Q stringlengths 18 13.7k | A stringlengths 1 16.1k | meta dict |
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Why should the perturbation be small and in what sense? In time-independent perturbation theory, one writes $$\hat{H}=\hat{H}_0+\lambda \hat{H}^\prime$$ where $\lambda H^\prime$ is a "small" perturbation.
*
*Why should the perturbation be small for perturbation theory to work?
*Both $\hat{H}_0$ and $\hat{H}^\prime... | Answer to (2); saying that the perturbation is "small"...all that means is that $\lambda << 1$.
As a silly example: if $\hat{H}_{0} = \left[ \begin{matrix} 1 & 0 \\ 0 & -1 \end{matrix} \right]$ and $\hat{H}^{\prime} = \left[ \begin{matrix} 0 & 1 \\ 1 & 0 \end{matrix} \right]$, and if you've got a tiny $\lambda = 0.0000... | {
"language": "en",
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Why is lens flare doubled if odd number of blades but equal to number of blades if even? An article in Picture Correct describes how the number of blades in a particular lens correlates to the number of starburst points associated with lens flare. The number of starbursts is double the number of aperture blades if the... | A straight edge causes diffraction in the direction perpendicular to that edge. When two straight edges are parallel to each other their diffraction patterns will overlap (point along the same line) - making it look like there is just one.
That happens when there is an even number of blades.
Note - I believe the diagra... | {
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How do EM Wave Boundary Conditions Comply with Conservation of Energy? One of the boundary conditions of an EM wave crossing a boundary (dielectric materials, wave is TE polarized), where part of the wave is reflected and part is refracted, is
$$E+E'=E''$$
where E is the amplitude of the oscillating electric field of ... | The boundary conditions for electromagnetic field of constant frequency $\omega>0$ at an interface of two media are that the tangential components (the components in the plane of the interface) of electric and magnetic fields $\overrightarrow{E}$ and $\overrightarrow{H}$ are continuous. If these conditions are satisfie... | {
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How to vary the current using batteries? I am making a door bell as a school assignment. It works by having a solenoid produce a magnetic field which attracts a pice of iron attached on a conductor. when the iron is attracted towards the solenoid the current is broken so it falls back, inducing the magnetic field again... | I had a similar problem and the best thing to use would be an Arduino. This is because firstly, Arduino is small - to fit in the project. Secondly, you can use resistors and program them to release certain volts of current. You can set the parameters. This worked for me!
| {
"language": "en",
"url": "https://physics.stackexchange.com/questions/298137",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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Why is the pressure gradient zero at a wall? It's accepted to impose a zero pressure gradient normal to a wall when solving the Navier-Stokes equation. Is there any mathematical reasoning for that? Which pressure (static pressure, total pressure...) is actually meant by that?
| This usually only applies to a wall bounded flow and is normally restricted to incompressible fluids. This result usually manifests in boundary layer theory and can be obtained through order of magnitude analysis of the Navier-Stokes equations. The steady, incompressible, and constant property momentum equation in the ... | {
"language": "en",
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High(very high) frequency sound waves = heat? I had this question in mind and did not quite found the answer on google. If heat is a vibration of particles in matter, and sound is pressure wave moving using particles (causing them to fluctuate), could a very high frequency sound wave raise the temperature of matter whi... | Sound waves can definitely be used for heating of matter. High intensity ultrasound waves are (among other applications) used for internal heating of parts of the human body for medical therapy of a number of conditions. See Therapeutic Ultrasound. The extreme heating of gas bubbles in water by high-intensity ultarsoun... | {
"language": "en",
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use of static vs kinetic friction when orthogonal forces are applied Suppose I have a mass sitting on a surface with friction. Now I start pushing on the mass in one direction (call this direction the x direction). To get this mass accelerating, I have to push the mass with a force greater than $\mu_{s}mg$. Assuming th... | If you are applying two orthogonal forces their resultant (Which is always greater than both the constituent forces) should be greater than static friction or:
Lets say your forces are $ F_x $ and $ F_y$
The magnitude of these forces' resultant is $ \sqrt{(F_x)^2 + (F_y)^2} $
For the block to move the resultant must be... | {
"language": "en",
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Which form of Einstein's stress-energy tensor $T$ is physical, the covariant or the contravariant? Using Einstein's Field Equations for a specific metric I am interested in, I have calculated the first diagonal term of the stress energy tensor $T$, which is the energy density. In my calculations, the covariant density ... | Generally speaking the contravariant form $T^{\alpha\beta}$ is the one most naturally related to what we think of as physical observables. My favourite way of thinking about this is to start with the stress-energy tensor of a point particle, and we can understand the more complicated forms as made up from point particl... | {
"language": "en",
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Why is it not possible to measure the individual neutrino mass from $\beta-$decay? Why do we have to rely only on neutrino oscillations, to measure the mass squared differences of neutrinos? Why is it not possible to measure the neutrino masses directly, say, from $\beta-$decay?
*
*When Pauli hypothesized the existe... | There cannot be enough accuracy in the momentum and energy measurements of the end products of beta decay, only limits can be determined because of measurement errors.
See this link for a recent review.
The paper reviews recent experiments on tritium β-spectroscopy searching for the absolute value of the electron neu... | {
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Do unstable equilibria lead to a violation of Liouville's theorem? Liouville's theorem says that the flow in phase space is like an incompressible fluid. One implication of this is that if two systems start at different points in phase space their phase-space trajectories cannot merge. But for a potential with an unsta... | Simply, Liouville's theorem implicates that the two particles can not take the same state at t=T because their state trajectories behave as currents in incomprisible fluid.
Physically, when the first particle come to B, it will push the second particle and throw it to the left side.
| {
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Is the universe non-linear? First of all, I've read this other question Is the universe linear? If so, why? and I'm aiming at a different kind of answer.
Theories like General Relativity or QFT, which are believed to be quite fundamental, are strongly non-linear. However, in the end, both theories must be just low ener... | First things first, there is no proof that the universe is either. An outstanding question in philosophy is the ontological question of whether the universe is defined by mathematics, or if we created mathematics to understand the universe. Your question only makes sense in the former.
With sufficient feedback, you c... | {
"language": "en",
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If the ground's normal force cancels gravity, how does a person keep rotating with the Earth? When I am on earth, the weight of my body is countered by the reaction of the ground. So, there is no net force acting on me.
But I am spinning with earth. But if there is no centripetal force then why am I spinning? And the e... | Say you stand on a scale on the surface of Earth, and that it shows your weight $\vec{W}=m\vec{g}$. It is precisely balanced by the normal force $\vec{N}$. The local gravitational constant, little $g\approx 9.8 ~\mathrm{m/s^2}$, is not just due to gravity, despite the name. It is actually a vector sum $\vec{g}=\vec{g}_... | {
"language": "en",
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Perturbation Theory for a ring in an Electric Field
A particle of mass $m$ move on a circular ring of radius $a$. The only variable of the system is the azimuthal angle, which we will call $\varphi$. The state of the system is described by a wave function $\psi(\varphi)$ that must be periodic,
$\psi(\varphi + 2\pi)... | Let $\epsilon$ point towards positive x.
Then potential energy according to electrostatic force is proportional to $(a \cos \varphi)$ only.
Schrödinger's equation states $$
-\frac{\hbar^2}{2m} \nabla^2 \psi -(a \cos \varphi) \epsilon q \psi(\varphi) =E_n \psi.
$$ According to your problem, we choose $\varphi$ to be t... | {
"language": "en",
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Van der waals equation derivation? He assumed that the intermolecular forces result in a reduced pressure on the walls of the container which has a real gas in it. Also that the molecules are finite in size which means they do not have the entire volume of the container to themselves; something less than that. So when ... | The more formal derivation of the van der Waals equation of state utilises the partition function. If we have an interaction $U(r_{ij})$ between particles $i$ and $j$, then we can expand in the Mayer function,
$$f_{ij}= e^{-\beta U(r_{ij})} -1$$
the partition function of the system, which for $N$ indistinguishable part... | {
"language": "en",
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Theta Vacuum of Yang-Mills theory and Baryon number violation Background 1. In classical SU(N) Yang-Mills theories, there are a countably infinite number of homotopically inequivalent gauge field configurations of zero energy labelled by a winding number $n\in \mathbb{Z}$. In the corresponding quantum theory, the state... | There is a definite fermion number only before and after the transition, as one can see from your equation for divergence of baryon current. Analogously, the system is in the definite vacuum state only at $t= \pm \infty$.
| {
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Can we measure the exact value of the Fermi Level in semiconductor? Or is it always measured relatively to the Conduction/Valence Band energy level? From the books that I read, the discussion and the formulas related to the Fermi Level are always relative to the energy level of Conduction/Valence Band, or Fermi Level i... | Experimentally, the most straightforward way of measuring this is photoemission spectroscopy. But it is often difficult to measure the position of the Fermi level (chemical potential of the electrons) in an intrinsic semiconductor. The charge carrier distribution is small, and the Fermi level is often pinned by surface... | {
"language": "en",
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Is there a standard, coded table of physical units? I am a programmer in the medical/biosignals area, and I want to represent physical units in a database table. Ideally, I would like to have a code that uniquely identifies a given physical quantity.
As an example, ISO defines strings to represent languages, such as "e... | As far as I know, no standard provides a list of unique identifiers for each quantity. However, a fairly complete list of quantities with recommended names and symbols is provided by IUPAC in the so called Green Book.
Elecrical quantities are also defined by IEC in its online Electropedia, which provides also translati... | {
"language": "en",
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Concept of negative mass in solving problems I have searched a lot on the internet regarding negative mass. And in the meantime, I came across this question.
The question states:
Consider two spherical empty regions (C1 and C2) in an otherwise
uniform and essentially infinite intergalactic gas cloud of density
$\r... | They would actually repel. Yes, the force will act towards the middle but as $F=ma$ and you're looking at negative masses, it will cause repulsion.
How can we see this without negative mass voodoo? Easy, just use test particles.
Put a test particle on the left side of $C_1$, there are 2 holes on the right and 0 from th... | {
"language": "en",
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"source": "stackexchange",
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Confusion about the calculation of 1PI effective action using path-integrals The bare Lagrangian of the $\phi^4$-theory can be written in terms of bare parameters as $$\mathcal{L}=\frac{1}{2}(\partial_\mu\phi_0)^2-\frac{1}{2}m_0^2\phi_0^2+\frac{\lambda_0}{4!}\phi_0^4\tag{1}.$$ The same bare Lagrangian, in terms of reno... | A.Z. uses the full Lagrangian $\mathcal L$, not only $\mathcal L_\mathrm{renorm}$. He omits the counter-terms at first to keep the notation as simple as possible, but he includes them back later on: see equation $(15)$ (it seems odd to me that you decided to stop reading at equation $(11)$). You can repeat the calculat... | {
"language": "en",
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Reversible process in General Physics Usually, for christmas , I have lunch with my family and a couple of other families. Most of the people got a Phd on chemistry, or molecular biology, and are high academics (they're in they 50-70). On the other side, i'm the only one who studies physics there, and 2 years ago, in t... | Any inelastic deformations and ferromagnetic cycles are always irreversible processes.
| {
"language": "en",
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"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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Change in pressure due to dissociation of gas Let's say I have a container with fixed volume, containing Hydrogen Gas at some predefined temperature. Now I pass an electric spark in the whole container such that this reaction takes place
$$H_2 \rightarrow 2H$$
Now actually the number of moles of Hydrogen(atoms) remain... | We use the ideal gas law:
$$PV=nRT$$
Here, $n$ is not the number of moles of hydrogen, but rather the number of moles of gas particles, whatever those may be. Before the spark, there are $n$ moles of hydrogen molecules. After the spark, each molecule dissociates into two hydrogen atoms, making $2n$ moles of hydrogen at... | {
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Conduction of semiconductors at atomic levels Speaking in terms of energy levels:
At 0K (absolute zero) all states below valence energy band of electrons are occupied and all states above the conduction energy band are empty.
At higher temperatures some valence electrons are excited from their parent atom.
My question ... | This is correct! At finite temperature, the valence electrons acquire a specific probability, given by the Fermi-distribution, to enter the conduction band of the semiconductor.
| {
"language": "en",
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After measuring momentum, it seems like the particle's position could be literally anywhere? Once measuring momentum, the wavefunction "collapses" into something that looks like this
If you were to then measure the position, couldn't it be literally anywhere? What am I missing? Is it even possible to measure momentum ... | Real measuring devices all have a granularity. Your experiment will never tell you that a particle has momentum exactly $4.03752\,\mathrm{MeV}/c$; it will tell you (assuming it is very precises indeed) that it has momentum $(4.037 \pm .014)\,\mathrm{MeV}/c$ which is completely compatible with the particle still being f... | {
"language": "en",
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"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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Nature of metallic bonding in solid state What is the reason behind attraction of metal kernels & free electrons in electron sea model?
| It's mechanically not that different from dropping a lot of small magnets into a sea of iron filings (or better, magnetite sand). The positively charged metal ions attract the diffuse fermi sea of delocalized electrons, and vice versa. It's the ability of the electrons to delocalize that enables this, and that gives me... | {
"language": "en",
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Lowering the type-I seesaw scale without fine-tuning The type-I seesaw mechanism yields the effective neutrino mass $$m_\nu\sim -M_DM_N^{-1}M_D^T.$$ Here, $M_D$ is the Dirac neutrino mass coming from Yukawa coupling of the left-chiral neutrino with the standard model (SM) Higgs and $M_R$ is the mass of the right-chiral... | Small neutrino masses from a rather small right-handed neutrino mass scale always imply small Yukawa couplings. Note, however that $M_D \sim 100$ GeV assumes Dirac neutrino masses of the order of the top quark, by far the largest Yukawa coupling in the Standard Model. If you assume that the neutrino Dirac masses are of... | {
"language": "en",
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Thermodynamics Question: Does measuring the temperature of an object change its temperature? Suppose that I want to measure the temperature of an object, such as a pot of hot water. When I stick the thermometer into the pot, I know that the temperature measured by the thermometer is its own temperature when it reaches ... | If you use a temperature measuring device that has mass, the answer is "yes", you slightly changed the temperature of the pot of water. If you use a temperature measuring device that doesn't have mass, such as an infra-red thermometer, the answer would be "no", since you didn't contact the water with anything that has... | {
"language": "en",
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Projectile Motion - $V_f = V_i + at$ - Divide by zero If I have a projectile that is thrown at some horizontal velocity at some height, and horizontal acceleration is zero, can't I use the equation $v = v_0 + at$? The problem is when I use it since $v$ will equal $v_0$ (acceleration is zero so velocity won't change) I ... | I was just thinking about it and I think I realize why that equation didn't work as expected. That equation will always fail to calculate time correctly when acceleration is 0 as it depends on there being a change in velocity between the initial state and the final state. If acceleration is 0 then velocity will always ... | {
"language": "en",
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How does a small object move with constant velocity when drag force is equal to its weight? When drag force ($bV$) equals to object's weight (mg) then upward and downward force becomes equal. As a result the object comes to rest. If this is true, how is a body moving with constant velocity?
| An object in such a state has reached what is called a dynamic equilibrium where a constant velocity, free of acceleration is occurring. This, opposed to what is called static equilibrium where the object has reached a position with zero velocity.
For a falling object that experiences body forces due to gravity ($mg$) ... | {
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What do the results of a quantum fourier transform describe? The classical discrete fourier transform takes a sequence of values and outputs another sequence of values that describe a set of coefficients for complex sinusoids which can be used to reconstruct (or approximate) the original input.
In contrast, what exactl... | The quantum Fourier transform applies a discrete Fourier transform to the amplitudes in a superposition. This is, if your input is
$$
\sum a_n |n\rangle\ ,
$$
then the output is
$$
\sum \hat a_n |n\rangle\ ,
$$
where the vector $(\hat a_n)$ is the discrete Fourier transform of the vector $(a_n)$.
The point is that if... | {
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Is current density (J) in Ampere's law derivable? In Ampere's law:
$$
\nabla\times\mathbf{B}=\mu_0\mathbf{J}
+\mu_0\epsilon_0\frac{\partial\mathbf{E}}{\partial t}
$$
the current density is listed explicitly as a separate term from the change in electric field. My understanding of the history (perhaps completely wrong)... | Nothing in Maxwell's equations depends on the fact that the charges that we encounter in the real world are all tied to individual particles.
So we can imagine that we have an infinite rod of charge in space and it's moving with uniform velocity along its axis, and Maxwell's equations will still apply to this situation... | {
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Confusion with partial derivatives as basis vectors So I have seen that the directional derivative can be written as
$$ \frac{df}{d\lambda} = \frac{dx^i}{d\lambda}\frac{df}{dx^i} $$
And we can identify $ \frac{d}{dx^i} $ as basis vectors and $ \frac{dx^i}{d\lambda} $ as components. What I don't understand is why is $... | I think the physicspages author is just confused. $df/d\lambda$ is a scalar, not a vector. It's the scalar product of the covector $\nabla f$ with the vector $d\mathbf{x}/d\lambda$. They say, "Regarding the partial derivatives as basis vectors, ..." and go on as if $\partial f/\partial x$ and $\partial f/\partial y$ we... | {
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Why does stacking polarizers of the same angle still block more and more light? I have some sheets of polarization film. They came in a big box, all stacked at the same angle. I noticed that the entire stack of them lets almost no light through, even though they're all at the same angle.
I pulled out two, and those two... | A high-quality supplier of polarizers and other optical equipment would be able to offer you data on the transmission characteristics of even their cheapest polarizers:
I interpret this plot to mean that if you bought two of these devices, aligned their axes parallel to each other, and shone unpolarized $\lambda=550\r... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/302795",
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Understanding thermodynamic equilibrium for a relativistic system The conventional books on thermodynamics that I know, do not talk about the thermodynamics of relativistic systems. But in Cosmology, the thermodynamic concepts are often applied to the whole universe.
My question is about the concept of thermodynamic e... | 1) Thermodynamics for relativistic systems is pretty straightforward, and discussed in many text books (Landau, Greiner, $\ldots$). The only difference is that in relativistic systems the total number of particles is not conserved (and the associated chemical potential is zero), only the total charge (electric, baryon,... | {
"language": "en",
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Light reflected in a cylinder I was cooking and noticed a funny pattern appearing when i was looking in on of my pans. When light fell into a pan with high edges, it seemed to reflect into a hart-shaped pattern. Can anyone explain how the light gets warped into this shape, and does anyone know why the light gets reflec... | You want to look up Caustics in optics.
The specifics of your example boil down to the way the geometry works out. In this case the simplest model would be something like a Nephroid, where you have a circular shape which ( in terms of illumination ) is similar to a half circle, and that makes that particular caustic.
| {
"language": "en",
"url": "https://physics.stackexchange.com/questions/303515",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "1",
"answer_count": 1,
"answer_id": 0
} |
Grashof number as a ratio of buoyant and viscous forces The Grashof number is supposed to be a ratio of buoyant forces to viscous forces.
I find this hard to believe, since if
$$F_b=\beta g \rho \Delta T$$
is the buoyancy force, the definition of the Grashof number,
$$\text{Gr}=\frac{\beta g\Delta T L^3}{\nu^2},$$
imp... | I don't agree with @Pirx that it is to be understood as vague metaphors although I admit it sometimes is a little bit difficult to understand exactly how they are ratio of scales as you have clearly found out.
What makes it a bit difficult is that dimensionless numbers are sometimes themselves ratios of other dimension... | {
"language": "en",
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"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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How are water vapors not visible? This site says that water vapor isn't visible.
However, take a look at this picture:
Isn't that water vapor?
| Water vapour is a clear and colourless gas, so it can't be seen by the naked eye.
What you see in the photo in your second link is (partially) condensed water vapour, i.e. fog (or mist). Fog contains tiny, discrete water droplets and light bounces off their surface in random directions, causing the visibility.
Water va... | {
"language": "en",
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"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "32",
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Phase Transitions and Bubble Nucleation The potential for a first order phase transition is shown below
The phase transition occurs from the spontaneous formation of bubbles. Inside the bubbles the field value is at the "true vacuum" and outside the bubble the field value is at the "false vacuum". In many texts, a se... | I think the most accurate answer is that we probably do not know. I wrote the following paper which looked at inflationary cosmology as a quantum critical version of Landau's tri-critical point. If this is right, or some variant similar to this is right, the tri-critical point falls below the valued of the Landau param... | {
"language": "en",
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"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "2",
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Why does torque produce a force on the axis of rotation? If a door is rotated about its fixed axis in (outer) space, a force parallel to the door on the hinges will arise due to centripetal force on the centre of mass and conservation of momentum (Newton's third law).
But any torque on the door will create a force on ... | An object can be in rotational non-equilibrium while simultaneously being in translational equilibrium depending upon the arrangement of the forces. In other words, an object can undergo an accelerating spin without translating. You can add rotational energy to an object without adding translational energy.
What I wrot... | {
"language": "en",
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"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "2",
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How can I handle divergence that appears in many physical problem? I came across with the following type of integration with singularity.
$$\int_{s_2=0}^{s_2=\infty}\int_{s_1=0}^{s_1=s_2}\left(\frac{1}{s_2-s_1}\right)^{3/2} \,ds_1\,ds_2 \, .$$
How can I solve it?
| As suggested I have expanded my comment into an answer.
There's no general prescription for dealing with divergent integrals in physics. Typically when an integral like this shows up it means is that the integral is not the full story, but the missing pieces of the puzzle depend on exactly what it is you're trying to ... | {
"language": "en",
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Can a ship float in a (big) bathtub? I am confused.
Some sources say it is possible at least theoretically ( http://www.wiskit.com/marilyn/battleship.jpeg ) and some say it is not true ( http://blog.knowinghumans.net/2012/09/a-battleship-would-not-float-in-bathtub.html )
Is it necessary or not that there exists an amou... | Some of the comments on the answers here show that the Archimedes Principle is being thought of by many people as a force that somehow arises literally as a direct result of the fluid's being displaced by a boat. In fact, Archimedes Principle is only a mnemonic for the results of the full calculation of what is actuall... | {
"language": "en",
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"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "16",
"answer_count": 8,
"answer_id": 1
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Are the diffusion terms conservative? Generally the diffusion terms are of the form $$D = \dfrac{\partial}{\partial x} \left(\mu \dfrac{\partial u}{\partial x} \right) .$$
Is this this term conservative or nonconservative?
| In terms of fluid dynamics, a conservation law is one in which the net flux in is equal to the net flux out. This is typically represented as the PDE,1
$$
\frac{\partial u}{\partial t}+\nabla\cdot\mathbf F=S\tag{1}
$$
where $u$ is the conserved quantity, $\mathbf F$ the flux and $S$ the source term.2 In your case, $\ma... | {
"language": "en",
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"source": "stackexchange",
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4-Vector Potential Notation How am I supposed to interpret this notation:
$$F^{uv} = \partial^uA^v-\partial^vA^u$$
I know that $\partial^u = (\frac{1}{c}\frac{\partial}{\partial t},-
\vec\nabla)$
So for example for the potential $$A=\left(\begin{matrix}
0 & 0 & 0& E_z\\ 0 & 0 & B_y & 0\\ 0 & -B_x & 0 & 0\\ E_z & 0&0&0\... | The indices come with ordering $(0,1,2,3)$ so that $\partial^0=\frac{1}{c}\frac{\partial}{\partial t}$, $\partial^1=-\frac{\partial}{\partial x}$ etc.
$A^\mu$ is a 4-vector with components $(A^0,A^1,A^2,A^3)$,
not a matrix as your notation suggest. Thus, in your specific example,
$$
F^{23}=\partial^{2}A^3-\partial^3... | {
"language": "en",
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What did the big bang "look like"? I've been reading here for a while now and something I always see is people saying "the big bang happened everywhere" or "the center of the universe is where you are", explaning that the big bang didn't happen from a single point, but everywhere at once.
The problem is that I am unabl... |
I know that this might make sense from a mathematical point of view, but what would it actually look like?
Why not start with the data, which tells us what it actually looks like?
The observations tell us that all galactic clusters are receding from each other. In an explosion in three dimensions, one could track th... | {
"language": "en",
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"timestamp": "2023-03-29T00:00:00",
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Sound wave coherent time Put an ordinary light bulb in front of a double slit and you will not observe interference due to the short coherent time compared with the observation time.
What about sound waves? What is the typical coherent time of sound waves? Is it usually much longer than the observation time?
| Sound waves are macroscopic phenomena, and not affected by the quantum effects in the same way as the double slit experiment with light.
Sound waves do "degrade" in real life because when they travel through non-uniform media (e.g. in air, scattering may be caused by temperature gradients, convection currents, variatio... | {
"language": "en",
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"source": "stackexchange",
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Why don't humans burn up while parachuting, whereas rockets do on reentry? I guess it has something to do with their being both a high horizontal and a vertical velocity components during re-entry. But again, wouldn that mean there is a better reentry maneuver that the one in use?
| A human parachuting from $h=4000\,\mathrm m$ (cf. http://adventure.howstuffworks.com/skydiving1.htm) needs to get rid of their potential energy $mgh$.
If we assume that all this energy is used to evenly heat up the skydiver, who essentially consists of water with its well-known specific heat capacity $c_{H_2O}=4182\fr... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/304992",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "18",
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Where does all the heat go during winter? I do not understand where actually the heat in our surroundings go during the winter season. Is it radiated out into space? I know it cannot coz global warming would not be a issue then. It might get absorbed but where? I tried figuring it myself but couldn't please help.
| The heat gets "smeared out" everywhere. It dissipates all around the Earth. This raises the Earth's temperature by an absolutely miniscule amount, because the amount of heat involved is tiny compared to the incoming energy from the sun. And because the Earth is a little bit warmer, it radiates heat into space a little ... | {
"language": "en",
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"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "3",
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How force exerted by spring is always opposite to the direction of displacement in Hooke's law Suppose a spring lying on a horizontal table, displaced from its equilibrium length by an external agent. The external agent is removed, the spring will head back to its equilibrium length. Here, the direction of spring force... | What you say is correct. But, it's not what Hook's law tells you.
Hook's law says, the force exerted on a mass, permanently or temporarily attached to the spring, is proportional to the difference between the instantaneous length of the spring and the equilibrium length. In the direction which points toward the equilib... | {
"language": "en",
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"source": "stackexchange",
"question_score": "3",
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Does folding a paper towel help dry your hands faster by creating interstitial forces? The question is based on a TEDx video, where the speaker claims that folding a paper towel before using it creates interstitial forces which help dry your hands faster.
The question:
Does this effect actually occur? If it does, then ... | After searching more for an answer to this, I found the following:
It appears that folding does allow the paper towel to absorb more water, due to the fact that the water is stored between the folds of the paper towel (what the speaker refers to as "interstitial suspension", I mistakenly called this "interstitial force... | {
"language": "en",
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"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "4",
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Pauli matrix for triplet state? Question is, what would be the result of applying the operator $\hat A = [3I + \vec\sigma_1 . \vec\sigma_2]$ on the |singlet$\rangle$ and |triplet$\rangle$ states ($\vec\sigma_1$ acts on the 1st particle and $\vec\sigma_2$ acts on the second particle ONLY), ie, $$\hat A|singlet\rangle=?|... | Setting $\hbar=1$ for simplicity, the matrices you need are the $S=1$ matrices. One easily obtains
$$
S_z=\left(\begin{array}{ccc}
1&0&0\\
0&0&0\\
0&0&-1\end{array}\right)\, ,\quad
S_+=\sqrt{2}\left(\begin{array}{ccc}
0&1&0\\
0&0&1\\
0&0&0\end{array}\right)\, ,\quad S_+=S_-^\dagger,
$$
from which one recovers $S_x$ an... | {
"language": "en",
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"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "4",
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Confusing working of lens Why do lens don't splits light into its seven constituent colors, like Prism?
*
*Why is lens left is correct, not right one?
*How does lens came to know that rays are coming from infinity or are at Focus and converge/diverge them at different point accordingly?
| This dispersion curve from Wikipedia Commons shows how the index of refraction varies with wavelength. It is this dispersion property which results in the splitting of light into a variety of colors, as observed in prism demonstrations and rainbows.
We see that if Dense Flint is used for a lens, there will be quite a... | {
"language": "en",
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"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "2",
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Guided waves equations In Griffiths's Introduction to Electrodynamics, monochromatic guided waves are proposed to have the form
$$\mathbf{\tilde{E}}(x,y,z,t)=\mathbf{\tilde{E}}_0(x,y)e^{i(kz-\omega t)}$$
$$\mathbf{\tilde{B}}(x,y,z,t)=\mathbf{\tilde{B}}_0(x,y)e^{i(kz-\omega t)}$$
where
$$\mathbf{\tilde{E}}_0=E_x\mathbf{... | $\omega=kc$ for plane waves which have spatial variation only along $k$. In a waveguide, the field varies in other directions as well and the relation is incorrect.
You can think about a waveguide mode as being composed of a standing waves pattern in the plane of the waveguide combined with the propagation along the no... | {
"language": "en",
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How molecules radiate heat as electromagnetic wave? an object of higher temperature radiate infrared rays as a way to decrease the temperature. how a molecule produce a electromagnetic wave? in atoms electromagnetic radiation is caused by electrons. what is responsible in molecules?
|
in atoms electromagnetic radiation is caused by electrons. what is responsible in molecules?
There exist atomic and molecular orbitals of the electrons composing atoms and molecules.
This means that the charge distribution around an atom or a molecule in space is uniform only for some quantum numbers. Otherwise there... | {
"language": "en",
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Can an accelerating frame of reference be inertial? In physics problems, the earth is usually considered to be an inertial frame. The earth has a gravitational field and the second postulate of the general theory of relativity says:
In the vicinity of any point, a gravitational field is equivalent to
an accelerated ... | An inertial frame is equivalent to a frame's velocity at any given time. An accelerating frame still has intertial frames for the same reason that we can calculate instanteous slopes of a function. An accelerating frame is changing inertial frames constantly but that doesnt mean it isn't an inertial frame at a given po... | {
"language": "en",
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"source": "stackexchange",
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Is the magnetic field of a moving electron caused by length contraction in the direction of motion? Consider an electron moving relative to us. Because the space in the electron's rest frame is contracted relative to us in the direction of the electron's velocity, the electric field lines are squeezed in the same direc... | The electric field for a charged particle moving in the $x$ direction of motion is Lorentz transformed as
$$
E'_x~=~\gamma E_x,~E'_y~=~\gamma(E_y~-~vB_z/c^2),~E'_z~=~\gamma(E_Z~+~vB_y/c^2).
$$
The motion of charge transforms the electric field components into magnetic field components.
| {
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Fluid velocity in a vertical pipe Consider a pipe with length $L$ and uniform radius $A$ is held vertically. According to the continuity equation, the velocity of water going into the pipe seems to be the same as the velocity of water coming out. But according to Bernoulli's equation:
$$P_{atm}+\frac{1}{2}\rho v_1^2+\r... | Consider a vertical pipe connected to a shallow reservoir:
There are mainly 3 points of interest:
*
*The outlet of the vertical pipe:
The heads are:
$P_{atm}+\frac{1}{2}ρv^2$
*The inlet of the vertical pipe:
By continuity, the stream has same velocity at inlet and outlet
$P_{in}+\frac{1}{2}ρv^2 + ρgL = P_{atm}+\fra... | {
"language": "en",
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Can a line of finite point charge configuration be in equilibrium? Can we arrange a finite number of point charges in a line so that they are all in equilibrium? Earnshaw's theorem proves that there cannot be a stable equilibrium point in an electric field, but what about unstable equilibrium? If not, how to prove it?
| If I put a charge of $+4q$ at $x=+x_0$ and $x=-x_0$ and have charge of $-q$ at the origin then the force on the charge at the origin is 0 by symmetry and the force on the outer charges is $$\frac{1}{4\pi\epsilon_0}\left(\frac{-4q^2}{x_0^2} + \frac{16q^2}{(2x_0)^2}\right) = 0$$
so the system is (unstable) equilibrium.
| {
"language": "en",
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"timestamp": "2023-03-29T00:00:00",
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Relation between perturbation theory and Taylor expansion in QM So I am looking at non-degenerate perturbation theory. The idea is that the perturbing term in the Hamiltonian is small so you somehow expand the energies and wave functions in this small term and collect orders.
Now I did an exercise in which you apply pe... | Yes.
Suppose
$$
H=H_0+\epsilon H_1=\left(\begin{array}{cc}A & 0 \\ 0 & B\end{array}\right)+
\epsilon\left(\begin{array}{cc}a & b \\ b & c\end{array}\right)
$$
where $a, b$ and $c$ are real for simplicity. You can easily work out that
the exact eigenvalues are
$$
\lambda_\pm =
\frac{1}{2}\left(A + B +\epsilon (a+ c) ... | {
"language": "en",
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"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "6",
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time dilation in a gear chain system Thought experiment...
suppose we have a mechanism connecting two chain gears as follows:
gear A rotates at 2 rpm. gear B is near a massive star. because of time dilation, time is slower at B, lets say half the time at A. therefore, as seen from observer at A, the gear at B will rot... | 1) Special Relativistic Effects (for relative velocity) for observer at A
1a) Belt (and wheel) travelling towards them appears time dilated and length contracted.
1b) Belt (and wheel) travelling away from them appears time dilated and length contracted.
2) General Relativistic, (gravitational effects) for observer A
... | {
"language": "en",
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"source": "stackexchange",
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Is hermiticity a basis-dependent concept? I have looked in wikipedia:
Hermitian matrix
and
Self-adjoint operator,
but I still am confused about this.
Is the equation:
$$ \langle Ay | x \rangle = \langle y | A x \rangle \text{ for all } x \in \text{Domain of } A.$$
independent of basis?
| The definition that you have cited is indeed basis-independent as it only makes reference to the inner product $\langle\cdot,\cdot\rangle$ and the domain of $A$, neither of which is basis-dependent.
Note that "symmetric" in your above sense and "self-adjoint" in the broader sense are connected by the Hellinger-Toeplitz... | {
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Pauli- Villars regularization in the Electron Vertex Function: Evaluation I'm studying one loop contribution for electron vertex function form Peskin and Schroeder's book " An introduction to quantum field theory " Section: 6.3. I have some troubles with Pauli- Villars regularization and getting the final results, so a... | All they've done is taken the limit of large $\Lambda$. Then
\begin{align}
\Delta_\Lambda=-xyq^2+(1-z)^2m^2+z\Lambda^2\rightarrow z\Lambda^2
\end{align}
and
\begin{align}
\log\left(\frac{\Delta_\Lambda}{\Delta}\right)\rightarrow \log\left(\frac{z\Lambda^2}{\Delta} \right)+\mathcal{O}(\Lambda^{-2}).
\end{align}
This i... | {
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"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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2D elliptic gaussian beam on tilted wall I can calculate laser's beam cross section at every point along z-axis. But how to do a "projection" of this beam on tilted wall? I see option to use ray tracing, but there is possibly a better way.
Ordinary projection using Camera Matrix does not takes into account beam propag... | You can do a coordinate transformation $x \rightarrow x', y \rightarrow y', z \rightarrow z'$ for a coordinate system in which the $x'y'$ plane is aligned with the wall.
| {
"language": "en",
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How can a generic potential transform under Lorentz transformations? The standard relativistic particle Lagrangian is
$$L = - \sum m_i \sqrt{1-v_i^2} - V(x_i).$$
The first term contributes a scalar to the action, as it should, but the second term is not clearly a Lorentz scalar; it contributes $\int V(x) \, dt$, so to ... | Your question has no answer since there is no sensible classical relativistic multi-particle picture. A corresponding no-go theorem was proved by Currie, Jordan and Sudarshan, Reviews of Modern Physics 35 (1963), 350.
See also https://physics.stackexchange.com/a/32401/7924
| {
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"source": "stackexchange",
"question_score": "6",
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What is an induced electric field? I have read in many books about induced current in a coil (Faraday's law), and also the motional emf across a moving conductor in a magnetic field. But somewhere I read about induced electric field due to a time varying magnetic field.
And I think that Induction of electric field is... | You are right that a changing magnetic field creates (induces) an electric field, this is an actual law of nature.
Now if you put a conductor where the magnetic field is changing, you will get a current due to the produced electric field.
But in the case of the moving conductor moving through a magnetic field the reaso... | {
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"source": "stackexchange",
"question_score": "2",
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Is short circuit technically the same as overloading? Taking the simplest circuit: battery and resistors.
If I connect lots of resistors in parallel, wouldn't that increase the current to an extent that it would be technically be very similar to shorting the circuit?
| If you have $N$ resistors in parallel, all of which have a resistance of $R$, the total equivalent resistance will be
$$ \left( \frac 1 R + \cdots + \frac 1 R \right)^{-1} = \left( \frac N R \right)^{-1} = \frac R N \;. $$
So yes, if you take a sufficiently large amount of (identical) resistors in parallel, it's the sa... | {
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Why is perturbation theory always implemented around $\alpha=0$? In the perturbative approach to field theory we expand whatever we are computing on a power expansion in some coupling
$$
\sum^nd_n\alpha^n
$$
then in principle we can compute all the $d_n$. This series is in general expected not to be convergent, but it... | It is because one wants to do a perturbation theory around the known solution. Of course, you can denote by $\alpha$ anything you want, but usually it is some coupling constant. The limit $\alpha \rightarrow 0$ corresponds to a free theory, which can be easily solved. After it is done, one computes the corrections to t... | {
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} |
Why does a wet towel become more hot than a dry one? I remember a long time ago my mum had told me not to use a wet tea towel when taking food out of the oven because you can burn your hands - lo and behold, it came time to make dinner and I did not head my mother's warning from all them years ago and my hand got burne... | Water has a high heat capacity and is also a pretty good conductor of heat.
The dry towel has a lot of air pockets and doesn't have a lot of heat capacity in general.
Essentially you're bridging the air gap that was acting as an insulator. The water also provides a sink for the energy instead of just going into the ai... | {
"language": "en",
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relation between mass of black holes and tempereture? As we know, by increasing the mass or energy of a black hole, its event horizon radius will increase, but why its temperature should increase too?
Really I want the relation between mass and temperature of black hole!
| Higher temperature means it's hotter for a lower mass, i.e., it emits more and higher freq radiation. Micro black holes which evaporate away quickly do so at the end in a burst as they are the hottest. You have to get the details from the paper.
The temperature is the one that would define that of a black body radiato... | {
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Synchronized Clocks in Inertial frame Will the synchronized clocks placed in an inertial frame remain synchronized forever?
| Yes, they will.
"Synchronization" in a strict sense means that both clocks are said to define one and the same inertial frame. At the moment of synchronization they are said to share same velocity and direction. They will carry the inertia defined at the moment of sychonization with them, all the time. Any accelerat... | {
"language": "en",
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"source": "stackexchange",
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Doppler effect and apparent frequency What is meant by "apparent frequency"?
I mean the answer we get by applying the formula; what does it signify?
If it is the frequency received by the observer, does it mean that the observer receives the same frequency no matter what the distance of the source?
Shouldn't distance o... | Actually, in an ideal situation distance of the source will not matter. In real life, the farther the source, the greater the damping effect on the wave. The sound loses energy and hence the amplitude and intensity fall.
However, this does not affect the frequency. Frequency is given by the formula fλ=v where symbols h... | {
"language": "en",
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How to calculate rate of water heating with pulsed near infrared laser? I'm designing something that requires me to heat a small volume $( <10 ml)$ of water with a $2100 nm$ pulsed near-infrared laser with settings between $1 J$ and $1.5 J$ and $5-15 Hz$. I'm heating the water in the range of $20-70$ degrees C. I thoug... | No, there is no specific effect related to heating with pulses compared with any other heating method. Your calculation should give the correct result. You should treat this as a systematic error and look for a physical explanation.
Perhaps your assumption of perfect absorption is incorrect? Absorption is not affected ... | {
"language": "en",
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Maxwell energy Distribution in One dimension Maybe my question is too specific but I could not find the answer.
Abstract from:
Yield Optimization and Time Structure of Femtosecond Laser Plasma
$\kappa \alpha$ Sources
The generation of femtosecond $\kappa \alpha$ x-rays from laser-irradiated plasmas is studied with ... | Yes, there is. You can look here. It is the Maxwell-Boltzmann distribution of the energy per degree of freedom. This is a chi-square distribution and note that
$$\int_0^\infty \frac{1}{\sqrt{EkT}}e^{-\frac{E}{kT}}dE=
\frac{2}{\sqrt{kT}}\int_0^\infty e^{-\frac{x^2}{kT}}dx$$
that is finite as it should. The authors of ... | {
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How do we know which lighter elements fuse to form heavier elements? Formation of lighter elements is fairly straightforward: $^4$He + $^4$He + $^4$He = $^{12}$C. However for each heavier element (heavier than Fe in particular), is there exactly one combination of (two lighter) elements that can be fused? Is it poss... | You are, in fact, correct : there's more than one way to combine elements to form other heavy elements.
What we can predict to some extent is the relative probability of different combination (different fusion reactions). We also have knowledge of how relatively stable the different nuclei are. Some reactions are muc... | {
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Why does a wave not interfere with its secondary wavelets? Huygens principal says that every point wavefront is the source of a secondary wavelet. If this is true, why do those wavelets not interfere with the main wave? Shouldn't waves looks like a circle of interfering circles?
| I suggest you find a good source, and sit down and draw the wavelets out to understand it visually. As user45664 pointed out, thinking about the "main wave" is a bit misleading. Because, in this picture that you posted, you need to account for Huygen's Principle:
"...Every point on a propagating wavefront serves as th... | {
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Proof of the generalized equipartition theorem The generalized equipartition theorem (where variables need not be quadratic) states that if $x_i$ is a canonical variable (position or momentum variable), then
$$\left\langle x_i \frac{\partial \mathcal{H}}{\partial x_j}\right\rangle = \delta_{ij}\ k T$$
where the average... | J. A. S. Lima and A. R. Plastino published the article On the classical energy equipartition theorem back in 1999. In their article they derive a generalized equipartition theorem. Their generalized approach is valid for systems with arbitrary distribution functions and for systems with non-quadratic terms in the Hamil... | {
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What constitute the secondary particles beam when a high energy proton beam hits a target material? Basically I want to know what particles emerge along with high energy photons(not sure about it) as the second beam when a specific high energy proton beam is incidented upon a target material such as iridium or gold. Ca... | News to me about the photon. I thought that was still theoretical.
Since we are talking unproven things, the rest of your question is hard to definitively answer. I'm going with pions.
| {
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Why does a force not do any work if it's perpendicular to the motion? I have a book that says the Moon's orbit is [in this context assumed to be] circular. The Earth does no work on the moon. The gravitational force is perpendicular to the motion. Why is there no work done if support force is perpendicular to the motio... | As others have already explained. Well its because there is no displacement in the direction of the gravitational force. It is assumed that the orbit stays the same during our observation. The Earth is pulling the moon towards the centre but the moon is moving in a circular orbit, with no displacement towards the centr... | {
"language": "en",
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"source": "stackexchange",
"question_score": "22",
"answer_count": 9,
"answer_id": 7
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Speed of block sliding on frictionless ramps Here's the question:
My book says the answer is C. How is it not A?
I know that all the potential energy is transferred to kinetic energy. With algebra, knowing Kinetic energy is (1/2) * m * v^2 and gravitational potential is mgh, I solve for h which results in (v^2)/2g
Ok ... | The potential energy at the start is $mgh$, which is converted into kinetic energy of $\frac 12mv^2$ at the bottom. When the velocity is $\frac v2$ the kinetic energy is $\frac 12m(\frac v2)^2=\frac 18mv^2$. As $\frac 14$ of the energy is now kinetic, the rest must be potential, so the potential energy is $\frac 34mg... | {
"language": "en",
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What is the significance of the phase constant in the Simple Harmonic Motion equation? The displacement of a particle performing simple harmonic motion is given by $x = A \sin(\omega t + \phi)$ , where $A$ is the amplitude, $\omega$ is the frequency, $t$ is the time, and $\phi$ is the phase constant. What is the signif... | The equation of motion for a simple harmonic oscillator is
$$
\ddot x+\omega^2 x=0
$$
and the most general solution to this is
$$
x(t) = A_1 \cos \omega t + A_2 \sin \omega t
$$
Note there are two constants of integration that correspond to the equation being a second order differential equation. More physically, the... | {
"language": "en",
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Uncertainty principle and the speed of light If an EM wave only gives us a probability of where a photon may be at a given moment, and the HUP tells us that we can't know the exact location of the photon. Then would it be correct to say that a photon does not travel in a straight line?
If this is true, wouldn't the pho... | Your crooked path argument holds for a classical electromagnetic wave going through a medium. That is why the speed of light in a medium can be less than c, the speed of light in vacuum. At the photon level it is that photons effectively go a larger distance at velocity c, as they interact individually with the lattice... | {
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Acceleration of car. One dimensional motion easy problem A car starts from rest and accelerates uniformly over a time of 5.21 seconds for a distance of 110 m. Determine the acceleration of the car.
My attempt at solving the problem:
$$a(x) = \frac{v - u}{t}$$
where
$v =$ final velocity
$u =$ initial velocity
$$$$
I get... | That equation is not the most straight foreward for this situation but it can be used, here's how. If you divide the displacement, 110 m, by the time of 5.21 s you will get 21.1 m/s. But that is the average velocity over the entire displacement. The average veloctiy, when v is changing uniformly, is found by adding the... | {
"language": "en",
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Ampere's Law Confusion I had this question recently in a test. Different methods are yielding different answers. Can someone point out the mistake?
We are given 4 infinite wires carrying current out of the plane as shown. Find $$\int_{-\infty}^{+\infty} \vec{B}\cdot\,\mathrm d\vec{x} ,$$ (along x axis)
My logic f... | When you do the loop integral about one set of wires you are ignoring the other set of wires. Going from $-\infty$ to $+\infty$ around your first loop, you "collect" half of the B field due to one set of currents (the other half comes when you go back in the other direction - your assumption that it's zero "because you... | {
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A question on Collison of macroscopic particles
Hello,
In the above question I could solve for average elastic force by taking velocity with respect to wall and finding change in momentum of the ball after that divided change jn momentum by time interval. Answer comes out to be option b.
But as it is written in the qu... | I think d is incorrect because the kinetic energy increases due to the massive moving wall hitting against the ball.
Kinetic energy before the collision should be equal to kinetic energy
after the collision
will only be true if the wall is static, not moving.
Just like hitting a ball with a bat.
| {
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"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "1",
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Time reversal and Antilinear operators I'm struggeling to solve this question. Can anyone help me please?
Let us consider a generic quantum mechanical system governed by
the Hamiltonian $\ H(t) $.
In what follows we denote the evolution operator by
$\ u(t, t_0) $. Hence,
$\ |Ψ(t)> = u(t, t_0)|Ψ_0> $
satisfie... | Let's make $u(t)=e^{it}$ ($H$ is hermitian)
Then $u^\dagger u=e^{-it}e^{it}=e^{it}e^{-it}=u u^{\dagger}=1$
Let $e^{it}$ and $U$ act on $\phi$:
$$(e^{it} U-U e^{it})\phi=(-e^{it}U+ e^{-it}U)\phi,\quad \text{or}\quad (-e^{it}+e^{-it})U\phi.$$
Now $U\phi=-U\phi$, so $(-e^{it}+ e^{-it})=-(-e^{it}+e^{-it})$ and therefore $0... | {
"language": "en",
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Equation of motion from Polyakov action If I write (my understanding of) how to derive the equations of motion from the Polyakov action, I come up missing a term.
Beginning with the basic Polyakov action
\begin{equation}
S = -\frac{T}{2}\int\sqrt{-h}h^{ab}g_{\mu\nu}\partial_aX^\mu\partial_bX^\nu\,d^2\xi
\end{equatio... | It's easier to compute the equations of motion by using variations of the inverse metric.
$$ \frac{\delta S}{\delta h^{ab}}=0 $$
You can use the distributive property of the variational operator and make use of the identity
$$ \frac{1}{\sqrt{-h}}\frac{\delta\sqrt{-h}}{\delta h^{ab}}=-\frac{1}{2}h_{ab} $$
| {
"language": "en",
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"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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Short question about moment force I have a question about moment Forces. Let $\mathbf{e_1}$, $\mathbf{e_2}$ be the unit vectors defining a Cartesion coordinate system $Oxy$.
Let $\mathbf{F}$ be the force applied at point $A$.We have:
$$\mathbf{F} = F_x \ \mathbf{e_1} + F_y \ \mathbf{e_2}$$
where
$$\begin{cases} F_x &=... | For 2D problems with cross products always make it a 3D problem with the z-coordinate 0. The cross product is uniquely defined for 3D problems.
This results in the following 2D cross products
$$ \begin{align}
\omega \times (x,y) = \begin{pmatrix} 0\\0\\ \omega \end{pmatrix} \times \begin{pmatrix} x \\ y \\ 0 \end{pm... | {
"language": "en",
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"source": "stackexchange",
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Glasses underwater So I figured the refraction of the cornea is based on the index of air and the vitrous humor to make a perfect image. Underwater this is messed with because water has the same index as the eye. Hence you can't see clearly underwater without making an air pocket with scuba goggles for example.
Would ... | Trivially no. To see this, construct the glasses out of a material with the same refractive index as water.
| {
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Why doesn't current decrease in series combination? I know that the question is quite stupid but I want to get an insight of this case. consider 3 resistors connected in series with a battery, after the current passes through resistor 1 it loses some of its energy, the kinetic energy of the charge carriers will definit... | Current is due to the drift velocity of electrons . In the Transient State when the current sets up there is an accumulation of electrons at places like bends in the wire. There is an electric field ( small) in the wire that drives the current. At any place where there is an accumulation of charges the outflowing curre... | {
"language": "en",
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Do physicists use particle "energy" to refer to kinetic energy? In 1963, this paper was written about the effects of radiation on solar panels. The paper states that:
When electrons at energies greater than 145 KeV and protons at energies
greater than 98eV bombard a silicon crystal, they can displace an atom from t... | Special relativity theory gives you $(mc^2)^2 = E^2 - (pc)^2$, where $m$ is the rest mass of particle (511 keV for electrons), $p$ is the momentum and $E$ the total energy. When you have the natural unit system where $c = 1$, the equation becomes
$m^2 = E^2 - p^2$,
which might be strange looking for you.
When an electr... | {
"language": "en",
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Translation of Vectors I am a bit confused about translation of vectors. In the first class in physics itself we are told that we can translate vectors as we like to the desired position to do whatever that we are trying to do. For example, if someone draws two random vectors then to get the sum, we translate them, ma... | Yes, we are allowed to translate vectors. To put it simply, think of coordinate geometry. When you shift the origin, it doesn't effect the orientation and length of a line segment. Similarly, in vectors, translation doesn't effect the vector as a vector is defined by its magnitude and direction. You can move it to anyw... | {
"language": "en",
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Dirac delta function property in a scattering proof I'm studying the proof for the decoherence of the off diagonal elements of a density matrix through scattering with the environment and I'm stuck at a certain point:
My problem is A1.14 relation. (A1.13 as well to be honest, but I guess that the $(2\pi/L)^3$ is just ... | In one dimension we have
$$(2 \pi)\delta(p) = \int_{-\infty}^\infty \mathrm{d}x~e^{ipx}$$
And so, formally,
$$ (2\pi)\delta(0) = \int_{-\infty}^\infty \mathrm{d}x$$
If we imagine that we are actually working in a large but finite space with length $L$, then we can intepret $(2 \pi) \delta(0)$ as this length $L$. The r... | {
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Infinite array of capacitors and inductors You may be familiar with the surprising result one gets when calculating the equivalent of an infinite array of resistors. What if we change this circuit and replace the resistors with capacitors and inductors?
Following the notation given in the link I've provided above, let'... | Initially I thought you had just rediscovered the Telegrapher's Equations - but then I realized you had your capacitors and inductors "the other way around" from that more usual scenario (described here)
Even though your situation is unusual, there is a way to understand what is happening. The capacitors in your networ... | {
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If magnetic fields are created by moving charges, how do magnets work? This is probably is stupid question but I think it must clear up some misconception I have. Magnets, presumably have magnetic fields. But where are the moving charges? Don't we need a current?
|
How do magnets work?
The subatomic particles electron, proton and neutron have magnetic dipole moments. This magnetic fields are intrinsic properties, means this fields exist under all circumstances. In nonmagnetic materials the sum of all magnetic dipole moments is zero.
In permanent magnets the sum over all this ma... | {
"language": "en",
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Is the Moon in a "Freefall" Around the Earth?
The force of gravity keeps our Moon in orbit around Earth. Is it correct to say that the Moon is in “free fall” around Earth? Why or why not?
I think the answer is yes. The moon is falling towards the Earth due to gravity; but, it's also orbiting the Earth as fast as it's... | Yes, it is in free fall towards the Earth and that is what allowed Newton to unify the terrestrial and the celestial mechanics, one of the greatest advances on Science ever. He did that by assuming that both the Moon and a falling apple (allegedly) falls toward Earths due to a gravitational force. Using his newly disco... | {
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"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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Sea quark parton annihilation? Consider the figure below1:
This can be read as follows (please correct me if I am wrong): two particles come in and 'fragment', a parton from each particle $C$ and $D$ annihilate to form the particle $X$. An intuitive guess is that the partons $C$ and $D$ must correspond to valence quar... | Assume proton proton scattering: something has to be exchanged in order to interact. Because they are strong interacting particles they exchange at least a gluon with the out going protons absorbing the energy and breaking out into jets.
A gluon leaves from a quarq of one of the protons and gives energy to one of... | {
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"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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Experimentally measure velocity/momentum of a particle in quantum mechanics In the context of quantum mechanics one cannot measure the velocity of a particle by measuring its position at two quick instants of time and dividing by the time interval. That is,
$$ v = \frac{x_2 - x_1}{t_2 - t_1} $$ does not hold as just af... | A particle's velocity can be measured just as you've described. If you shoot the particles through apertures that are much larger than their wavelength, the wavelike effects are minimal and they continue with basically the same momentum. If you squeeze the target aperture, though, particles that pass through continue w... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/312834",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "8",
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How does the temperature of an ideal gas exhausting into vacuum vary? Since a gas at a certain pressure exhausting into vacuum has no atmospheric pressure to push against, there shouldn't be any adiabatic cooling taking place.
But looking at the energy conservation:
$TdS=dU+VdP+PdV$
$TdS = 0$ {Adiabatic process}
$PdV =... | TdS is not zero for all adiabatic processes. It is only zero for all adiabatic reversible processes, and the process you describe is not reversible. If you have an adiabatic chamber with gas on one side of a barrier and vacuum on the other side and you suddenly remove the barrier, the gas does not do any work on the ... | {
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Why a 3D Universe? The universe as it stands is perceived by us to be 3 dimensional. Why is it that the universe formed into 3D space and not 4D or 5D space for example?
| Assuming you're asking for a "first principles" explanation, there currently is none. That the world around us has three spatial dimensions is an obvious experimental fact, a raw input to our theories, not a derived statement.
Neither general relativity nor quantum field theory, which are our currently most fundamental... | {
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Bell's theorem and how it solves the EPR paradox Could someone explain to me how Bell's theorem solves the EPR paradox and 'spooky action at a distance'?
From what I understand, when measuring a state, say spin up in the x direction, the wave function collapses and the other particle must be spin down in the x directio... | Bells inequality is derived by assuming 'local reality'. This inequality has been shown to be violated by experiment and by theory (quantum mechanics). So the conclusion is: nature doesnt always posess local reality. Assuming local reality made EPR a paradox, so without this it is resolved.
| {
"language": "en",
"url": "https://physics.stackexchange.com/questions/313667",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "4",
"answer_count": 1,
"answer_id": 0
} |
Current as the time derivative of the charge I have been told that the current $i$ can be defined as
$ i = \displaystyle\frac{dq}{dt} $,
where $q$ is the charge and $t$ is the time.
I do not understand this definition because, if the charges are moving so that the net charge remains constant in an infinitesimally thin... | Electric current can be understood through the analogy of water flow.
Just as the 'water current' in a river is the amount of water which passes a point in a given time interval, similarly, the electric current can be understood as the amount of electric charge passing through an area in a given time interval.
Of cours... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/313765",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "1",
"answer_count": 4,
"answer_id": 0
} |
Condensation of Water. Classroom Controversy In our test there was a question that went like so:
Question 4 You have a glass of iced water on an unshaded picnic table and went for a walk for 30 minutes. When you return you noticed
the glass has water on the outside of it.
a. In terms of heat transfer explain what ha... | Consider the possibility that there is no "correct" answer.
Maybe the purpose of the question was just to get you to think about and discuss a physically interesting situation.
Condensation will depend on at least the following factors
*
*Air humidity
*Air temperature
*Air circulation
*Water temperature
It is p... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/313863",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "40",
"answer_count": 10,
"answer_id": 7
} |
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