Q stringlengths 18 13.7k | A stringlengths 1 16.1k | meta dict |
|---|---|---|
Is it more efficient to drive fast uphill? I know that for a rocket escaping the atmosphere, it's not efficient to travel slowly because even staying stationary consumes a lot of fuel. Does the same apply to a vehicle traveling uphill? In other words, is it more efficient for a car/bike/runner to accelerate and go over... | Some preliminaries: there is no time limit, no specific initial conditions and there is no wind. The road is straight and empty. There is no speed limit and safety is of no concern. In short, this has to be cheap.
Make sure you arrive at the speed $v > \sqrt{2gh}$. You need an excess to compensate for rolling resistanc... | {
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Fuel in Nuclear physics Why $^{233}\mathrm{U}$ is an efficient nuclear fuel and $^{239}\mathrm{Pu}$ cannot be used in thermal reactors??
I couldn't find a good answer for this question in the introductory course I am taking. Could someone explain this? I know that both need to be breeded!
| You start by looking as to whether the absorption of a thermal neutron will provide enough energy (binding energy of last neutron) to exceed the activation energy (critical energy) for fission.
Both isotopes satisfy that requirement which is shown in the table below which has been taken from this question where the ter... | {
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How detectable is the error in special relativity experiments because of general relativistic effects at the surface of the Earth? I believe that experiments done on special relativity in a laboratory at the surface of the Earth usually do not consider the effects of general relativity (since the gravitational field at... | Nice question.
One way of stating the equivalence principle (e.p.) is that locally, spacetime is flat, so that special relativity is valid. Therefore any experiment in a small enough laboratory, if the apparatus is in free fall, is predicted by GR to give the same results as in SR. For example, SR predicts that if we r... | {
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Why does plasmon have higher erngy than phonon? In my mind plasmon is movement of electrons and phonon is movement of atoms in an lattice. movement of atoms should have a large energy because atom is larger.
| Fundamentally the plasmon is at higher energy because electrons weigh much less that atoms. In fact phonons are simply plasmons of the atoms.
One can see this from the classical formula for the plasma frequency.
$$\omega = \sqrt{\frac{4\pi n q^2}{m}}$$
Assuming you have an equal concentration of free electrons and atom... | {
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What's the Lagrangian for a freely rotating rod? This is one of those problems that I thought would be easy, then spent forever on it and realized that I know nothing:
A rigid rod of uniform density has mass $M$ and length $L$ and is free to rotate about its center without a fixed axis. Consider its center to be fixed ... | We can just go back to basics, and integrate the contributions to the kinetic energy along the rod. Let the linear density be $\lambda = M/L$. The square of the velocity in spherical coordinates is
$$v^2 = \dot{r}^2 + r^2(\dot{\theta}^2 + \sin^2 \theta\, \dot{\phi}^2);$$
at all points on the rod we have $\dot{r}=0$ and... | {
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Difference in calculation of Ginzburg Criterion in Gaussian and Mean-Field theory? In the past I asked this question asking about a subtlety in the Ginzburg criterion for mean field theory and the Gaussian approximation.
I am now having a hard time determining in general what is different between the calculations of ... | I believe this to be explained in (Dimo, 1993; sections 7.5.2 and 7.11)$1$.
Saddle Point Approximation
In the saddle point approximation we have a thermodynamic potential given by$^2$:
$$\Phi_G=-V \frac{r_0^2}{16 u} -\ln \int \mathcal{D} \delta \phi e^{-\mathcal{H}_G}$$
In the mean field approximation we assume that th... | {
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Can you sail up/down a moving river on a windless day? It's not possible to sail into the wind directly, but only at an angle. It can be shown (it may help for below) by considering the pressure forces on a flat sail and flat keel that sailing upwind is only possible because of the angle between the sail and keel.
Supp... | Yes. If the wind is moving fast enough, and moving sideways across the river. The wind will hit the bottom of the sail if it is at a slight angle, and therefore push it up stream. The speed of wind required depends on a lot of factors having to do with the boat, but it would be possible with high enough winds perpendic... | {
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Should we take the elevator instead of the stairs to save energy? In our university there's a posted sign that encourages students to take the stairs instead of the elevator to save the university electricity during the hot NYC summers.
When you climb the stairs you generate something like 8x your mechanical energy in ... | I wondered the same thing and so did some empirical testing with my elevator.
TLDR;
The elevator uses a huge amount of energy to move just the elevator.
For 5 floor ascent using my single piston hydraulic lift elevator on the day I tested...
Elevator: ~550KWs
Stairs: 92KWs / (22 calories)
If the elevator is going up ... | {
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How can gamma rays affect a human body if they can move through atoms without colliding with them? I found this answer on this SE about why mirrors don't reflect gamma rays, and the answer says that it is because gamma rays are so, so small that they "see mostly empty space between the atoms of the solid.".
If that is ... | It's like this bro, if you look down a perfectly repeating crystal lattice at the top, you will see little holes depending on the packing structure, through which the gamma rays will just pass through the but if you align the nuclei, and have a long enough Crystal, and you turn it a very small degree the holes will clo... | {
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Can we measure Earth's gravity without a pendulum? I'm wondering how can we measure Earth's gravity without pendulum? of course we can do it by using Newton's laws of physics but the air friction might change the actual value also how physists measure distant planets gravity that are found by transit's (by detecting di... | The conventional method for measuring the Earth's acceleration of gravity is that of measuring the trajectory of a free-falling body. The instrument that implements this principle is called the absolute free-fall gravimeter.
In this type of gravimeter, the free-falling body is usually a retroreflector (corner-cube) con... | {
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Do magnets wear out? Can a magnet ever wear out or lose strength?
If you break a magnet it (seemingly) gets weaker, but what about from normal use?
Or even very heavy use, like placing 2 magnets facing each other, so that they detract from each other, does that strain cause it to wear quicker?
(Note, I'm not looking f... | Yes, a magnet, as time passes, will lose part of his strength. There are two main reasons:
*
*Thermal energy: it causes the disorientation of the atomic magnetic momenta.
*If you have a bar magnet free in space it’s easy to see (using Ampère’s law) that there is inside it a magnetic field $H$ opposite to the magne... | {
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Entropy of the ideal gas - How to derive the $S(U,V,N)?$ I'd like to derive the $S(U,V,N)$ function. In the lecture, we were using the $S=k_b \log(\Omega)$, some combinatorics, approximation, $6N$ dimensional spheres, etc. But I'd like to avoid that if it's possible. So I think I should do it from the first and second ... | From the definition of chemical potential:
\begin{equation}\mu = \left(\frac{\partial U}{\partial N}\right) = cRT \end{equation}
where c = 3/2 for a monatomic ideal gas, c = 5/2 for a diatomic ideal gas.
To verify the consistency of the derivation:
From the “fundamental equation” of an ideal gas:
\begin{equation} PV = ... | {
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Notation question in calculus of variations -- QFT these two integrals below are equal, but I am not understanding where the $x'$ variable comes from.
\begin{align}
I_0&=e^{ i\int d^4x \left\{ \frac{1}{2}\left[ \left( \partial\varphi(x) \right)^2-\varphi(x)^2 \right] -\big[\varphi(x)\big]^4 +J(x)\varphi(x)\right\}... | The issue is really what it means to to compute one functional derivative $\delta/\delta f$. Once we get that part, we can raise it to the nth power and get the result.
How to compute one variation?
\begin{align}
\dfrac{\delta}{\delta J(x')} K&=\dfrac{\delta}{\delta J(x')} e^{ i\int d^4x \left\{ \frac{1}{2}\left[ \le... | {
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Is an atomic clock's measurement principle independent of what a light clock provides Special Relativity has the light clock which basically counts how often a photon goes forth and back along a fixed distance.
Our most accurate clock, defining the second (at least as of today), is an atomic clock.
These seem to be two... | Starting with Einstein's 1905 paper on special relativity, the implicit operational definition of time has been that time is what a clock measures, and the implication of this definition is that all clocks measure the same time. Before Einstein, people had been pursuing systems of thought in which such things were expl... | {
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Why does an axially loaded column break along a 45 degrees plane? In this video, at 7:57, the speaker mentions that columns under compression roughly break along a plane that is at 45 degrees to the axis of loading. If this is true, can someone explain why this happens in terms of inter-molecular forces between the col... | Experimental measurements have shown that the mode of failure of many materials is along a plane of maximum shear stress. For the rod loading that you have described, the maximum shear stress occurs on a plane oriented at an angle of 45 degrees to the load direction.
| {
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Statistical Mechanics: Boltzmann partition function I’m a high school student and was recently studying basic statistical mechanics (for use in physical chemistry).
In the derivation of the Boltzmann derivation or the partition function we arrive at a factor $e^{-\beta T}$.
So I searched for the connection of $\beta$ t... | From (2) and $\Omega = \Omega_A \times \Omega_B$ one can see that the fractional change of the number of microstates with energy $\frac{1}{\Omega}\frac{d\Omega}{dE}$ must be equal for two systems in thermal equilibrium. This is the thermodynamic beta $\beta.$ At room temperature it is about 4 % per meV.
Now consider a ... | {
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Can we (in principle) obtain molecular bound systems by modelling fundamental particles and their interactions? Is it possible, at least in principle, to start with the Schrodinger/Dirac/Klein-Gordon equations to model elementary particles and their interactions and to obtain in the end molecular bound systems? In othe... | In principle, yes, this is done in theory of atoms and molecular bonds, also known as quantum chemistry. One can begin with Schroedinger's equation and derive much of the observed properties of atoms and molecules - their energy, spectra, bond lengths and stable arrangements of atoms in space (shape of molecules) which... | {
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Density matrix of a partially polarized beam of electrons The following problem is from Huang's Statistical Mechanics (2nd edition):
8.1 Find the density matrix for a partially polarized incident beam of electrons in a scattering experiment, in which a fraction $f$ of the electrons are polarized along the direction of... | Generally speaking:
*
*If you prepare a system in the pure state $|\psi\rangle$, then the density matrix of the system in that state will be $\hat \rho = |\psi\rangle\langle \psi|$.
*If you have $N$ preparation procedures which produce the system in states with density matrices $\hat\rho_1,\ldots,\hat \rho_N$ with ... | {
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Is the string-net model Hermitian? In Kitaev and Kong's paper, they define the Hermitian inner product on morphism spaces in Eq. (11).
My question is that:
Given that F symbols satisfy the pentagon identity, does that the string-net Hamiltonian (13) is Hermitian follow from the Hermitian inner product on morphism spac... | We should recall that the Hamiltonian is a construction that satisfies hermiticity. The Hamiltonian is not a derived mathematical object from some theorem.
If you follow Kitaev and Kong's exposition, then I think you are right. The hermiticity of the Hamiltonian results from the hermitian inner product of morphisms def... | {
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How does rotation of fan blade produce wind? I observe that the blades are slanted to an angle, but if it produce a lower pressure in one region, is it not possible that the wind from both side will go in?
| Take a ceiling fan. If the blades were not slanted, as the instantaneous momentum of the rotation will be in the plane of the blades, only the thin sides would move air, very inefficiently.
Slanting the blades pushes air in a perpendicular direction to the plane of rotation , the air filling up the vacuum behind come... | {
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How to average the loudness of a audio file from its amplitude? I would like to average the loudness of different sounds so that their means could be used as a dependent variable in a statistical regression, but I have some troubles to understand how loudness works.
Assume that I have large number of different audio ... | I don't think there's a generic physics answer to your question. It depends on what you're trying to accomplish in this analysis. You haven't said whether it's a psychology experiment, or a study of the effect of sound waves on materials, or something else. The reason we often use the dB scale for sounds is that the ea... | {
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Interaction of Magnetic field with light Can there be any interaction of a varying magnetic field with light? (Please explain using electromagnetic waves as both are)
(Say we have an alternating current of 60Hz and He-Ne laser (632.8 nm wavelength)
What all different kinds of interaction may happen? In free space or i... | In matter, there is Faraday rotation.
In vacuum, hypothetical axions would also cause a rotation of the plane of polarization. Experiments have been done with superconducting magnets and ultra-high vacuum. This gave a zero-result, within experimental boundaries. (University of Rochester and Brookhaven)
| {
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Do the ladder operators $a$ and $a^\dagger$ form a complete algebra basis? It is easy to construct any operator (in continuous variables) using the set of operators $$\{|\ell\rangle\langle m |\},$$ where $l$ and $m$ are integers and the operators are represented in the Fock basis, i.e any operator $\hat M$ can be writt... | Theorem: any operator $\mathcal O$ may be expressed as a sum of products of creation and annihilation operators:
$$
\mathcal O=\sum_{n,m\in\mathbb N} (a^\dagger)^n(a)^m c_{nm}\tag{4.2.8}
$$
for some coefficients $c_{nm}\in\mathbb C$.
This theorem can be generalised to field theory, where $a,a^\dagger$ are indexed by co... | {
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Is there a material emitting light when changing phase? I think a substance which emits light when it gets vaporized could have numerous applications, for example in display technology or in leakage detection.
The only problem is: I'm struggling to find a explanation how this should work.
Light emission from atoms stem... | There is heat emitted or absorbed during phase changes. This is infrared rather than visible light. This is because phase changes involve intermolecular interactions with lower energies than the atomic interactions associated with electrons jumping between different levels in atoms. So there are photons involved in ph... | {
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How come I can kick a football further when it's moving towards me? If a ball is moving towards me, I can kick it further than if I were to kick it if it was stationary. But surely if the ball is moving in the opposite direction, it should take more force to kick it the same distance as I am accounting for the initial ... | A short answer to this: I will treat the event of the ball being kicked as an elastic collision between two bodies (the foot (with the body attached) moving with initial velocity $u_1$, and the ball approaching with negative velocity $u_2$.
The problem of elastic collisions of 2 particles is a problem from various phy... | {
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Does an electron accelerated in a linear accelerator lose any energy? In a circular one, it would lose energy due to bremsstrahlung (synchrotron emission), but if it is accelerated from rest to ~GeV energies, does it lose any energy in this acceleration process?
| According to Larmors' formula in Lorentz invariant form the power loss $P$ of a accelerated particle is given by (cgs-units are used, $e$ is the electron charge, $c$ speed of light, $m_0$ the rest mass of the electron):
$$ P = - \frac{2}{3}\frac{e^2 c}{(m_0 c^2)^2}\left[ \frac{dp^\mu}{d\tau} \frac{dp_\mu}{d\tau}\right... | {
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Is potential Difference Really a Measure of Electromotive force? If I separate some amount of positive and negative charge a certain distance I will create some voltage. If I then separate the same amount of positive and negative charge a longer distance I will create an even bigger voltage since more work would've bee... | Let me offer an Old fashioned answer: Voltage is NOT like push! Voltage is more like pressure in a fluid, where now “pressure gradient” causes push. Electric fluid gets pushed from high pressure to low. So voltage gradient or volts per metre gives electric field or force per coulomb. Hope this helps too.
| {
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Does a vibrating string produce changes in tension in the string? A taut string anchored at both ends increases in tension as the string is displaced to a side. When released the string will vibrate at whatever frequency to which the system is tuned.
If this were a simple standing wave it seems that tension would drop... | String vibration, as well as vibration of other mechanical oscillators (springs, pendulums, etc.) involves periodic back and forth transitions between its kinetic and potential energy.
The potential energy of a string is associated with its tension, the kinetic energy - with its velocity.
So, if the tension of a stri... | {
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How can there be single electron, while we observe many simultaneously? Wheeler and Feynman's idea of single electron universe says that all the electrons and positrons are in fact a single particle bouncing forward and backward in time.
I don't get the nature of bouncing phenomenon here. We observe multiple electrons ... | It was just a "what if" discussion, as this link shows;
Feynman was struck by Wheeler's insight that antiparticles could be represented by reversed world lines, and credits this to Wheeler, saying in his Nobel speech:
“ I did not take the idea that all the electrons were the same one from [Wheeler] as seriously as I... | {
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Breaking of a commutator involving Dirac spinors and gamma matrices I'm trying to understand a particular step in the solution to problem 27 in THIS solution sheet. By the middle of the page, they start with the simplification of this expression
$$\left[s^{\mu}\left(x\right),s^{\nu}\left(y\right)\right]\overset{(1)}{=}... | Using the formula
\begin{equation}
[AB,CD] = A\{B,C\}D - AC \{B,D\} + \{A,C\}DB - C \{A,D\}B \quad,
\end{equation}
and setting
\begin{equation}
A = \bar{\psi}(x) \quad,\quad
B = \gamma^\mu \psi(x) \quad,\quad
C = \bar{\psi}(y) \quad,\quad
D = \gamma^\nu \psi(y) \quad,
\end{equation}
one gets (spinor... | {
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Weird Reflection Pattern in Reading Glasses While fidgeting with a pair of reading glasses, I noticed a strange reflection pattern (shown in video and photo).
I would appreciate it if anyone that knows more about this could help me figure out why there were eight dots in the reflection instead of four, and why there we... | You might want to investigate your glasses further with some soap water, like in the photos below. The reflection of a window at the front surface and its reflection at the back surface are green due to the anti reflection coating of the lens, if it is dry. Both reflections could be identified by wetting the front or t... | {
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Why isn't work done when carrying a backpack with constant velocity? Here's an excerpt from my textbook:
In the following situations, state whether work is being done, and why or why not.
A) A person carrying a backpack walking across a floor
B) A person shoveling snow across a driveway at a constant speed
The soluti... | After reading your statements, I think you may also look at this from the point of view of the work-kinetic energy theorem ($W_{net}=\Delta KE$).
In the first scenario, the bag is moving as constant speed, then $\Delta KE = 0$ which implies no work done. From the point of view of forces acting on the bag, $\vec{a}=\vec... | {
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Expansion wave in a hermetically sealed room Suppose there is a human in a hermetically sealed room who takes in a small amount of air without letting it out. The room is initially at atmospheric pressure. The suction is similar to the case in which a piston is withdrawn to generate an expansion wave in the surrounding... | Let's do a simple analysis. Let quantities with subscript "r" and "l" correspond to the room (excluding the lung) and the lung respectively. Since in a sealed room total mass of air $m_0$ must remain constant, we have: $$m_r+m_l=m_0$$
Assuming that temperature is uniform and steady, ideal gas law gives:
$$p_rV_r=m_rRT\... | {
"language": "en",
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"timestamp": "2023-03-29T00:00:00",
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How to mathematically prove that point charge and infinitesimal volume charge are same? In electrostatics, while deriving certain elementary equations, I have seen all the books just assuming that point charge and infinitesimal volume charge are same.
How can we rigorously, mathematically and formally prove that point ... | The Dirac delta function formalizes this equivalence mathematically. It took mathematicians some time to make this object rigorous and led to the development of the theory of distributions.
Addendum
$\def\vr{{\bf r}}$The Dirac delta function is defined such that
(1) $\delta(\vr) = 0$ everywhere except at $\vr={\bf 0}... | {
"language": "en",
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Relative size of the 2 tidal bulges I am interested in making a simplified model that represents only the effect that the moon has on Earths tides.
In this model I am going to assume that the earth is completely spherical (with no continents or surface variation) and covered entirely by a single ocean of water.
In sim... | The tidal force on the point on the earth nearest to the moon, is roughly 1/20 greater than than on the point furthest from the moon, which is what I think was being asked, not 1/90 as stated in the other answer.
The moon is roughly 60 earth radii from the earth, so if we call the gravitational force of the moon on the... | {
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Ionization Energy Confusion In my Barron's SAT Physics book, it states that ionization energy is equal to the absolute value of the ground state energy. This doesn't make sense to me because ionization energy is the minimum amount of energy required to eject an electron from an atom, which I would think would require a... | The "absolute" energy of the ground state is simply the energy of the ground state with respect to the vacuum. So the 0eV state you describe is a free election that is at rest in the vacuum, it is not a bound state, since its radius is essentially infinity (in comparison to the ground state radius).
In other words, th... | {
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Can you isolate a system from conduction and convection, but not radiation? Can you create a 'box' that isolates the inside from conduction and convection, but lets infrared and visible light pass?
| Certainly. This is how solar heat collectors work. You surround the thing you wish to heat with double-paned glass windows. Visible and (some) IR go through the glass by radiation, and the glass blocks conduction and convection losses.
Please note that when the object inside the glass box gets hot enough, it will begi... | {
"language": "en",
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When will velocity and acceleration vectors be perpendicular?
Suppose a particle is moving in the $xy$ plane with
$$x=at, \quad y=at(1-bt),$$
where $a$ and $b$ are positive constants. When will the velocity vector and acceleration vector be perpendicular?
I know that these vectors are perpendicular in circular mo... | No, circular motion is only one of the cases where the acceleration and velocity are perpendicular, you should definitely not be using that.
You have a position vector, $\vec r(t) = [a~t,~~a~t(1-b~t)]$.
Its first and second derivatives are velocity and acceleration vectors, and you want to take the dot product of those... | {
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Why are photo electrons emitted instantly from metal surface just nanoseconds after the light falls upon it? Why are photo electrons emitted instantly from metal surface just nanoseconds after the light falls upon it? How does the quantum theory of radiation explain it? Why can't classical physics explain this?
| The photoelectric effect, which is what you are describing, is one of the basic experimental effects that forced the invention of Quantum mechanics.( The other reasons were black body radiation and the atomic spectra.)
Classically there should not be this behavior, because classically the frequency of the light should... | {
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Why is a fermion field complex? The Lagrangian of a fermion field is
\begin{equation}
\mathcal{L} = \overline{\psi} (i\gamma_{\mu} \partial^{\mu} - m)\psi
\end{equation}
It is said that the fermion field $\psi$ is necessarily complex because of the Dirac structure. I don't quite understand this. Why is the fermion fiel... | Fermions are not necessarily complex. Majorana spinors fulfill a reality condition $\Psi=\Psi^\mathcal{C}$, and in the Majorana basis a Majorana spinor is manifestly real. Clearly, only neutral fermions can be described by Majorana spinors, and neutrinos are candidates for such fermions, even though at present it is no... | {
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What effect does gravity have on a spinning object? If gravity was the only force present would gravity, beside pulling, also stop the rotation / spin of a small object its pulling towards it over time?
What would be the effect on an uneven object and what would be the effect on a perfect sphere?
| The gravity acting on a body, spherical or not, is, by definition, equivalent to a single force applied to the center of gravity (and, therefore, mass) of that body, which means that it won't produce any torque relative to the com and, therefore, won't cause any angular acceleration.
Hence, the gravity should have no ... | {
"language": "en",
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Rectilinear image projection in image stitching For the pinhole camera model, the mapping from 3D to 2D coordinates is described by a perspective projection(rectilinear projection).
However for the image stitching application, perspective projection will bring some problems. Its primary disadvantage is that it can gre... | The rectilinear projection keeps all straight lines straight. As a result, the image stretches increasingly stronger toward the far edge. The answer to your question is that the right side of the right image is much closer to the right edge of the stitched image and for this reason is stretched more.
In contrast, some ... | {
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If object size increases, shouldn't magnification decrease by formula According to the magnification formula, magnification is the image size by object size
According to this if object comes near and its size increases shouldn't magnification decrease?
| Magnification of the focused object can be shown to be:
$m = \frac{f}{s-f}$,
where $f$ is the focal distance and $s$ distance from the object to the lens. So if you keep your subject in focus as it comes closer, magnification will indeed increase, not decrease.
In case you only focus the lens once and then move the obj... | {
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Photomulitplyer Tubes and NaI(TI) crystals in Gamma Camera, Energy and spatial resolution I am trying to understand how the PM tubes and NaI(TI) crystals are used for the energy and spatial resolution.
I understand the principle behind how the crystals and PMT work, but very confused to how they relate to the different... | For nuclear medicine imaging, a good scintillator will produce flashes of light that are proportional to the energy deposited in the scintillator. A gamma ray that deposits more energy will produce a brighter flash of light. This is where the energy resolution of the detector comes from.
Spatial resolution is determine... | {
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What's the cause of sideways pressure (and why pressure is scalar)? Since I think the two questions are related that's why I decided to put them together. Why pressure is a scalar ? It's the ratio of two vectors (force and directed area) right ?
Also, suppose you have a cylinder filled up with water, and at a point $P... | It's because water molecules are slippery. If they were not (e.g. compare with atoms in a solid) then the pressure would not be same in all directions.
When some higher up molecule gets pushed down onto one below, it is very unlikely for them to happen to be exactly at a point where the top one could balance on the one... | {
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If gravity reaches infinite intensity on the all event horizon surface, doesn't this fact exclude the black holes central singularity? Aren't this two singularities an excess or an unnecessary redundancy?
| A comment to the question states it is motivated by my answer to Surface gravity and mass of a black hole. Specifically that answer explains that the gravitational acceleration experienced by a user hovering at a distance $r$ from the black hole is:
$$ a=\frac{GMm}{r^2}\frac{1}{\sqrt{1-\frac{r_s}{r}}} \tag{1} $$
and th... | {
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Why the pressure at siphon 1 atm at the bottom of the pipe?
I assume the area of horizontal cross section of beaker at the top to be way larger than the area of horizontal cross section of pipe
I think at the same depth pressure of a specific liquid which are connected to each other, as in manometer, should be same. B... | As @Chet Miller shows, friction effects explain how the pressure at both free surfaces is the atmospheric pressure. One more point. If the elevation at the top of the siphon is too high, the pressure drops to the saturation pressure of the liquid at its temperature, the liquid flashes to vapor and the siphon ceases to... | {
"language": "en",
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What are the types of infrared scattering? There are various types of scattering of electromagnetic wave. what type of scattering involves infrared electromagnetic wave?
| The question is rather broad, so I will provide a broad answer.
It really depends on the energy level structure of the scatter (atom? molecule? free electron?). Classically, scattering happens because the incoming EM wave induces and drives an oscillating dipole moment in the scattering object, and that oscillating di... | {
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Why $\rm Pt$-$\rm Ir$ Alloy or Tungsten is used for the tip in scanning tunneling microscopy? Just want to know the properties which qualify these materials to be used as the same.
| "Role of Tip Material in Scanning Tunneling Microscopy", C. Julian Chen, https://www.cambridge.org/core/journals/mrs-online-proceedings-library-archive/article/role-of-tip-material-in-scanning-tunneling-microscopy/B32182D2E29CDC6656348326D7AF243F :"In this paper, we show that atomic resolution in scanning tunneling mic... | {
"language": "en",
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$SU(5)$ representation and higher anti-symmetric traces In Zee QFT book v2 p.411 eq.16-17, he shows the SU(5) gauge theory anomaly cancellation by the following:
The 1st line in fundamental of SU(5)
$$
tr(T^3)=3(+2)^3+2(-3)^3=30,
$$
is easy to follow, which sums over 3 U(1) charge 2 fermions and 2 U(1) charge -3 fermi... | Yes, there is a representation-theoretic way to do this in one step. Zee is taking a slightly different approach, showing the cancellation of the $U(1)^3$ anomaly where $U(1)$ is the hypercharge subgroup of the SM gauge group embedded in $SU(5)$. But actually it's easier to do the whole calculation in one go, looking a... | {
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Newbie question: Atom identity. How can you talk about two electrons if electrons are identical? How can you talk about two electrons if they are identical (indistinguible)? Does it make sense to let an electron to have an identity by itself?
If they are on diferent places the place they are is a diference (they are no... | We can do an experiment that distinguishes a box with two electrons in it from a box with just one electron in it. Just measure the electric field near the box and the field near the two electron box will be larger.
We cannot do an experiment that distinguishes between a box with electron A on the left and electron B o... | {
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Stars filling up the night sky Due to the huge number of stars in the universe, will there ever be a time that the night sky is filled up completely with stars such that the night sky is as bright as it is in the daytime?
| No.
The fact that the night sky is not currently filled up with stars is due to the finite speed of light, so that the light of very distant stars hasn't reached Earth yet. However, the universe is expanding, and that expansion is accelerating. This expansion is not bound by the cosmic speed limit of the speed of lig... | {
"language": "en",
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Why arent black holes bright due to the bent light from nearby stars? If black holes change the path of incoming light in a gradual way (from very slight changes to 180 degrees), only depending on how close the light is passing by, the black hole external layer (where a perpendicular light beams are curved but are not ... | Black holes make gravitational 'lenses'. Lenses don't just bend light toward an observer, they also bend light away. There's situations where a background star can be seen in duplicate, but also where a background of black void can be seen
in duplicate. There is no net light-enhancement.
| {
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What does electrical potential at a point mean? From my understanding, potential difference (or voltage) between point A and point B is the difference in electrical potential at the two points. The potential difference is also, the work done per unit charge in moving charges from point A to point B.
But apparently, the... | In the definition of electric potential at a point in space, the reference point is usually assumed to be at infinity. So, the potential at point A is defined as the work that needs to be performed to move a positive unit charge from infinity to point A.
| {
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How is work transferred to the system recognised? For example, a potato initially at room temperature $25 \sideset{^{\circ}}{}{\mathrm{C}}$ is baked in an oven that is maintained at $200\sideset{^{\circ}}{}{\mathrm{C}}.$
I made potato as the system and the outer surface of the skin as the system boundary. While the ove... | While it may be (I haven’t researched it) that the potato “expands” a bit during the cooking process, I would think the amount of work to do this would be extremely small (as JMac pointed out) compared to the heat transfer to the potato that increases its internal energy.
Regarding your question “isn’t the oven worki... | {
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Why do distinct temperature layers form in bodies of water? This may not be the correct place to ask a question about limnology (which I just found out is the science of lakes) but it seems like the place most likely to produce a good answer.
In my diving lessons I learned that there is a layer of water in lakes where ... | Typically, the temperature of a lake is pretty uniform with depth in winter--the surface cools, driving convection, and even if there are periods with heat input at the surface, wind mixing keeps things homogenous. In the summer, there is significant heat input from the sun. Wind still mixes the surface, but the ther... | {
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Trace of 4 Gell-Mann matrices Does any one know what would be $tr(t^a t^b t^c t^d)$, where $t^a$ etc are Gell-Mann matrices?
This came about when analyzing the color factor for the compton effect for QCD. So, must be pretty common, but I could not find a proper reference.
In general is there any reference for tra... | I take the SU(N) generators in the fundamental representation normalized such that
$$
\text{Tr}\left[T^a T^b\right] = \frac{1}{2}\delta^{ab}
$$
The commutator of two generators define the structure constants $f^{abc}$
$$
\left[T^a,T^b\right] = if^{abc}T^c
$$
The anticommutator of two generators is
$$
\left\{T^a,T^b\rig... | {
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A slipping cylinder comes into contact with friction Suppose a cylinder is slipping rigidly on a frictionless horizontal surface. Then, at $t=0$ it reaches a different ground. The coefficient of friction between the cylinder and this new type of ground is $\mu$. What happens?
- assuming usual high-school friction to b... | If you analyze a (non-rotating) block in the same situation, you will see similar behavior.
As the block reaches the surface with friction, the frictional force appears and the block decelerates. When the block's speed becomes zero, the modeled frictional force becomes zero.
| {
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Classical theory fails to explain quantization of motions?
I understand everything written here.
But the last point, I cannot get, at all.
How does it point towards Quantization of the two motions, since the energy change is not sudden, but gradual?
And if anything is wrong with the given image, please tell what it is... | Because the degrees of freedom look like they're 'frozen' at low T. Statistically, we know there's going to be an average energy of $RT/2$ per mole for each degree of freedom. If you have translation, rotation and vibration that makes for a total of 7 degrees of freedom. By classical mechanics, there should be no lower... | {
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Was the universe already expanding before inflation occured? Was the universe already expanding before inflation occured or did inflation cause the universe to start off expanding?
By “cause it to start off expanding” , I mean the cause of the initial expansion.
|
Was the universe already expanding before inflation occured or did inflation cause the universe to start off expanding?
It's not possible for the universe to be in a non-expanding phase and then enter an inflationary phase.
The idea of cosmological expansion is based on two pieces of evidence, one theoretical and on... | {
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Why does $H_2$ have $C_V$=$7/2 R$ at high temperatures, while the total number of degrees of freedom is 6? The two hydrogen atoms have 6 degrees of freedom in total. Of them, $3$ contribute to translation, $2 $contribute to rotation and $1$ contribute to the vibration.
I know that the vibrations motion is frozen at low... | quoting from wikipedia on heat capacity:
Each rotational and translational degree of freedom will contribute R/2 in the total molar heat capacity of the gas. Each vibrational mode will contribute R to the total molar heat capacity, however. This is because for each vibrational mode, there is a potential and kinetic en... | {
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Can electrons jump between levels in same shell with constant $L$? I see many cases where electrons jump from various energy levels of some $L$ value to various levels of other $L$ value. But is there any transition in same $L$ level between its different orientations?
$EDIT $
(How to calculate energy difference?)
| They can, following selection rules. As an example the line of hydrogen $\lambda=21 cm$ corresponds to a transition with $\Delta L=0, \Delta S=1$
| {
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A harmoinic oscillator in the Heisenberg picture Considering the Hamiltonian of a harmonic oscillator
\begin{equation}
H=\frac{p^2}{2m}+\frac{m\omega^2 x^2}{2},
\end{equation}
the time evolution of the Heisenberg picture position and momentum operators is given by
\begin{align}
\dot{x}&=\frac{i}{\hbar}[H,x]=\frac{p}{m... | Your solution $ x = x_0 e^{-i\omega t}$ is not complete. The equation you are solving is second degree. It should depend two initial values $ x = x_0 e^{-i\omega t}+ x_1 e^{+i\omega t}$
| {
"language": "en",
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Have any experiments been performed on the magnetic properties of neodymium at high pressure and temperature? As probably everyone here knows, the magnetic property of neodymium disappears at temperatures above ~590°F (310°C) depending on the mix of alloys. Have there ever been any experiments performed to examine how ... | Don't think that pure Nd is ferromagnetic (maybe it's antiferromagnetic?), so your question about the Curie temperature really applies to just certain ferromagnetic alloys of Nd. Not aware of any high-P studies on those ferromagnetic alloys offhand. I was a co-author of a paper that looked at the magnetic properties of... | {
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Why do spheres roll so far? Say you have a sphere and a cuboid, both of equal mass and material. You push both on a ground of the same material over the same period of time with an equal force. Intuition tells you that the sphere would roll much further than the cuboid. Why is this?
The most common model of friction, $... | For any wheel, it undergoes sliding and rolling friction as it moves. Do note that sliding and rolling friction act in opposite directions, so they cancel out. In a circular wheel both of the frictions are roughly equal due to contact at a point, so the wheel experiences little or no friction. However, a square wheel h... | {
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Experimental tests of QFT in curved spacetime In terms of QFT in curved spacetime (qftics), are there any known tests that confirm/void it to be a correct prescription for a first order approximation quantum theory of gravity? Obviously the extension makes some sense but how is it confirmed?
I know there are a lot of ... | *
*By its very definition, QFT in curved spacetime assumes the background spacetime to be fixed and is a framework to treat quantum fields on the fixed spacetime. Hence the question "are there any known tests that confirm/void it to be a correct prescription for a quantum theory of gravity?" is ill-posed; as the menti... | {
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The dependence of capacitance on the ratio of radii in a cylindrical capacitor Why does the capacitance of two cylindrical capacitors of same length stay the same if the ratio of the outer radii to the inner radii of one capacitor is same as the other.
The capacitance of a cylindrical capacitor is C = (2πel)/(ln(R2/R1)... | The capacitance of a capacitor, in general, is proportional to the plate area and inversely proportional to the distance between the plates. So, if we keep the ratio between the area of the plates and the distance between the plates the same, the capacitance should remain the same.
If the ratio of the inner and outer r... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/423814",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "2",
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Max Born's statistical interpretation of the wave function How did Max Born derive the probability of finding a particle between $x$ and $x+dx$ at instant $t$?:
$$ \left |\psi(x,t)\right|^2dx$$
Was this result mathematically derived? Or is it just a postulate, like the Schrödinger equation itself?
| This statement is equivalent to the statement that $|\psi(x,t)|^2$ is the probability density function for the particle, because the definition of the probability density $p(x)$ is such that $p(x)dx$ is the probability of an event occurring between $x$ and $x+dx$.
The statement that $|\psi(x,t)|^2$ is the probability d... | {
"language": "en",
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"timestamp": "2023-03-29T00:00:00",
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Can a photon be called a disturbance in the electromagnetic field? Total noob here.
I know that electromagnetic waves do not need a medium to travel. I analogize a photon as a single pulse/oscillation in the electromagnetic field and its propagation is the motion of that pulse through the electromagnetic field. Kind of... | Yes that is a correct understanding, you could also use the pebble in a pond analogy as light/photon seems to spread out. There are many posts on this forum some very good, some not so good. Keep reading and you will get a good feel for the photon etc.
| {
"language": "en",
"url": "https://physics.stackexchange.com/questions/424111",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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When are we required to use the Wess-Zumino term? I was recently reading about non-Abelian bosonization, and I had a question concerning the Wess-Zumino term. In particular, I have been reading this short introduction by Ivan Karmazin, which states that
A non-abelian bosonisation introduced by Witten in 1983 allows t... | For starters, the WZ-term is needed to get EOMs that factorize in right- & left-movers, similar to the dual fermionic theory, cf. eq. (15) in Ref. 1.
References:
*
*E. Witten, Non-Abelian Bosonization in Two Dimensions, Commun. Math. Phys. 92 (1984) 455.
| {
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"timestamp": "2023-03-29T00:00:00",
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How to put $c$ back into relativistic equations? Many books set the speed of light $c=1$ for convenience. For example, Weinberg in his textbook "Gravitation and Cosmology" (though $G$ is still left as a constant):
$$\begin{align}
\mathrm{d}\tau^2 &= \mathrm{d}t^2 - R^2(t)~[f(r,\theta,\phi)] \tag{11.9.16} \\
t &= \frac{... | Putting the factors of $c$ and $G$ back can be a tedious business. Many of us do it by (educated) guesswork, followed by checking that the guesses give sensible results.
The rigorous way to do this is using dimensional analysis, that is checking that when adding quantities they must all have the same dimensions, and th... | {
"language": "en",
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Pulley problem, wrong decomposition of forces The mass of the red block is $M$. The rope is inextensible and its mass isn't relevant. The mass of the sphere is $M\sqrt{2}$. The angle between the rope and the horizontal is $45°$.
I'm looking for the acceleration of the body but I'm doing something wrong. I want to und... | Consider the tension present in the rope to be T.
So, for the sphere,
$$M\sqrt2g - T = M\sqrt2a_1$$
Similarly, for the block,
$$\frac{T}{\sqrt2} = Ma_2$$
[Here, $a_1$ and $a_2$ are the acceleration of sphere and block respectively.]
Now, assuming that the rope remains taut, the components of $a_1$ and $a_2$ along the r... | {
"language": "en",
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"timestamp": "2023-03-29T00:00:00",
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Virtual work - Tension in a string I am confused about the way Tension or Thrust is used in equation of virtual work. I mean whether to use $ T\cdot dr$ or $-T\cdot dr$ (work done by tension). For instance in the below case :
A string of length a forms the shorter diagonal of a rhombus of four uniform rods each of le... | Work done by Tension in virtual work equation should be simplified in the following way.
If the length of string is increasing (decreasing) -> 'dr' is positive(negative).
If the Change in length is in the direction (opposite) of force -> Tension is postive (negative).
| {
"language": "en",
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The definition of the hamiltonian in lagrangian mechanics So going through the "Analytical Mechanics by Hand and Finch". In section 1.10 of the book, the Hamiltonian $H$ is defined as: $$H = \sum_k{\dot{q_k}\frac{\partial L}{\partial \dot{q_k}} -L}.\tag{1.65}$$
And then author affirms that this quantity is constant and... | The first equation is the definition of the Hamiltonian. This definition is an application of the Legendre transformation, which converts a function of one variable to a function of another in a particular way to preserve the information contained in the first, but might allow a more practical or useful calculation sc... | {
"language": "en",
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Calculating angular velocity of rolling object with just gravity? From what I have learned, you can calculate what the angular velocity of an object will be based on its potential energy.
Say there is a situation where:
*
*acceleration due to gravity = 10 m/s²
*friction = infinite (object is in pure rolling motion)... | Yes, of course you can apply energy conservation or by simple work done by rotating force is given as
The mechanical work applied during rotation is the torque ($\tau$) times the rotation angle ($\theta$):
$$W = \tau \theta$$
so that the work done is equal to $\frac{1}{2}I\omega^2$.
| {
"language": "en",
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Why is the gravitational potential energy (or electrical) the work done to move a point mass $m$ from infinity to that point in a gravitational field? To be specific, I'm asking why does the mass need to be moved "at a constant speed"?
My textbook says it is so that no kinetic energy is involved. But shouldn't kinetic... | If you consider a generic stationary mass distribution, it generates a gravitational stationary field in all the space around:
$$\mathbf G=\mathbf G(x,y,z)$$
You can demonstrate that always exists a function called potential (not potential energy) for which:
$$grad(V(x,y,z))=\mathbf G(x,y,z)$$ in every point of the spa... | {
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Calculating the Instantaneous speed When we are calculating speed from the graph for a uniform motion the speed which get as an answer is actually the average speed and since in uniform motion the average speed is same as that of instantaneous speed so its correct,right? Now if this is right if we calculate the variabl... | Average velocity between two points in time is given by the slope of the secant line between the two corresponding points on the position vs. time graph.
Instantaneous velocity is found at a point in time. It is given by the slope of the tangent line at that point on the position vs. time graph.
In the case on constant... | {
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Do compact symplectic manifolds play a role in physics? In classical mechanics, the phase space is the cotangent bundle of the configuration space, and it is a symplectic manifold, but not compact.
Do compact symplectic manifolds have physical meaning? Or just of mathematical interest?
| The phase space for a spin-$J$ system is the the two sphere $S^2$ with symplectic structure $\omega= J \sin \theta d\theta \wedge d\phi$, i.e. $J$ times the area 2-form. The unit vector ${\bf n}$ that specfies points on the sphere correponds to the direction of the spin: ${\bf S}= J{\bf n}$.
In general, any Hamilt... | {
"language": "en",
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Why does a bird not get electrocuted when it is sitting on a high tension electric wire? Why does a bird not get electrocuted when it is sitting on a high tension electric wire?
| This is because the bird is not grounded. That is, there is no potential difference for electricity to flow (eg. It is not touching anything conductive that touches the ground - air doesn't count because its conductivity is very poor and hence negligible). But, as soon as the bird touches the pole, the bird fries becau... | {
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What direction does electric current flow in when the voltage drop is negative? We were given the below diagram, and we needed to determine whether the unknown component is supplying energy into the system.
$\hspace{200px}$
I thought the unknown component was supplying energy since charge is flowing to a higher potenti... | in these kind of problems first always try to find which component is acting as source (energy supplier) and which is acting as sink (energy consumer)and then,the rest follows
absorb negative signs of voltage by interchanging polarities of upper and lower terminals respectively and that of the current by changing it's ... | {
"language": "en",
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"source": "stackexchange",
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Explanation for observed short while winding coil around iron core I'm winding a coil, 230 turns #23 enameled magnet wire on a 1/2" diameter solid iron core 6" long ( on a lathe, hand feeding the wire )
When finished, I check continuity ( wire to rod ) with a multi-tester.
Tester shows wire is shorted to the core. OK ... | Wrapped paper around a new core, wrapped by hand, no short.
Has to be poor technique, or bad wire insulation.
Mystery solved.
| {
"language": "en",
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Stress Energy Tensor in language of differential forms The motivation for this is that quantities like the electric current $J$ in maxwell's equations of motion can be expressed as a differential 3-form, so that the continuity equation can be written just as
$$dJ=0$$
Which is really nice because it can all be done with... | With the help of a Killing vector field $\xi$ one can define the current 3-form
$$J_\xi = \star\ \iota_\xi T$$
of which you can then take the exterior derivative to obtain the conservation law
$$\operatorname d J_\xi = 0.$$
Note that the metric is hidden inside both $T$ and $\xi$.
| {
"language": "en",
"url": "https://physics.stackexchange.com/questions/425388",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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Intuition behind group velocity
Why is the group velocity of the wave given as $\frac {\partial w
}{\partial k}$?
I understand what the group velocity means but its always given as a definition and I would like to have some intuition behind it. The $k$ derivative confuses me.
| Let there be 2 waves of unit amplitude with similar angular frequencies $\omega_1$ and $\omega_2$, and angular wavenumbers $k_1$ and $k_2$ respectively. Therefore, adding these 2 waves, we have $$y = \sin(k_1x-\omega_1 t) + \sin(k_2x-\omega_2 t)$$ Using the factor formula, we can express this as: $$y = 2 \sin \left( \f... | {
"language": "en",
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"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "2",
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Euler-Lagrange equations using $\vec{E}$ and $\vec{B}$ instead of $A^\mu$ We all know that the lagrangian for the free electromagnetic field is given by $$ \mathscr{L} = -\frac{1}{4}F^{\mu \nu}F_{\mu \nu} $$ where $ F^{\mu \nu} = \partial^\mu A^\nu -\partial^\nu A^\mu $ is the electromagnetic field tensor. But also we ... | $\vec{E}(x,t)$ and $\vec{B}(x,t)$ are not totally independent variables.
I'm not familar with field theory, but have simpler example with LC circuit, a zero dimensional field theory:
$$
H=T+V=\frac{L}{2}I^2+\frac{1}{2C}Q^2 \quad \sim \quad \frac{1}{2}(|\vec{B}|^2+|\vec{E}|^2)
$$
$$
L=T-V=\frac{L}{2}\dot{Q}^2-\frac{1}{... | {
"language": "en",
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"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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Precision in cosmological constant The observed cosmological constant, what is its precision? How precise do we know is it not a fluke or misinterpretation of cosmological data?
| The best values of the cosmological parameters available, are those published by Planck Collaboration 2018.
In it, the values of the Hubble constant and the dark energy density ratio are:
$$\displaystyle H_0 = 67.66 \pm 0.42 \, (km/s)/Mpc$$
$$\Omega_{\Lambda_0} = 0.6889 \pm 0.056$$
Remembering that:
$$\displaystyle \L... | {
"language": "en",
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Reason for black and white colour We always say that an object is black to a person's eyes if it absorbs all incident light or doesn't reflect anything, and white if it doesn't absorb and reflects all.
My question is which specific property allows black objects to absorb and stops white objects from absorbing.
| A black object is black because it has many internal degrees of freedom that are in the energy range of the visible spectrum. This leads to light in the visible spectrum being absorbed and the energy used to fill those degrees of freedom. In the visible range, those transitions usually correspond to electronic excitati... | {
"language": "en",
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Do quantum fluctuations cause variations in energy density across space? Suppose that the early universe was filled with energy uniformly. Would quantum fluctuations cause variations in energy density across space resulting in regions with higher and lower energy density around the mean?
I read about quantum fluctuatio... |
Suppose that the early universe was filled with energy uniformly. Would quantum fluctuations cause variations in energy density across space resulting in regions with higher and lower energy density around the mean?
The inflation period and the inflaton field were proposed in order to explain the high uniformity of t... | {
"language": "en",
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Why isn't average speed defined as the magnitude of average velocity? Speed is usually defined as the magnitude of (instantaneous) velocity. So one could assume that average speed would be defined as the magnitude of average velocity. But instead it is defined as
$$s_{\textrm{average}} = \frac{\textrm{total distance t... | As you wrote these quantities are different and give you different information so why would you want to call the magnitude of the average velocity the average speed?
If you are travelling in a car it is the average speed for the journey which you might want even if the start and finish point were the same.
What use w... | {
"language": "en",
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How can the solutions to equations of motion be unique if it seems the same state can be arrived at through different histories? Let's assume we have a container, a jar, a can or whatever, which has a hole at its end. If there were water inside, via a differential equation we could calculate the time by which the conta... | An ODE for some physical situation is just some mathematical model of reality. Such models always have limitations and almost always only holds in a probabilistic sense.
Let's take a very simple example and assume the container is filled with atoms of some radioactive material that decays with a half-life $T$. The ODE ... | {
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Magnetic field of a solenoid Why, when explaining the magnetic field of a solenoid, are the individual "quasi-rings" split up into two layers with opposite direction of current (see attached pictures; where the x-es and the dots indicate opposite directions). The original picture given clearly states the direction of t... | that cross and dots indicates the direction of current "cross" means current enters that point and corresponding "dot " means current leaves that point - as shown in figure (in my figure current is in opposite direction to yours but i hope you'll understand)
solenoid is nothing but stack of rings with same central a... | {
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How to simulate possible trajectories of particles after $\beta$ decay? I'm a programmer trying to simulate the movement of the particles involved in $\beta^-$ decay, or at least an approximation of it, for fun, in a 2D universe. I would like to keep the simulation realistic in some ways though, so I would like to obey... | Yes there are an infinite number of solutions.
Indeed, this is how the neutrino was discovered. If a neutron simply decayed to a proton and an electron then the electron KE would always be the same fixed value. However when we measure the electron energy in beta decay we find there is a spread of energies. Wikipedia sh... | {
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Why is the pressure same in a horizontal plane in a static fluid? One of the common explainations involve a cylindrical flask filled with fluid and Newton's second law. But such explainations is specific. What could be possible explanation in a case in which the fluid is filled in some randomly shaped flask?
| Let's take two random points, $x_1$ and $x_2$, lying in the same horizontal plane in a liquid inside a randomly shaped flask.
Now let's draw a very skinny right circular horizontal cylinder, such that points $x_1$ and $x_2$ lie in the centers of its two circular bases , each having area A.
The only horizontal forces ... | {
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How to calculate the dipole potential in spherical coordinates I want to calculate the dipole potential in spherical coordinates. I know that the potential can be calculated with
$$ \phi = - \int \mathbf E \cdot\mathrm d\mathbf r,$$
but I don't know the electric field. I would say
$$ \mathbf E = \frac{1}{4 \pi \epsil... |
see above is a dipole with electric dipole moment $\mathbf{\vec{p}}$
since you know potential due to dipole it means
$$\phi(r,\theta)=\dfrac { \mathbf{\vec{p}}\cdot\mathbf {\hat r}}{4\pi \epsilon_{0}r^2}=\dfrac{p\cos\theta}{4\pi\epsilon_{0}r^2}$$
To find radial component of field
$$E_{r}=-\dfrac{\partial \phi}{\part... | {
"language": "en",
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Why don't we use infrared light to heat food? Why don't we use infrared (IR) or even the far IR just to heat food in a microwave oven instead of, of course, the conventional 2.45 GHz microwaves? Don't people call IR heat waves?
| We do use (near) infrared radiation to heat food – whenever we toast food or grill (UK)/broil (US) by beaming infrared downwards on to food! The point is that the infrared is strongly absorbed by the food we cook in this way, and doesn't penetrate significantly beyond about a millimetre. So the surface of the food is s... | {
"language": "en",
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"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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$\sqrt{-1}$ coefficient in a function In a simple harmonic oscillator with $\ddot{x} = -\omega^2x$, it can be shown through differentiation that one solution can be given by $\dot{x} = i \omega Ae^{i \omega t}$. What does the factor of $i$ do here? What effect does it have on velocity?
| $$
\ddot x + \omega^2 x =0
$$
Is a second order linear differential equation so there will be two solutions as the basis functions adding which you can get any solution. What you have to note is that the equation allows complex solutions. That doesn't mean you have to take the complex solution. In particular if you sta... | {
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How are different metrics for spacetime constructed? is a metric something derived? for example where does the extremal Reissner Nordstrom metric come from?
| A metric in general relativity is a solution to a wave equation called the Einstein field equation (EFE). If you're familiar with Maxwell's equations for electromagnetism, the EFE is very similar. It relates the field to its sources. In a vacuum, its solutions are waves.
The Reissner Nordstrom metric is a general solut... | {
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Does anti-blue coating work less effective on high power lens? I purchased a spectacle from an online website with anti-blue coating. The features of this product is mention here.
Once I receive it, I started using the product without testing the anti-blue coating, recently, I visited the optics store and out of curios... | The blue is short wavelength and the coating might be designed for flat surface.
So the higher curvature will change a bit the angle of incidence and can make the coating less effective.
It is likely a design issue of the coating.
| {
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"url": "https://physics.stackexchange.com/questions/427477",
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How can I calculate the impulse caused by a nuclear bomb on structures? I want to calculate the impulse caused by a nuclear bomb on structures. Is there a function that I can use to calculate the amount of impulse acted upon by a nuclear bomb depending on its size? Also, is there a function relating impulse to overpres... | I presume you are addressing only blast (pressure damage from the shock wave) and not thermal effects. The blast magnitude depends on the position where the weapon is detonated: high altitude, low altitude, or on the ground. I presume you are considering low altitude air detonation.
There are detailed relationships an... | {
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Klein-Gordon-Equation contains no Spin I have a question about an argument used in Schwabl's "Advanced Quantum Mechanics" concerning the properties of the Klein-Gordan-Equation (see page 120):
Since the eigenenergies of free solutions are $E= \pm \sqrt{p^2c^2+m^2c^4}$the energy states aren't bounded from below. But I ... | The components of every field must satisfy the KG equation, regardless of its spin. This makes sense, since it is nothing more than just the Einstein energy momentum relation.
The idea is that the KG equation doesn't require that particles be spinors, so it can't be the full story since we know particles have spin (i.e... | {
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How do I know that gauge fields are bosons? QED and the Dirac equation have field operators $\psi$ interact with a gauge field $A^{\mu}$.
We identify $\psi$ as a fermionic field and $A^{\mu}$ as a gauge boson - the photon.
Do we or can we know that one is a fermion and the other is a boson?
Or do we get that informat... | The possible Lorentz invariant wave equations is a relatively limited set of equations. Most wave equations one can write will not be Lorentz invariant under any transformation law you can think of.
We know all the possible finite dim Lorentz invariant field equations. One of the properties of these equations is that e... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/428080",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "1",
"answer_count": 2,
"answer_id": 1
} |
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