Q stringlengths 18 13.7k | A stringlengths 1 16.1k | meta dict |
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I've a problem understanding Absolute Gravitational Potential Energy? My current concept about potential energy is that 'If work is done on a body when it is at a point (taken as zero P.E), it covers some distance. Afterward, when it is allowed to move freely it does the same work. So, I get my work back as if I stored... | In case $x$ the system starts with Gravitational Potential Energy (GPE) of $-5$ and ends with GPE of $0$. So the GPE has been increased by $+5$ because $-5+5=0$. The amount of work done is $+5$.
In case $y$ the system starts with GPE of $-50$ and ends with GPE of $0$. So the GPE has been increased by $+50$ because $-50... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/365781",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "1",
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Centre of mass and Rotational kinetic energy
A massless rod of length $l$ is pivoted at the upper end and two equal point masses of mass $m$ are attached to it, one at the centre of rod and one at its lower end. Then how much horizontal velocity must be provided to the lower end so that the rod just becomes horizontal... | The CM can be used to calculate the change in the gravitational potential energy of the system in this example, but it does not always give the correct result. It works here because the gravitational field is assumed to be uniform. If the gravitational field were not uniform, using the CM would not give the correct res... | {
"language": "en",
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"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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Why don't spectacles form these weird images? It's an established fact that:
*
*Convex lenses produce inverted images of objects beyond the focus, on the other side of the lens.
*Any object placed at a finite distance from a concave lens appears to be somewhere between the focus and the optical centre when viewed f... | Objects through spectacles appear both at a different distance and magnified. It turns out these effects cancel out, and the object subtends the same solid angle in your vision as without the spectacles. Your eye cannot directly perceive distance- your brain estimates it in several ways.
One way is by comparing the an... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/367331",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "3",
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Relation between particle numbers and collisions between gas molecules inside a closed container I'm not a physicist, nor studying physics, so this may be a dumb or a very hard question, I don’t know. I'm not sure if I used correct tags, feel free to correct them if you feel like it is necesary. Forgive me about my Eng... | For an ideal gas, PV = nRT.
Pressure is proportional to the number of collisions each gas molecule sees-- not just the collisions with walls, but the collisions with other gas molecules as well. Hence how you can have different air pressures at different altitudes even though there are no "walls."
| {
"language": "en",
"url": "https://physics.stackexchange.com/questions/367625",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "1",
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Why do phones land face down? Layman here.
I'm not sure if this is the case or not, but my anecdotal evidence is that mobile phones, especially large screen phones, tend to fall face down when you drop them; much to the owner's dismay, this leads to cracked screens.
I'm sure there is a scientific explanation for this, ... | I think one of the commentators summed is up nicely, that you are more likely to forget the times when it lands face up.
It's a psychological phenomenon that Christopher Chabris and Daniel Simons touch on in their book: "The Invisible Gorilla".
In short, it comes down to the fact that a phone falling face-down tends to... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/367792",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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Electrically charged comb reacts to water Correct me if this is wrong, if a negatively charged comb reacts to water(ex. tapwater), the water will bend towards the comb because the water molecule has a slight positively charged "side" and because of that the free electrons on the comb and the water molecule will attract... | Either a positive or a negative charge will attract a stream of water.
This happens because the charged object causes the water to become polarized. Say you have a negative comb - the positive side of the water molecules are attracted to it and the negative sides are repelled. This makes the positive sided a bit clos... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/367951",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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Wave function of many particle I read that the wave function of a system of many particles is formed from the product of the wavefunctions of the individual particles. What is the logic behind it?
| If the particles are not interacting then the Schrodinger equation for the 2-particle system will be
\begin{align}
H&=H_1+H_2\nonumber \\
H\Psi(x_1,x_2)&=
\left(-\frac{\hbar^2}{2m_1}\frac{\partial^2}{\partial x_1^2}+V_1(x_1)-
\frac{\hbar^2}{2m_2}\frac{\partial^2}{\partial x_2^2}+V_2(x_2)\right)\Psi(x_1,x_2)
=E\Psi(x_1,... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/368140",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "1",
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Poisson's equation in regions Suppose I have two regions in space. Region 1 and region 2.
In Region 1 I have a bunch of charges, and in region 2 I have no charges.
Is it true that Laplace's equation is satisfied in region 2?
| Yes, indeed. The electrostatic potential $V$ satisfies
$$\nabla^{2}V\left(\vec{r}\right)=-\frac{\rho\left(\vec{r}\right)}{\varepsilon_{0}}$$
so in a region $U\subset\mathbb{R}^{3}$ in which $\rho=0$, one also has
$$\nabla^{2}V\left(\vec{r}\right)=0$$
Note, however, that it doesn't mean you can always do something with ... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/368283",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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Why do you have to include the Jacobian for every coordinate system, but the Cartesian? In physics and engineering it is common to convert between different coordinate systems - spherical, polar, Cartesian, e.t.c. - depending on the problem. Physically, they are all clearly equivalent and it shouldn't matter which one ... | The original question: "Why do you have to include the Jacobian for every coordinate system, but the Cartesian?"
Perhaps you should elaborate on why │J│=1 for Cartesian coordinates, and the rest of your answer will hold perfectly.
Why does some one not write $1 x = 2$ and instead of $x = 2$? This is the same question.
... | {
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"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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Direction of velocity vector in 3D space According to a well-known textbook (Halliday & Resnick), the direction of a velocity vector, $\vec v$, at any instant is the direction of the tangent to a particle's path at that instant, as is illustrated below in 2D.
According to the same textbook, the same holds for 3D. Howe... | Since asked in Physics.SE I'll project the Physics point of view.
This can be answered intuitively. Imagine yourself flying aimlessly in air. At certain instant you are heading to somewhere. Where will your velocity vector point to?
Find a plane containing smallest part of path curve at that instant. The velocity vecto... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/368634",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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Why is the correlation function a power law at the critical point? I’m taking my first exam in statistical field theory and critical phenomena. I’ve reached a point in which we use the fact that the pair correlation function decays as a power law at the critical point:
$$\left<\psi(x)\psi(0)\right> \sim\frac{1}{x^{D-2+... | I cannot derive the behavior from a microscopic theory, but I can motivate it somewhat.
The general relation (away from the critical point) includes a factor of $\exp(-\frac{r}{\xi})$, where $r$ is the distance and $\xi$ is the correlation length, which can depend on, for example, temperature. At the critical point thi... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/368947",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "11",
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Why we see things on distances we shouldn't see? One person took experiment from Montenegro and with distance 201 km he saw clearly montains that are 1521 meters high. He was on 189 meters above the sea level. Official calculator says you cannot see less than 1811 meters from that distance. My question is: Why he saw t... | Per @John Forkosh, the refraction phenomena is called "looming":
https://en.wikipedia.org/wiki/Looming_and_similar_refraction_phenomena
| {
"language": "en",
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"timestamp": "2023-03-29T00:00:00",
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Why is work done equal to $-pdV$ only applicable for a reversible process? In thermodynamics, when we're interested at gases, I know that the work done can be written to be $-pdV$ for a reversible process ($p$ is the pressure of the system, and $V$ is the volume of the system).
This is because $$dW=Fdx=-pAdx=-pd(Ax)=-p... |
why is it not true also that the work done is for non-reversible processes as well?
The general expression for infinitesimal work done by contact pressure forces on a system inside a closed boundary surface is actually
$$
-p_{ext}dV
$$
where $p_{ext}$ is the external pressure. This follows from mechanics, where net w... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/369188",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "9",
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Turning a bike, why does it lean? I realize this seems like a pretty simple issue of drawing a free body diagram, but I just can't seem to figure it out.
If a bike leans, then it must have had a torque that made it lean. I considered the centripetal force, in this case friction, as a possible source for this torque, b... | Two things that need to be considered. Often it is not the cyclists weight that causes the lean in. Subconsciously, as people learn to ride a bike, they do something called counter-steering.
So for example coming in to turn right, a cyclist will quickly turn the handlebars left to lean the bike to the right due to cent... | {
"language": "en",
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How is it possible that particles maintain continual motion? The kinetic theory of matter (particle theory) states that: "all matter consists of many, very small particles which are constantly moving or in a continual state of motion".
Given the 1st law of thermodynamics, how is this possible? That is, how are particl... | All particles are always moving because they have thermal energy which makes them vibrate and randomly move around. We could say that when particles get warmer then they vibrate with a higher frequency and move a lot faster. When they get cooler, then the particles move and vibrate slower. There is the theory that if a... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/369630",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "1",
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Mass and Newton's Second Law While trying to understand the second law of Newton from "An Introduction to Mechanics" by Kleppner and Kolenkow, I came across the following lines that I don't understand:
"It is natural to assume that for three-dimensional motion, force, like acceleration, behaves like a vector. Althoug... | The accelerating system may be more complex that a single body. Consider an example of a ball in a pipe. If you apply a force to a ball along the pipe, then you would move only the ball inside the pipe. So your effective mass for the equation is the mass of the ball. However, if you apply a force to the ball at 90 degr... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/369817",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "23",
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What is the "surface term"? In Peskin's quantum field theory book, There is a sentence in page 17:
...
More generally, we can allow the action to change by a surface term, since the presence of such a term would not affect our derivation of the Euler-Lagrange equations of motion ...
...
\begin{equation}
\mathcal{L}(x)... | *
*We use the divergence theorem to connect boundary terms to divergences, as already mentioned in kryomaxim's answer.
*It should be stressed that the relevant divergence term $d_{\mu}{\cal J}^{\mu}$ is a total spacetime derivative, not a partial/explicit spacetime derivative $\partial_{\mu}{\cal J}^{\mu}$, even if m... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/370185",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "4",
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$SU(2)$ to $U(1)$ symmetry breaking Why does electroweak theory have $SU(2) \times U(1)$ to $U(1)$ symmetry breaking. Is it not possible to have simply $SU(2)$ to $U(1)$ symmetry breaking?
| There is the Pati-Salam model that has an electroweak field $SU(2)_L\times SU(2)_R$. With the strong nuclear interactions it is $SU(4)\times SU(2)_L\times SU(2)_R$. There are some problems with the idea of an $SU(4)$ strong nuclear interaction theory. The recent results by the LLNL lattice group might breath some life ... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/370573",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "4",
"answer_count": 3,
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$dU=dQ$ and $dU=TdS$, but $dQ$ not always equal to $TdS$? Why? $$ dU = dQ+dW $$ $$ dU=TdS-pdV $$ The equations above are always true for a thermodynamic state of a certain system. Now let's say that we have a situation where $dW=0$, this tells us that $$ dU=dQ $$ $$ dU=TdS $$But still I can't write $ dQ=TdS $, since th... | Even if dW = 0 (e.g., constant volume), you can't write dQ=TdS for an irreversible process because, for irreversible heating or cooling of a body, T is not constant spatially within the body (i.e., T varies with spatial position). For transient irreversible heating, the temperatures near the boundary are hotter than i... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/370926",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "5",
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Shouldn't pressure be dependent on volume? Pressure is defined as $\frac{F}{A}$ And while this makes sense when you are talking about pressure at the surface of a fluid, deep within a fluid it doesn't make sense, at least not to me.
It especially doesn't make sense to me if you are in a body of water. You will have for... | If you are in a body of fluid of density $ \rho$ at a depth $h$ below the surface,
The net pressure acting would be
$P= \rho gh$
Remember that pressure is defined to be force acting per unit area of surface i.e., Pressure is always considered to be acting normal to the surface( This is why even though it has a direct... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/371051",
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What law or formula discusses the relationship between pressure and dew point? A lot of times, dew point is focused primarily upon temperature and relative humidity. However, that same point of saturation is affected by the pressure, but I can't find a formula, or law even, that discusses this.
It's possible that my p... | Even though I am not an expert on this, I found some information that can help. Check out this website
https://www.vaisala.com/sites/default/files/documents/Dew-point-compressed-air-Application-note-B210991EN-B-LOW-v1.pdf
and this website
https://en.wikipedia.org/wiki/File:Dewpoint.jpg
| {
"language": "en",
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"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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Is an electric field a transverse wave not in a vacuum? According to "Introduction to Plasma Physics and Controlled Fusion 3rd Edition", in discussing electromagnetic waves in a plasma, $\vec{E}$ is said to be a transverse wave. Is $\vec{E}$ a transverse wave even in a plasma? I only know the proof that $\vec{E}$ is a ... |
$\vec{E}$ is not a transverse wave, is it?
There is nothing wrong with transverse ($\mathbf{k} \cdot \mathbf{E} = 0$, e.g., O-mode) or longitudinal ($\mathbf{k} \times \mathbf{E} = 0$, e.g., ion acoustic waves) waves in a plasma.
Is $\vec{E}$ a transverse wave even in a plasma?
It can be, but again it is not requir... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/371693",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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Physics interpretation of the expectation value of an electrons spin components Suppose I have an electron that is in the spin state
$$\chi =A\begin{bmatrix}3i \\4\end{bmatrix} $$
If I calculate the expectation values of its spin components $S_x$ $S_y$ $S_z$, I get
$$\langle S_x \rangle= 0$$
$$\langle S_y \rangle = -\h... | Average values do not tell you about probabilities (which must be non-negative numbers). In particular, if your particle is describe by a state $\vert\xi\rangle=\frac{1}{\sqrt{2}}\left(\begin{array}{c}1\\1 \end{array}\right)$ the average $\langle S_z\rangle=0$ but the probability of having the system in the spin-up st... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/371884",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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How can entropy increase in a reversible process? According to Wikipedia, a reversible process is "a process whose direction can be "reversed" by inducing infinitesimal changes to some property of the system via its surroundings, with no increase in entropy."
However, for isothermal processes, any reversible heat adde... | When one says that entropy does not increase for a reversible process, the entropy they are talking about is the total entropy of an isolated system. If we consider the universe as our isolated system total entropy is equal to the entropy of system + the entropy of the surroundings.
So, for a reversible process where h... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/372152",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "1",
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Do higher frequency/energy levels in the EM spectrum mean higher temperatures? I am trying to find concrete evidence that for example, light in the optical spectrum would be hotter than infrared light because it has a higher frequency, and that is directly proportional to energy. Is energy directly proportional to temp... | Light of a specific wavelength does not have a well-defined "temperature" - however, it does have energy.
The Planck law tells us that the spectrum of a black body of a certain temperature covers a range of wavelengths, and the Wien displacement law tells us what the peak of that distribution is as a function of temper... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/372530",
"timestamp": "2023-03-29T00:00:00",
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Why X-ray emission is able to exit the volume without essential photo-absorption My question is written in the title
I am currently studying of radiation of plasma
And I can't get it why it works like this.
"Why X-ray can penetrate the volume without photo-absorption."
| There is always some absorption. But maybe the point is that the x-ray emission lines of an element are lower in energy than the corresponding x-ray absorption threshold energies.
For example, the Cu K$\alpha$ and K$\beta$ x-ray emission lines are below the Cu K absorption edge. At energies just above the Cu $1s$ bindi... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/372806",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "2",
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Loss in energy during gravitational redshift We know from General Relativity that light needs to expend some energy to overcome the gravitational pull of massive objects. This is done by decreasing it's frequency and so it's colour shifts towards red. But what I don't understand is that where does this energy go? Accor... | We know from General Relativity that light needs to expend some energy to move into the upwards direction. This is done by decreasing its frequency and so its colour shifts towards red. According to law of conservation of energy, the total energy in a closed system must be constant. This is true in the case of gravitat... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/372920",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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If an astronaut orbits earth, can both Time Dilation and Gravitational Time Dilation affect it? I am very new at all of this stuff and this one thing bugs me very much...
If an astronaut is orbiting earth, it should be experiencing Time a bit faster than those on earth, correct?
Well then because of the speed he is tra... | Yes, as astronaut will be at relatively high speed then it will experience time dilation and also earth gravitational pull is not strong compare to others there will be negligible affect of gravitational time dilation.
| {
"language": "en",
"url": "https://physics.stackexchange.com/questions/373054",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "1",
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What exactly is The Big Crunch? What exactly is The Big Crunch? I want to know exactly what happens. Does the universe come back in on itself entirely? I did research and it says it could result in a pre-Big Bang particle. The universe is expanding quicker so the chances are smaller of it happening but what chance coul... | For an body to escape another body's gravitational influence, the 1st body's velocity has to exceed the 2nd body's escape velocity, e.g. to get to a speed where the sum of an object's kinetic energy and its gravitational potential energy is equal to zero. The formula for escape velocity is given as V=the square root of... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/373189",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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Why does a room not warm up faster when I put the heater's thermostat on a higher value? I would say it should warm up faster because the difference in temperature between the room and heater is higher.
Edit: I am talking about a convection heater.
| In addition to answers, I simulated an example setup to show the differences. In your case, only the referance value of the controller is changing.
I have trouble with imgur, so I also posted images online.
Model:
https://s18.postimg.org/71vo9wq0p/image.png
Plot: https://s18.postimg.org/rm0i8el7d/image.png
Comparison: ... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/373298",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "23",
"answer_count": 4,
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Can stellar nucleosynthesis processes other than deuterium-lithium, i.e., oxygen-burning, take place in a reactor? It is known that gravitational confinement and supernovae facilitate the synthesis of heavy nuclides; and, that magnetic confinement is thought to facilitate the deuterium-lithium fusion in human-construct... | A big problem with fusing heavy elements with magnetic confinement is that the reaction rate will peak at higher and higher temperatures. For example, this article shows the cross section for carbon peaking at a few MeV:
https://www.researchgate.net/figure/Carbon-fusion-cross-section-as-a-function-of-energy-from-variou... | {
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Why won't the water pour out? A couple days ago I was at a restaurant drinking my cup of water through a straw. I childishly put my finger on top of the straw in the cup of water, and I pulled out the straw. I noticed that the water was not pouring out from underneath the straw. I found this very confusing since I only... | There is air in the straw between your finger and the fluid level in the straw. If only a few drops of liquid come out of the straw before it stops flowing, then, by the ideal gas law, the air in the head space will have expanded, and its pressure will have dropped to a little lower value than atmospheric. Basically, ... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/373755",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "5",
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Adding gauge fixing directly by hand is different from by Lagrange multiplier? Why is adding gauge fixing directly different from doing so by Lagrange multiplier? For simplicity, we don't use field model.
Direct method
Consider a system
$$L(x,\dot x,y,\dot y)=\frac{\dot x^2}{2}+\dot x y+\frac{(x-y)^2}{2} \tag{1} \, .$... | Let me summarize some key points in my opinion:
*
*$y$ is not a free variable that can be arbitrarily fixed (like a gauge field) but instead is an auxiliary variable.
*The Lagrangian you start with is actually a total time derivative.
*You change the Lagrangian in the Lagrange multipliers case.
Since there are n... | {
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"timestamp": "2023-03-29T00:00:00",
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Viscosity and energy balance When solving Navier Stokes equations for viscous fluid over rigid surface, the viscous term in the momentum equation accounts for the momentum transfer between the fluid and surface in the near wall region, i.e. part of the fluid momentum is extracted by the act of viscosity. This is manife... | The viscous dissipation of mechanical energy to internal energy is occurring not only at the walls of the duct, but throughout the duct. The local rate at which this is occurring is proportional to the viscosity times the second invariant of the rate of deformation tensor (typically, the square of the shear rate). Th... | {
"language": "en",
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Probability of finding a particle in a region in a state given for a wave function plus a constant This is the problem:
A particle is restrained to move in 1D between two rigid walls localized in x=0 and x=a. For t=0, it’s described by:
$$\psi(x,0) = \left[\cos^{2}\left(\frac{\pi}{a}x\right)-\cos\left(\frac{\pi}{a}x\r... | In a $1D$ box your wave function must vanish at $x=0,a$. In particular
$$\psi\left(x=0,t=0\right)=B=0$$
| {
"language": "en",
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Does temperature affect the index of refraction? I would like to know the physical reasoning behind the fact that temperature indeed does change the index of refraction of a certain medium.
(Is there an easy experiment for me to try this at home?)
| Light is an electromagnetic radiation having both electrical and magnetic fields . It’s motion through a matter has its interactions with it which depends on the matter through which it has to pass. The molecules themselves are moving with Brownian motion as in liquid or vibrating about its position , a property relate... | {
"language": "en",
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Ball swung in a horizontal circle, can the string ever by exactly horizontal to the ground? You swing a ball on the end of a lightweight string in a horizontal circle at constant speed. Can the string ever by truly horizontal? If not, would it slope above the horizontal or below the horizontal? Why?
|
Let's assume the ball is rotating in a circle (in the horizontal plane) with radius $R$ at angular velocity $\omega$.
In order for the ball to stay on its circular path, a centripetal force $F_c$ has to act on it, given by:
$$F_c=mR\omega^2$$
This force is the resultant of the tension in the string $T$ and the weight... | {
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Questions about Berry Phase I'm learning about the Berry Phase from the original paper, and from the TIFR Infosys Lectures The Quantum Hall Effect by David Tong (2016).
I have some questions regarding the original derivation of the phase, and an example.
*
*In the derivation, Berry derives the phase as
$$\gamma_n(C... | For the result $\int F_{ij}dS^{ij}=4\pi g$, just use Gauss's law same as electric field.
For electric field, we have $E=\frac{1} {4\pi \epsilon_0} \frac{q}{r^2}$ and $\oint EdS=\frac{q}{\epsilon_0}=\frac{q}{4\pi \epsilon_0}*4\pi$, where $\frac{q}{4\pi \epsilon_0}$ is the term in E field except $r^2$.
So similarly, we h... | {
"language": "en",
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How does Fermat's principle of least time follow from Huygen's principle? When I was first introduced to Snell's Law, I was shown a derivation using Fermat's principle of least time. Using this same principle you can show that the angle of incidence must be equal to the angle of reflection. I was later again shown this... | The only way of doing so that I can think of is demonstrate that Huygen's Principle and Fermat's Principle are both equivalent to the eikonal equation. This involves the calculus of variations. I haven't studied optics in a pretty long time, so maybe there's a simpler derivation that I am unaware of or have forgotten. ... | {
"language": "en",
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Derivation of Total Momentum Operator for Klein-Gordon Field Quantization I am studying the second chapter of Peskin and Schroeder's QFT text. In equation 2.27 and 2.28, the book defines the field operators:
$$
\phi(x) = \int \frac{d^3p}{(2\pi)^3} \frac{1}{\sqrt{2 w_p}} (a_p + a^\dagger_{-p}) \, e^{ipx} \\
\pi(x) = \in... | From
$$\mathbf{P} = \int \frac{d^3p}{(2\pi)^3} \frac{\mathbf{p}}{2} \bigg( a_p a^\dagger_{p} -a^\dagger_{-p} a_{-p}\bigg)$$
you actually have $$
\mathbf{P} = \int \frac{d^3p}{(2\pi)^3} \left(\frac{\mathbf{p}}{2}a_p a^\dagger_{p} - \frac{\mathbf{p}}{2}a^\dagger_{-p} a_{-p}\right) = \int \frac{d^3p}{(2\pi)^3} \left(\fra... | {
"language": "en",
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What happens when a dielectric is inserted in a capacitor connected to a battery? The voltage across the capacitor has to stay the same since it is connected to a fixed voltage supply, which means that the potential before insertion and after insertion is equal. That would mean that the electric field within the capaci... | As you correctly observed, the electric field stays the same in the capacitor after insertion of the dielectric because the applied voltage is constant. This is accomplished by the increase in positive and negative areal charge on the plates of the capacitor which is provided by the battery. Before the insertion there ... | {
"language": "en",
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Proof of superposition principle for electric potential Superposition principle of electric force is empirical. However superposition principle of electric potential doesn't seem to be following from it. Is there a formal proof of superposition principle for electric potential?
Edit
$V_1+V_2+...+V_n=\int\vec{F_1}.\vec... | The superposition of the electric force is a consequence of the suporposition of electric fields. That is if we have two electric fields $\mathbf E_1$ and $\mathbf E_2$ then we add them to get:
$$ \mathbf E = \mathbf E_1 + \mathbf E_2 $$
This is equivalent to the superposition of the force because the force on a charge... | {
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Length contraction speed of light The Special Theory of Relativity tells us that a moving object eg spaceship measures shorter in its direction of motion as its velocity increases.
At the speed of light it would have zero length, but infinite mass.
*
*would the spaceship disappear from the perspective of an observe... | I asked a physicist this same question, and the question was answered in a straight forward fashion, which given my novice understanding of physics is what I had been seeking:
The most important thing to remember here is that you can’t actually get to the speed of light. More than merely hypothetical, this is impossib... | {
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Nuclear Fusion: Why is spherical magnetic confinement not used instead of tokamaks in nuclear fusion? In nuclear fusion, the goal is to create and sustain (usually with magnetic fields) a high-temperature and high-pressure environment enough to output more energy than put in.
Tokamaks (donut shape) have been the topolo... | Not an expert, but I believe the answer lies in the hairy ball theorem.
You see, for a magnetic field to turn charged particles back from a surface, the field must be parallel to the surface, which means that to have a fully confining geometry you must have a smooth, everywhere non-zero, and continuous vector field map... | {
"language": "en",
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Strange pattern on car windows
A couple of days ago I was in a friend's car, and I noticed this pattern on the windows; I took a picture of the sun through the window to make it clearly visible.
The night before had been quite cold, but I don't think that the temperature went below $0$ °C, even though I am sure that ... | From your question, I can guess that the weather is rainy in your region.
When you drive a car in the rain, the water drops pass your windows at an angle. This, plus wind and other winter stuff causes the path of the drops to twist and jiggle like in this photo
I would also guess that the rain stopped while still driv... | {
"language": "en",
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Which is the physical meaning of the evanescent wave? I was reading that for an incident angle greater than the critical angle, there will be a total internal reflection.
The cosine of the refraction angle is therefore an imaginary number.
If we make a straight forward derivation we get an exponential attenuation fact... | The evanescent wave is a form of light tunneling. It does propagate perpendicular to it. If a sufficiently thin sheet of air is bordered by glass of both sides, then the extinction at incidence beyond the limiting angle is not complete, and some light will come through on the other side.
It should be noted that an evan... | {
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Free electron gas in magnetic field I have a question regarding the calculation of "spin up" number of particles in a free electron gas, when placed in a uniform magnetic field $\textbf B$. In my lecture notes it's said that the spin up number of particles equals: $N_\uparrow=\int g(\epsilon-\textbf B\mu_m)f(\epsilon)\... | In this picture of the Pauli paramagnetism, all energy states with "spin-up" electrons are shifted by an energy $$\Delta \epsilon= B \mu_m$$ Thus the density of states of the "spin-up" electrons as a function of energy $g(\epsilon)$ is shifted to higher energies by $\Delta \epsilon$ while the density of states of the "... | {
"language": "en",
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How does tension in a rope change when you cut it? Suppose we have a mass $m$ dangling from the ceiling on a vertical rope of length $\ell$ with uniform mass density $\lambda$ per unit length. The weight of the mass $mg$ is balanced exactly by the tension in the rope.
Now, suppose the rope is cut at the top of the cei... | It would be very very hard to calculate this function.
Suppose that you're cutting the rope with a scissor and during that time, the rope will look like this:
Points $A$ and $B$ will have different mass densities per unit length as $B$ would be more stretched than $A$. This implies that each vertical section of the... | {
"language": "en",
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Lorentz Symmetry Group as continuous symmetry for limit of discrete spacetime There is a variety of models of quantum field theory, where discrete spacetime is used as technical support, or even suggested as physical reality. As far as I know, all of such models faced serious problems with restoring Lorentz Symmetry in... | There is absolutely no issue with restoring continuous $O(4)$ symmetry using lattice regularization. The idea is well understood at this point. The lattice spacing is simply a cut-off, and one looks for regions in the phase diagram of the model where the correlation length is much larger than the lattice spacing, mak... | {
"language": "en",
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Path integral kernel dimensions and normalizing factor I am currently reading Quantum Mechanics and Path Integrals by Feynman and Hibbs. Working on problem 3.1 made me wonder why the 1D free particle kernel: $$ K_0(b,a) = \sqrt\frac{m}{2\pi i \hbar(t_a - t_b)} \exp \left(\frac{im(x_b - x_a)^2}{2\hbar (t_b - t_a)} \righ... | This is a consequence of $K(a,b)=\langle x_a,t_a|x_b,t_b\rangle$, which you quote, and the requirement $\displaystyle \int\!\text{d}x\,|x,t\rangle\langle x,t|=1$ (which generalizes to $\displaystyle \int\!\text{d}^dx\,|\vec x,t\rangle\langle\vec x,t|=1$ in $d$ spatial dimensions). In principle, you could label the stat... | {
"language": "en",
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How can one calculate work produced by a flow? I know differential work is $p dV$, since all standard Thermodynamics textbooks cover this. But, almost every case that they cover is about a gas (continuum-mechanics) that has low density, so its pressure does not vary with vertical coordinates. Since thermodyanimics deal... | In the derivation of the energy balance equation in continuum mechanics, the rate of doing work at the boundary of the system is calculated by dotting the force per unit area (on the boundary) by the velocity vector (rate of displacement), and integrating over the area of the boundary. The force per unit area on the b... | {
"language": "en",
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Is nuclear power desireable in the long term, given the fact that it's an unnatural heat input to our planet? I've been reflecting on whether we want nuclear at all in the long term (compared to renewables like wind, solar, and hydro). There's a certain amount of heat (energy) entering our planet and leaving it. Greenh... | Why would the nuclear energy of unstable elements not turn into heat without us chain reacting it and using it for electricity first?
The radioactive isotopes also give off heat spontaneously as they decay to more stable elements naturally.
It would be interesting to see an estimate of how much energy is generated by s... | {
"language": "en",
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Interval Preserving in Minkowski Space The squared line element in any spacetime is given as $$ds^{2}=g_{ab}dx^{a}dx^{b}.$$ The use of tensors helps us to infer that the line element in some other frame would be $$ds'^{2}=g'_{ab}dx'^{a}dx'^{b}$$ where simply $dx'^{a}=\frac{\partial x'^{a}}{\partial x^{b}} dx'^{b}$.
My... | In fact THIS IS a postulate, the second postulate of Einsteins's special relativity, velocity of light must be invariant in any inertial frame of reference, so mathematically, for a light wave we have : $cdt^2-dx^2-dy^2-dz^2=0$ and $cdt'^2-dx'^2-dy'^2-dz'^2=0$ in another inertial frame, and so $ds^2=ds'^2$ ; this is th... | {
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Quantum thermodynamics: better than classical? I am wondering about the use of the so-called quantum thermodynamics and its theoretical advantage: can quantum machines outperform the classical analogues (supposing of course the absolute temperature is NOT zero)?
| To answer your question I must first clarify some ideas!
Engines transform some form of energy, such as thermal, chemical, mechanical, or electrical energy into useful work. Their efficiency, namely, the ratio of the output work to the input energy, is restricted to 1 at most by energy conservation. Engines converting ... | {
"language": "en",
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A star with its radius not much larger than its Schwarzschild radius I was asked about the question today:
suppose that you are observing from afar a spherically symmetric star of mass $M$. Its radius $R$ is $\textbf{not}$ much larger than its Schwarzschild radius. Due to the gravitational bending of light, you can see... | If space surrounding the observable universe wasn't filled with matter (which would be a universe that very fast resulted in a big crunch, but let's assume this for the sake of the argument), our visible universe would be a black hole with a radius much greater than the Schwarzschild radius. The light inside the radius... | {
"language": "en",
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Why does it take time to melt ice when the loss of magnetization of a material at its Curie temperature is immediate? Everything is in the title: Why does it take time to melt ice when the loss of magnetization of a material at its Curie temperature is immediate?
Have you an explanation for this difference?
| The melting of ice is a first order phase transition.
First order phase transition involve the release/absorption of a fixed amount of latent heat per unit volume. A finite amount of time is needed for the release/absorption of such heat, and thus for completing the transition.
The loss of magnetization of a ferromagn... | {
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Electric potential just outside a spherical shell We know that as we get closer and closer to a point charge, the electric potential approaches infinity.
Since electric potential at the surface of a spherical shell is finite (Gauss law) , so on moving away from the surface it would fall. In other words, it would be fin... | You may be somewhat confusing electrical field and electrical potential. But in both cases, the flaw in your reasoning is the same: the distance from the infinitesimal charge may be infinitisimal small but so is the charge (infinitesimal small). You cannot avoid a proper integral or using Gauss law.
| {
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Doubled velocity problem - alternative calculation Working through Tipler/Mosca I got stucked at a very simple task.
A stone is thrown up vertically (1 dimensional problem) with an initial velocity v and it is reaching a height of h. What happens to the height if you double the initial velocity
The solution is : solve... | $\Delta y$ denotes maximum height in initial case when the initial velocity is $v$. Now, that you have fixed $\Delta y$ you cannot treat it as a variable for different velocities because $\Delta y$ is $h_{max}$ (which is a variable) for a specific case when initial velocity is $v$ . The new maximum height is not equal ... | {
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Crater experiment for Newton's second law of motion I am looking for interesting, easy to do experiments to Newton's second law of motion. This is for a high school, so nothing is known about momentum and the law is just $\mathbf{F}=m~\mathbf{a}$.
I found that some people do "crater" experiments dropping objects into ... | Put an elastic string across a table and launch rolling marbles at it. Redo the experiment by weaving two strings, and then three strings. Notice that the stopping time gets shorter with more strings, and that more strings means a bigger force. A bit of fine-tuning is necessary to get a large enough difference of stopp... | {
"language": "en",
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"source": "stackexchange",
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Finding friction coefficient of materials against the hand with modified tilt/pull test I want to find the friction coefficient of various fabrics against human skin. I don't want to cut the material to a smaller size.
Would the following tilt test work?
*
*Get a rigid, square board. Likely the board with be 18 x 18... | What I think about this is following. I request others to correct me if I am wrong-
The normal reaction by the hand would be also due to weight of the board. This will increase the frictional force and so you have to keep track of the component of weight of board which is acting on your hand in your first experiment.
... | {
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How can we explain the linear relation between the temperature scales? In the proof of the relation F=(9/5)C+32 (degrees celsius to fahrenheit) we assume that there is a straight-line (linear) relation between the two temperature scales: F=mC+b. Then we need two "points" to find the equation for that line.
How can we e... | Since all of these scales could be printed on the same mercury thermometer, and because each scale is made of equal-length units, a linear relationship between scales is the only one possible.
This linear relationship is still true even if there is no mercury in the thermometer.
| {
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"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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How to determine movement made by ultrasonic load speaker? What we have:
Supposed that we have a loudspeaker-based ultrasonic levitator. including a low voltage sine wave generator, an amplifier and a loudspeaker + a metal plate and some clamp-stands +some small polystyrene balls to levitate.
Main idea:
This levitator... | Thank you for your comments but we need an equation to find the exact amount of movement; I saw someones told about there will be no movement, I should tell as we experienced in laboratory actually it works and we noticed those variables we brought in the last section are influencing the distance between plate and poly... | {
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L-band for search radars? I'm making my way through the Linesman-related section's of Gough's Watching the Skies. Linesman was developed to counter the carcinotron jammer.
The main solution was the Type 85, which had 12 frequencies switching each pulse at random.
However, they also deployed a second radar, the Type 84.... | S-Band is used for weather radar (signal for NWS, clutter for DOD)--that's in long range application. It's used for final approach in air traffic track surveillance. L-band is used for air-route surveillance (ARSR) and defense application (e.g. AN/FPS-117) in the long range (200 nautical miles).
Range resolution is det... | {
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Generalised Coordinates in 3D Rotation If you have N particles on a surface of a rigid body and the rigid body is rotating about some axis, we say there are six generalised coordinates for the system (N particles on the surface) and set up the lagrangian.
The constraints we know are
*
*The distance between any two ... | Your mistake is to assume that the number of constraints is $N(N-1)/2$. This number is only true for $N\leq 4$.
Let us label the particles by $1,2,\ldots,N$ and say that $\bar{ij}$ denotes the constraint between particles $i$ and $j$. For one particle there is no constraint. For two particles there is one constraint (... | {
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IR Laser focusing question This is for a laser cutter.
10.4k IR laser outputs a beam at approximately 1/4" diameter, 400 watts. The beam is then focused using a single ZnSe lens with a 2.5" or 5" focal length. The final cutting kerf ends up being about a 0.009" wide gap. We are interested in a tighter focus.
We have be... | The minimum spot size can be estimated by calculating the beam waist using Gaussian beam optics (wikipedia):
$$
\text{smallest spot size}= 2\omega_0=\frac{2\lambda}{\pi NA}
$$
Where $\omega_0$ is defined as the beam radius at the focus point, $\lambda = 10.4$ µm is the wavelength, and NA is the numerical aperture of yo... | {
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Probability of finding a particle with a particular value of momentum Given a particle's wave function, what is the general method of finding the probability distribution of momentum (i.e., the probability of finding that particle with a particular value of momentum)?
For example, given
$$
\psi(x) = a e ^ { ikx } + b e... | First of all, I assume that you know that the probability (density) distribution is given by the squared amplitude of the wavefunction. In your example, you are given the wavefunction in the position basis, so it gives you the position probability density. If you want the momentum probability density, you have to cha... | {
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Work done in moving a charge, from near a conducting plane to infinity A point charge $q$ is located at a distance $l$ from the infinite conducting plane. What amount of work has to be performed in order to slowly remove this charge very far from the plane? (Irodov 3.55)
I understand there is a method of images for sol... | Method of images is being used only to solve the problem, there is not any real point charge behind the plane. So in order to find the work done in dismantling the system if we follow the usual process by which we dismantle the two point charges placed at a distance, if we move one charge with respect to origin while k... | {
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In concerts, why is the audience never heard as off-tune? In concerts, when the audience sing, it sounds almost okay; not out of tune as if they sing all harmonious. However, if a small group of people sing, we can notice the off-tune singing.
Is it simply related to the average value of the sound waves or does it have... | Its the relative number of people singing the same false note. In a small group of, e.g. 4 people, one is a large fraction of the total number. For the same effect in a crowd, you would need 25% singing false at the same time in the same way to have a similar effect.
| {
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Direct product of spin representations Consider a system of two 1/2-spins. Under some conditions the Hilbert space can be decomposed into the direct sum of spin-0 and spin-1 representations:
$\frac12\otimes\frac12=0\oplus1$.
When I write this formula on the board, I immediately get an objection that $1/4$ is not equal... | Each spin-1/2 particle is associated with a $(2\times\frac{1}{2}+1)$=2-dimensional vector space $\mathbb{V}$ as far as its spin degree of freedom is concerned. A composite system of two spin-1/2 particles is associated with a 4-dimensional vector space which is a direct product $\mathbb{V}_1\otimes \mathbb{V}_2$ of two... | {
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Milky Way: where does it end? The milky way galaxy, as is typical for spirals (and others?), has a relatively flat rotation curve except very near the center:
Eventually, at great enough distances, almost the entire mass of the galaxy will be enclosed and the rotation curve must become nearly Keplerian and fall off (d... | Over at astronomy they have a post looking at this from the astronomical perspective. There is no clear boundary and it comes down to arbitrary definitions or decisions.
The rotation curve has been measured out to almost 100kpc. See this article for a nice and current review. From that paper comes this figure:
You can... | {
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In what sense are quasiholes and quasiparticles "excitations" in Fractional Quantum Hall (FQH) systems? In the theory of Fractional Quantum Hall states, one often sees quasi-holes and quasi-electrons (or quasi-particles) being called "excitations" from the ground state initially given by Laughlin (Jastrow-Laughlin styl... | I will first repeat some semiconductor physics and then move to the fractional quantum hall effect.
In an undoped semiconductor there are many real electrons and real protons that interact. For $T=0$ they condense into a stable neutral state. Let´s call this state the vacuum. We can create create quasi-electron and qu... | {
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Balancing an orange on a spoon experiment I did a little experiment with balancing an orange on a spoon.
And i realized i don't really understand why i feel a stronger force under both fingers, the further my forefinger is from the orange
(As shown in the first photos with the red arrows)
And why i feel a weaker force... | Three forces are acting in this scenario. Two are downwards: the gravitational force on the orange and the force applied by your thumb. The third is upwards: the force applied by your forefinger. Since the scenario is static, the sum of all three forces is zero (counting for example the upward direction as positive and... | {
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Why in an ideal gas as the volume increases, both the pressure and the temperature drop? I was reading Fundamentals of Physics(Halliday, 10th ed.), chapter 19, when I saw a statement "Figure 19-15a shows our usual insulated cylinder, now containing an ideal gas
and resting on an insulating stand. By removing mass from ... | The Combined Gas Law which is a combination of three other gas laws, states that
"The ratio between the pressure-volume product and the temperature of a system remains constant." (Wikipedia).
It is expressed mathematically as ${PV\over T} = k, \qquad\tag 1$ where $P$, $V$, $T$ and $k$ are the pressure, volume, tempera... | {
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Integral form for partition sum After reading the derivation of the discrete partition sum, it seems like my book finds the generalization to the continuous case trivial. Just change the summation to an integral and multiply with an differential.
However, I don't understand the validity of this, and I'm wondering where... | Let's take one classical particle confined in a volume $V$. The number of states per energy interval $ \Delta E$ will be: $\Delta i=(4 \pi p^2\Delta p V)/h^3 = 4 \pi (2 m^3 E)^{1/2} \Delta E V)/h^3$ and we see that $ \Delta E_i=\Delta E /\Delta i $ tends to zero when $V$ tends to infinity. For one particle partition ... | {
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Increased angle should lead to decrease height I'm having trouble understanding the answer for the following problem:
*
*The diagram below represents a 10-kilogram object at rest at point A. The object accelerates uniformly from point A to point B in 4 seconds, attaining a maximum speed of 10 meters per second at po... | If one ignores friction (say the surface is very smooth) then this is a classic problem on conservation of energy.
The total energy at the start of the motion is entirely kinetic:
$$
E=\frac{1}{2}mv^2 \tag{1}
$$
whereas, when the box reaches it maximal height, the velocity will be $0$ (otherwise it would continue going... | {
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Rho meson decay to three neutral pions In my assignment, I am asked to show whether $\rho^0\to3\pi^0$ is allowed. From the particle data group, I cannot find the decay mode; hence, I am guessing it is not allowed. Based on the knowledge that $\rho^0\to2\pi^0$ is not allowed, I focus on parity. However, the action conta... | I confess I might be overthinking this, having missed something more obvious (C? -- violated by the weak interactions).
The G-parity of the ρ is +, so it prefers to decay to 2π s, since the π has G parity -. (It requires an antisymmetric state because of angular momentum, as you already see.)
But G-parity relies on iso... | {
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Apparent decrease of the force between two electrons Suppose two electrons are moving along parallel paths at constant velocity. Then wouldn't the repulsion of the two electrons be slightly reduced because of the magnetic fields?
If so, how is the apparent decrease in force between the two particles explained in the fr... | There is no decrease of the electrostatic repulsion force (and magnetic field) between the two electrons in the co-moving reference frame where the electrons are at rest. The magnetic field appears only for a reference frame that is not moving with the electrons. This can be understood in the framework of Special Relat... | {
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Is there evidence that a = dv/dt and a = F/m are always equivalent? If the rate of change in velocity in a particle (of mass m) caused due to a force F is dv/dt, then
F = m dv/dt
It may be argued that this is how we define force. But my question is:
Can there be any kind of force, which is so strange that no matter ho... | The formula you mentioned is for a special case where the mass doesn't change. The general case is, $$\vec{F}=\frac{d \vec{p}}{dt}=\vec{v}\frac{dm}{dt} + m\frac{d \vec{v}}{dt}$$ where $\vec{p}$ is the momentum of the object.
For example, a missile loses mass by burning fuel, so your formula will not suffice to descri... | {
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Why is the constraint when maximizing entropy on energy rather than momentum? State in classical mechanics is specified by the position and the momentum. Yet, in statistical mechanics, the usual approach is to maximize the entropy of a system subject to an energy constraint. This gives a probability distribution of t... | In general, every conservation law is taken into account when maximizing entropy.
For example, consider an ideal gas in a box that's flying at nearly the speed of light, where the gas has some low temperature $T$ in the frame of the box. In our original frame, the maximum entropy configuration consistent with energy co... | {
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Software for simulating gas of hard particles (i.e. polyhedra?) I was wondering if there existed a kind of software I could use to simulate a gas of polyhedra, such as tetrahedra. They would interact through entropic interactions only, i.e. excluded volume.
I'm not an expert in simulation so any kind of suggestion is w... | HOOMD-blue is another excellent choice. It can leverage high-performance parallel Monte Carlo simulations to look at the collective behaviour of particles with very complex shapes. Here is the documentation for the Monte Carlo package, and here is the paper that describes its usage and implementation.
Note that HOOMD-b... | {
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Raychaudhuri equation v/s Einstein Field equations Raychaudhuri equation describes the evolution of a geodesic congruence in a spacetime.
While Einstein field equation tells about the curvature of spacetime. This helps in determining the motion of particles on various geodesics.
How are these two description different... |
While Einstein field equation tells about the curvature of spacetime. This helps in determining the motion of particles on various geodesics.
I don't think this is a good characterization of the Einstein field equation. The EFE relates curvature to stress-energy. "Matter tells spacetime how to curve, and spacetime te... | {
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Issue with the work of a reversible process
You consider a cylinder with a piston inside which can move without friction, and with diathermic walls. The piston divides the cylinder into two rooms: A-B, filled with two ideal gases. There is also a valve that connects B and the outside. Let's consider just the room A as... | In general, the 1st law would say that $dU=\delta Q +\delta L$ but you have postulated a purely mechanical energy exchange, that is one with $dU=\delta L$. This is called an adiabatic process.
If you further assume that the gas is internally frictionless, then the partition will oscillate back and forth just as an ide... | {
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Given a mass and position as a function of time, find work
A single force acts on a $7.0 kg$ particle-like object in such a way that the position of the object as a function of time is given by $x = 3.0t − 4.0t^2 + 1.0t^3$, with $x$ in meters and $t$ in seconds. Find the work done on the object by the force from $t = ... | The work done is equal to the change in Kinetic energy.
$v(0)=3m/s$
$v(7)=94m/s$
That gives: $\text{Work} = \text{KE}_7 - \text{KE}_0 =31kJ$
| {
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Is there an analogue of the LSZ reduction formula in quantum mechanics? In quantum field theory the LSZ reduction formula gives us a method of calculating S-matrix elements. In order to understand better scattering in QFT, I will study scattering in non-relativistic quantum mechanics and that question ocurred to me.
| In QFT, LSZ formula is a tool to obtain S-matrix from correlation function. In QFT correlation function is very easy to calculate(free and interacting theories). When outgoing particles became on-shell then we can relate S-matrix element to correlation function.
I QM all the particles are always on-shell. In non-relat... | {
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Cosmic ray shielding for electronics on Earth There are plenty of topics discussing cosmic ray shielding, but they all put emphasis on spacecraft shielding, where things like radiation and mass are a big problem.
So I decided to ask a question from a purely "particle physics" perspective.
Evidently, cosmic rays and the... | The cosmic rays that reach us are muons. They are very penetrating: first the atmosphere (equivalent to 10 meters of water). At sea level about 1 muon per cm$^2$ per minute. Still with a highly relativistic kinetic energy of a few GeV.
Then the concrete of the building. They penetrate tens of meters into the ground. S... | {
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Why do charged particles deflect one way but not the other in a magnetic field? I am well aware that a charged particle moving in a magnetic field will experience a force perpendicular to that magnetic field. But why is it that positive and negative particles experience a force in opposite directions?
What exactly dete... | The problem with the why in your question is that it will give rise to another why in the explanation to explain why that explanation occurs and so on; giving rise to an infinite number of whys. But to kick things off, I'll try and give an initial explanation:
Charges deflect in a magnetic field dependent upon their ch... | {
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Weak isospin current I cannot understand the product of a Dirac gamma matrix and a Pauli matrix in this formula of the weak isospin current:
$$J_α^i(x)=\frac12\bar \psi_L(x)\gamma_\alpha\tau^i\psi_L(x),$$ where $γ_α$ is a gamma matrix and $\tau^i$ a Pauli matrix.
(From Manda & Shaw, Quantum Field Theory 2nd, page 393.)... | Short answer: this is just an (outer) tensor product, not a matrix product. I agree that the notation is a bit confusing though.
To see this, try substituting the left chiral duplet of fermions, i.e. for leptons:
$$ \psi_L = \left( \begin{matrix} e_L \\ \nu_e \end{matrix} \right). $$
The matrix $\tau_i$ is sandwiched b... | {
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Are there any physical quantities whose units are defined using n-th roots, logs, sins, etc. of SI units? All the SI derived units I know are defined as products of SI units raised to an integer power (e.g. the coulomb is measured in $\text{s}\cdot\text{A}$, the pascal in $\text{kg}\cdot\text{m}^{-1}\cdot\text{s}^{-2}$... | It does not normally make sense to put anything but a unitless input into a transcendental function. However, as discussed in this question, it does make sense to take logs of quantities that have units. The result is that you get an additive constant that would depend on the choice of units, and this constant is often... | {
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Does a photon have any measurable size as a "particle"? Does a photon have any measurable size as a "particle"? If we determine its exact location and take away all motion in an isolated static environment, how large is it? Is it sub-Planck in size? If there is no motion in this static environment, is the photon also s... | In the standard model of particle physics which is continuously validated by experiments, the photon is a zero mass,spin one, point ,elementary particle in the table of particles that build up all that we know. Its energy is $h*ν$ where $ν$ is the frequency of the classical electromagnetic wave that it can build up in... | {
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Trouble in understanding AM modulation Amplitude modulation is in fact, superimposing the low frequency transmission signal into a high frequency carrier signal, right?
So, if the transmission signal can be represented as $c(t)=A_c \sin (\omega_ct )$ and the carrier wave can be represented as $c(t)=A_m \sin (\omega_mt)... | You are correct in your assertion that the AM procedure, when applied to a monochromatic signal, will generate a radio emission that, spectrally, has a spike at the carrier and then two sidebands on either side, separated from the carrier frequency $\omega_c$ by the modulation frequency $\omega_m$.
More specifically:
... | {
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References on how dimensionality relates to inverse square laws https://en.wikipedia.org/wiki/Spacetime#Privileged_character_of_3.2B1_spacetime
Does Coulomb's Law, with Gauss's Law, imply the existence of only three spatial dimensions?
Why are so many forces explainable using inverse squares when space is three dimensi... | It's pretty simple. In 3 dimensions when you transmit a wave uniformly in all directions the energy at any distance as it propagates is the same. Since the area of a sphere at distance r is $4\pi r^2$ the energy per unit area at any distance is inversely proportional to $r^2$. If the spatial dimensions were n it'd be i... | {
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The symmetry group and representation of spin-$N$ particle I am confused with the symmetry group and the representation of spin-$N$ particles, and will appreciate any help or suggestions of reference.
There are $2N+1$ internal states for a (massive) spin-$N$ particle. These internal states define a $2N+1$-dimensional H... | It is not the same. A $2N+1$ dimensional representation of SU(2) would have only three generators: $L_+, L_-$ and $L_z$. In particular, $L_+$ and $L_-$ only connect states with $\Delta m= \pm 1$, i.e. can only connect "neighbouring" states (this is loose terminology). In addition, the size of the matrix elements are... | {
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Symmetries of the theory that are not symmetries of the action nor of the measure? Can anybody think of an example of any theory in which there is a transformation law that does not leave the action nor the path integral measure invariant, but such that the product of both is invariant so that the transformation is a s... | The theory of a chiral fermion $\psi$ coupled to a Maxwell field in four dimensions has a famous anomaly in the chiral transformations
$$ \psi \rightarrow \psi'=e^{i \gamma_5 \theta} \psi $$
which arises from the non-invariance of the fermion path integral measure
$$
D\psi' D\bar\psi' = D\psi D\bar\psi \, {\rm\exp}... | {
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Spontaneous Combustion My teacher posed this question in class and it stumped me, primarily based on my lack of fundamentals of thermodynamics:
Peter Griffin was sitting around when all of a sudden he spontaneously combusts (Based on an episode). Is this possible and if not, under what circumstances is this possible?
M... | Good Effort!
We can make an analog case for "spontaneous". Assuming there is a hill, when you put a ball on top of the hill, it will spontaneously roll down the hill. On the contrary, if you put the ball at the foot of the hill, it will not spontaneously roll up the hill. Potential energy plays a role here.
For a chem... | {
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When does Rolling Friction come into play? According to Wikipedia, "Rolling resistance, sometimes called rolling friction or rolling drag, is the force resisting the motion when a body (such as a ball, tire, or wheel) rolls on a surface."
But at the same time, it is the static friction that is responsible for the forwa... | Static friction is what keeps the object rolling (where molecules of the object and the surface essentially act like cogs in a wheel).
Rolling friction refers to the processes of rolling that cause kinetic energy to be turned into heat (which by definition can't be static friction). For example, a rolling basketball b... | {
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How to calculate the maximal Lyapunov exponent(s) of a multidimensional system? I've been reading up about Lyapunov exponents for a university group project on chaos theory and I'm a little confused as to how they are calculated for a system of multiple dimensions.
From what I can tell, the maximal Lyapunov exponent $\... | The extension to several dimensions is natural:
*
*instead of a scalar, the state variable is a vector, and
*the derivative is substituted by the system's Jacobian.
Some earlier papers for numerical methods for calculating the Lyapunov exponents are mentioned in the Wikipedia entry and a more complete entry is f... | {
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Why is a black body visible? A black body absorbs all energy. It doesn't reflect or transmit energy. It also absorbs all light and doesn't reflect any light. Why, then, can we see it? For instance, burnt platinum is 98-99% black body and yet is visible.
| Different visible wave lengths make sense of different colors in our brain.If there are no visible wavelengths, it makes sense of black. In respect of black body, it doesn’t reflect any visible elecro-magnetic wave as you mention.So it’s black and visible
| {
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"answer_id": 4
} |
What is the shortest distance between electron and positron before they are annihilated? I just want to know how does an electron felt the presence of a positron before they are converted into energy? Also how does the electron tell if it is positron or proton if this makes any difference?
| In QED, the basic annihilation process is described by a $\bar{\psi }{{A}^{\mu }}{{\gamma }_{\mu }}\psi $ interaction term, in which the electron $(\psi )$, positron $(\bar{\psi })$ , and photon $(A)$ field operators act at exactly the same point. However, there are small, higher-order corrections to this term, which... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/389213",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "10",
"answer_count": 3,
"answer_id": 0
} |
$Q$ value of beta plus decay (positron emission) I am unable to understand Q value for positron emission. The general reaction is as follows:
$$p \to n + e^+ + \nu$$
$$ ^A_ZX \to ^A_{Z-1}Y+ e^+ + \nu \tag{1a}$$
This reaction $(1a)$ was giving in my text. First question is that where did one electron go? We began with ... |
We began with Z electrons but on the right side it seems only Z−1 electrons are present.
During beta plus decay we consider that electrons do not participate in the decay for easier calculations.(In reality they in fact must be included) Only nuclei participate. So their are no electrons on the left side and just a p... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/389442",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "2",
"answer_count": 2,
"answer_id": 0
} |
What does work mean as a concept and not as a mathematical equation? I know that work = Force times displacement or the dot product of the force and the displacement. But what does work mean in the physical world?
Just like we know that in the physical world, density is the compactness of a substance and we can deduce... | Work means that the barge owner pays the tugboat owner, in return
for being moved. Without the concept of work, many
exchanges involving force and distance would be
much less comprehensible.
Work also explains to the tugbboat owner why the vessel's fuel
consumption goes up during times that the tow cable is under
str... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/389629",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "2",
"answer_count": 2,
"answer_id": 1
} |
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