass sculpture is big enough to attract something. What is the largest particle that would "stick" to the underbelly of this sculpture beca... | This experiment is bound to fail, because a particle underneath the large mass will still be feeling the force of mg of the earth. The attraction of the large mass will have an upward force of (m_1xm_2/r^2)xG .
From the value of the gravitational constant one sees that the equivalent "g" for the attraction of the levi... | {
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visible light spectrum Why do we see black objects? Colors of objects are formed when the spectrum of that color is reflected. Example Green objects are green because they reflect the green spectrum of light, red objects are red because they reflect red spectrum of the visible light and white objects because they refle... | I will address the "see" part.
Why do we see black objects? Colors of objects are formed when the spectrum of that color is reflected. Example Green objects are green because they reflect the green spectrum of light, red objects are red because they reflect red spectrum of the visible light and white objects because t... | {
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Can the Heisenberg Uncertainty Principle be explained intuitively? I have heard several pseudoscientific explanations about the Heisenberg Uncertainty Principle and find them hard to believe.
As a mathematician mainly focusing on functional analysis, I have a considerable interest in this matter. Although I still have ... | Imagine that the information that describes position and momentum is digital and of limited precision. There is a constant total precision for both of them, but you can slice it up differently. If you dedicate more bits to momentum, you get fewer bits for position and vice versa.
| {
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How are orbits made stable? I understand the concept of object staying in some orbit due to centrifugal force and gravity.
However I do not understand how is orbit of a body like satellite or planet has perfect balance between gravitational pull and centrifugal force of revolution?
because if the angular velocity is ... | The reason why planets in our solar system have stable orbits is because, during the formation of the solar system, debris disk which consisted mostly of gas was orbiting the sun, During this period when protoplanets started forming they were interacting with this debris disk, due to this interactions(frictional forces... | {
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Kinetic energy of a rotating object in an exercise, a linear molecule is being subject to a force applied on the edge in its axis. Then $K_1=\frac{1}{2}mv^2$, all is well.
Then in the second point of the exercise, the force is applied on the same edge but in an orthogonal direction to its axis. Then the molecule begins... | The mistake in your reasoning is to assume that the same force does the same work. That is simply not true - as the force operates over a different distance.
To analyze the problem, you have to think in terms of impulse ($F\cdot \Delta t$) or work done ($F\cdot \Delta x$).
Let's assume that the same impulse is applied.... | {
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"answer_id": 0
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Thermodynamics and Newton's second law Is it correct to say, that the Newton's laws (or a Newtonian system) is reversible if the friction isn't considered (the fact that the time is of second order $\frac{d^2x}{dt^2}$) and an isolated thermodynamic system is irreversible due to the second law ($\frac{dS}{dt}\ge 0$)?
Ca... |
What I try to say, is that it makes equally sense if a ball rolls down
of tray or up (without friction) in a newtonian system. The "proces"
is then reversible. In thermodynamics a proces will only go one way in
a given situation therefore irreversible. – Hamid Mohammad 18 hours
ago
When you think of a ball ro... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/229510",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "4",
"answer_count": 3,
"answer_id": 1
} |
Where does the factor of half appear from in the Klein-Gordon Lagrangian for a real scalar field? The lagangian density of a scalar field or a Klein-Gordon field has the form of
$$\begin{align}
\mathcal{L} = \frac{1}{2} \partial_\mu \phi \partial^\mu \phi - \frac{1}{2} m^2 \phi^2.
\end{align}$$
Why is there a factor of... | According to these Cambridge lecture notes it's "conventional". I'm guessing that choice of constant gives you the right T-V energy when you integrate the Lagrangian density over a certain volume.
| {
"language": "en",
"url": "https://physics.stackexchange.com/questions/229648",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "1",
"answer_count": 2,
"answer_id": 1
} |
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