Q stringlengths 18 13.7k | A stringlengths 1 16.1k | meta dict |
|---|---|---|
Why do high current conductors heat up a lot more than high voltage conductors? 120 volts x 20 amps = 2,400 Watts
However, if I increased the voltage and lowered the current, you can also use a smaller wire size (more inexpensive), also have less heat and achieve the same watt Power.
1,000 volts x 2.4 amps = 2,400 Wat... | Amps travel in a straight line and so must travel inside the wire.
Volts travel around the amps and usually outside the wire.
So amps will generate heat - because of the atoms and valence electrons create degrees of resistance - while volts , generally, will not. But if you use thick enough wire you will not notice th... | {
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Non-locality and quanta Quantum mechanics is non-local in that long distance correlations are present, though there is no signalling possible. But QFT is Lorentz invariant and contains quantum mechanics as a special case. I assume this is not a paradox as paradoxes do not exist but I do not understand the details. Can ... | Pseudo- apparent "Long-distances" correlations exist in statistical classical physics too.
In fact, if you consider a system, which at some time, for some reason, in which two subsystems (of this system) are being locally correlated, and supposing, that, in the future, these two sub-systems are spatially separated , ... | {
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Applying multiple forces to one object and calculate net movement and rotation? I'm working on a small game as a hobby project, and I've run into a problem that would seem simple, to me, but that I can't find any information on or solution to.
How would one go about figuring out what happens to this object, in terms o... | I do not know if you remember Newton's second law from high school physics:
$$
\sum{\vec{F}}=m\vec{a}
$$
where $\vec{a}$ is the acceleration of the center of mass.
And similarly there is also a relation for angular acceleration:
$$
\sum{\tau}=I\alpha
$$
where $\tau$ is torque and $I$ is the moment of inertia around the... | {
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How do I find the tension in the cable from this problem?
I am trying to find the tension of the cable but I don't know what to do.
| You can approach this problem two ways:
*
*Balance the forces: Determine a coordinate system you would like to use, draw a free-body diagram, and do some bookkeeping as to which forces are completely or partly along the principle axes of your coordinate system (if partly, use your trig. identities to split up any fo... | {
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Synchronisation of clocks How can two clocks be synchronised with each other at some instant without being at the same place and same time $?$ considering that simultaneity is a relative concept .
| Here's the standard way in flat spacetime. Let's say you want to produce a synchronized pair of clocks that are a spatial distance $d$ away from one another, then perform the following steps:
*
*Construct two identical clocks such that they start ticking when they receive a special light signal. Call the clocks cl... | {
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Do centripetal and reactive centrifugal forces cancel each other out? In order for a body to move with uniform velocity in a circular path, there must exist some force towards the centre of curvature of the circular path. This is centripetal force. By Newton's Third Law, there must exist a reactive force that is equal ... | The centripetal force is the accelerating force acting towards the centre of the orbit; the centrifugal force can be considered its Newton's 3rd law pair. If you swing a stone attached to a string in a circle, the centripetal force is the pull of the string on the stone. But the pull of the stone on the string - whic... | {
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Will density of a metal increases during forging? This question is metallurgical engineering, but I had a similar doubt regarding density of liquids and what causing it.
Forged parts refines defects, dislocations will be moved strengthening the metal. But will the density of forged metal change?
My earlier question was... | The density of the metal, steel in this case, is a function of atomic weight, atomic spacing, and the volume of steel being measured. Since atoms in the metal crystal (no, there are no molecules in ordinary steel) are very small, it would take a huge change in the inter-atomic spacing to affect density to a measureabl... | {
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What happens to a conducting ring when exposed to an electric field? It might be a silly question, but one of my friends just got asked this question at an oral exam, and he could not answer it, and didn't receive the answer either (Or at least he forgot).
And I've been thinking a while, and I'm not sure what would rea... | The answer depends on some factors:
*
*Orientation of field.
A.If your field is horizontal and passes from the wedding ring, charges will be induced on the ring and it may/may not move depending on the field strength.
B.If your field passes vertically from the wedding ring, then if the thickness of the ring is negli... | {
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Does a photon instantaneously gain $c$ speed when emitted from an electron? An excited electron loses energy in the form of radiation. The radiation constitutes photons which move at a speed $c$. But is the process of conversion of the energy of the electron into the kinetic energy of the photon instantaneous? Is there... | Quantum Mechanics tells us that electrons only lose or gain energy equal to the energy of an incoming or outgoing photon. And by default, all photons travel at speed c in vacuum. As I understand it, there is no "conversion" time for energy. Photons are energy and energy comes in photons. What we choose to call them is ... | {
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Minimum seperation between two Airy disks as a function of the distance between two point sources of coherent light passing through the same objective I have two coherent point sources of light, $A$ and $B$, separated by a distance $L$, which I focus down to the diffraction limit using a high-powered objective (e.g. a ... | Look up the angular resolution of an optical telescope. It is given approximately by the equation
$$
\theta=1.22\frac{\lambda}{D}.
$$
From this you can convert to the linear separation between the two objects.
| {
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Efflux speed of ideal fluid dependent on diameter? I have a cylinder full of water with diameter $D$ with a round opening on the bottom with diameter $d$. The water is friction-free and incompressible. Now I need a relationship for the efflux speed $v$ with which water exits the cylinder and I shouldn't use the approxi... | If you are concerned about efflux speed you need not worry about the diameter of efflux hole. However If you are worried about Volume rate flow of fluid you need the diameter of the hole.
In that case ${dV/dt}$ =$ d * v $ ; where d is the diameter of the hole, and the v is the efflux speed.
| {
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During reflection does the emitted photon have same properties? When light (photon) is reflected the the original photon is absorbed by an electron and then emitted again. Does this "new" photon have the same wavelength, frequency etc. as the original?
| There is no absorption and re-emission involved in reflection. None whatsoever.
This can be proved with a laser; any colored laser.
Using a collimated expanded laser beam, incident on the reflecting surface, at an angle, you will get interference between the incident wave and the reflected wave. That is only possible ... | {
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How do I explain to a six year old why people on the other side of the Earth don't fall off? Today a friend's six year old sister asked me the question "why don't people on the other side of the earth fall off?". I tried to explain that the Earth is a huge sphere and there's a special force called "gravity" that tries ... | Explain that since the earth is round, and people do not fall down (as there is no absolute "down"), they fall towards the center of the earth.
| {
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Perpetual motion in spaces of different gravity? Imagine two locations with different amounts of gravity. I carry up a weight in low gravity, move it on this height over to the other place, and let it fall down there with higher gravity.
Wouldn't falling down release more energy than lifting up hast cost? If so, is it... | The main point is that Newtonian gravity fields are conservative. What that means is that it is impossible to have a configuration like the one you drew without there being gravitational fields pointing to the left and to the right in the regions where you want to do the 'horizontal' transfer.
For example, you might t... | {
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Dielectric constant of water I need the dielectric constant of water from $10^{-2}$ Hz to $10^4$ Hz. As stupid as it may seem, I cannot find much info. I've googled for days. All I can find is close to GHz. And the only info close to Hz, ($100$ Hz) shows a great variation. A relative dielectric constant at $100$ Hz of ... | EDIT#2:
*
*I'm now made aware that you need wavelengths that are much larger
than those presented here(a bit of an oops from reading this question quickly). This approach is still valid, but what you
need cannot be obtained from these data. I'm going to leave this here however to collect downvotes and if anyone need... | {
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Gravitational collapse and free fall time (spherical, pressure-free)
A very large number of small particles forms a spherical cloud. Initially they are at rest, have uniform mass density per unit volume $\rho_0$, and occupy a region of radius $r_0$. The cloud collapses due to gravitation; the particles do not
intera... | For a spherically symmetric distribution of mass, the acceleration felt by a test particle at radius $r$ is $-G M /r^2$ (negative because pointing in toward the center), regardless of the radial distribution of mass. This is a key part of the question, make sure you are comfortable with it. It is a concept that is rel... | {
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Why is the angle of a triangular prism equal to the result of the following 2 calculations? (Experiment with optical goniometer) I know there are two ways of measuring the angle of a prism with a goniometer:
let the collimator shine (monochromatic) light on 2 sides of the prism and measure the angle between the 2 refl... | I believe you only need one rule: "The angle of reflection equals the angle of incidence." Draw a triangle on a piece of paper. ( For this situation, the third dimension of the prism is irrelevant). Draw two parallel lines originating from roughly the direction the apex of the prism is pointing. It's not necessary t... | {
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What is a simple mathematical model of a star? I had a discussion at work regarding a recent fusion experiment in China that resulted in temperatures five times hotter than the Sun. Someone mentioned that no one can know the temperature of the Sun. I replied that we have mathematical models of the Sun, but I didn't hav... | The variable $M$ on that page is used instead of the radial $r$ coordinate; $M$ denotes the total mass inside the ball of radius $r$, the cumulative mass. These explanations are clear e.g. from this alternative presentation of the equations of the stellar structure:
https://en.wikipedia.org/wiki/Stellar_structure#Equa... | {
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Tricky operator identity: $[L^2,[L^2,\vec{r}]]=2 \hbar ^2 \{ L^2, \vec{r}\}$? This operator identity showed up in a course I was taking, and it was given without proof.
$$[L^2,[L^2,\vec{r}]]=2 \hbar ^2 \{ L^2, \vec{r}\}$$
The curly brackets denote the anticommutator, $AB+BA$. The $\vec{r}$ operator is the position oper... | The symbol $r$ in the identity represents (and will represent in the text below) the whole three-component vector of operators $\hat{\vec r} = (\hat x, \hat y, \hat z)$.
The simple way I found to prove the identity is to verify that all matrix elements of both sides match. Let's calculate the matrix elements of the ope... | {
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Can we calculate the frame dragging force of the Earth? Although clearly this force would be significantly greater with a rotating black hole, is it still possible to calculate this drag for say a satellite orbiting the Earth?
| Yes, as mentioned in the comments, the frame-dragging of a satellite orbiting the Earth was measured by the Gravity Probe B mission. The gyroscopes on the Gravity Probe B measured a frame-dragging drift rate of $−37.2 \pm 7.2$ mas/yr , where the theoretical prediction was $−39.2$ mas/yr (mas = milliarcsec). The results... | {
"language": "en",
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"source": "stackexchange",
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Centre of instantaneous rotation problem Is there a point of Centre of Instantaneous Rotation (CIR) for every type of motion or only for cases of rolling?
| For a 3D rigid body there is always an instantenous screw axis. This consists of a 3D line (with direction) and a pitch. The pitch describes how much parallel translation occurs for each rotation of the rigid body. A pure rotation has zero pitch, whereas a pure translation has an infinite pitch. ( 3D Kinematics Ref. ht... | {
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Can a mass matrix be asymmetric? I am developing a mathematical model of a mechanical device consisting basically of coupled harmonic oscillators. It turns out that the system mass matrix is asymmetric. I seem to read somewhere that a mass matrix has to be symmetric, but I am not sure. So I would like to know whether i... | In the world of robotics and dynamical systems the mass matrix is always symmetric. It is also positive definite, a result of kinetic energy
$$ K=\frac{1}{2} \dot{q}^\top M \dot{q} $$
being always positive.
| {
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"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "8",
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Why does ice form on bridges even if the temperature is above freezing? So with this "arctic blast" continuing, I've noticed that for my area, the temperature drops below freezing just long enough to cause freezing rain, but then the sun comes out and the temperature rises immediately. However, on bridges, ice continue... | Simply it is radiative cooling, or losing heat from a surface on earth to the outer space via thermal radiation. You can have an ambient temperature of 3 C, and the bridge temperature might be -2 C due to this mechanism of cooling.
Radiative cooling happen for materials that are good thermal emitters over the range of ... | {
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"source": "stackexchange",
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light beams of the sun
We receive sunlight on earth surface. What type of light beams are these?
Random/Parallel/Converging/Diverging
I think it should be Diverging as Sun is radiating these beams away. But in one book, answer is given as Random, in another it's Parallel.
| Jan L's answer is correct. Consider as well: when there's a solar eclipse, there is a penumbra because, as he said, the sun is not a point source.
However, when dealing with a focussing system, the angle of divergence is close enough to zero that setting the lens to "infinity" is quite sufficient to focus an image of ... | {
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Do solar neutrinos actually oscillate between electron, mu and tau? I was reading up on the history of the solar neutrino problem, and as far as I can understand it, neutrinos supposedly oscillate from one form to another, thus explaining why there were only one-third the number of neutrinos detected than were expected... | http://en.wikipedia.org/wiki/CERN_Neutrinos_to_Gran_Sasso
Neutrino flavor oscillation is facilitated by passage through matter. They travel hard by lightspeed, but not faster.
Solar core fusion emits two electron neutrinos/helium output. They scramble flavors during passage to the surface, traveling through our a... | {
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How do photons 'connect' during wireless connection? So wireless router broadcasts a signal and then your device searches. So what actually happens when the photons 'meet' it's kind of like saying, 'ah your one of us, so we will follow you, show us the way'
It's so bizarre, how do photons connect during wireless connec... | In principle the wireless router is sending out radio waves (photons) in all directions. Some of those are picked up by the antenna in your phone or laptop, which turns it into an electrical signal.
It's similar to broadcasting in public radio: the broadcasting station is sending out radio waves in all directions. Your... | {
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What is average life in radioactivity and what is its significance? By definition, average life of radioactive sample is the amount of time required for it to get decayed to 36.8% of its original amount.
But what is the significance of 36.8% and why has that value been chosen?
| I endorse Kyle's answer. Just two short comments.
The number 36.8% is literally
$$ 36.8 \approx 100 \exp(-1) =\frac{100}{2.71828\dots} $$
Moreover, it is right to call this quantity "average lifetime" or just "lifetime" because it is literally the average value of the time for which a nucleus (or something else) from t... | {
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Wavefunction of a Baryon How to write the total wavefunction of a Baryon including space part, spin part, isospin part and color part such that the net wavefunction is antisymmetric? What is the difference in wavefunctions of two different baryons but of same quark content say proton $p$ and $\Delta^+$ baryon?
| To write the wavefunction of a baryon, you write it as a direct product of the different parts of the wavefunction (just as you would for any other particle):
\begin{equation}
\left| \psi \right\rangle = \left| \mbox{spatial} \right\rangle \otimes \left| \mbox{spin} \right\rangle \otimes \left| \mbox{Isospin} \right... | {
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What is the constant $K_1$ in these orbital equations? I want to compute the derivatives of argument of periapsis and longitude of the ascending node of the orbit of a GPS satellite from the following formula.
$$\frac{d\Omega}{dt} = -K \cos{i} \\
\frac{d\omega}{dt} = K ( 2 - 2.5 \sin^2{i}) \\ K = \frac{nK_1}{a^2(1-e^2... | I found the solution by myself. $K_1$ is a constant describing the flattening of the earth $$K_1 = 66063.1704 ∗ 10^6 \space[m^2]$$
| {
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Why are temperatures generally hotter in the Middle East than in Europe? How come the average temperature in the middle east (Israel, Saudi Arabia, Sudan or lower) is always so much significantly higher than in Europe (say Germany, England etc.)?
I know that the sun rays pass a greater distance to Europe than the midd... | As a visual demonstration of Luboš Motl's answer, this:
Image obtained using Climate Reanalyzer (http://cci-reanalyzer.org), Climate Change Institute, University of Maine, USA.
is the average surface temperature on earth for 2013. This:
is the solar flux by Luboš' formula. And here:
I've tried to replicate their c... | {
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Isotropic systems and homogeneity In isotropic systems, the atomic arrangement is homogeneous in all directions. In the case of glass, which has the atomic structure of a liquid and, therefore, a random atomic structure that is definitely not homogeneous, is it that the atomic arrangements in each direction are equally... | First, an isotropic system need not be homogenous. We say the electric field from a point charge is isotropic although it is inhomogeneous. However, an isotropic, translation invariant system must be homogeneous.
While you are correct that a class is truly inhomogeneous as it is described by discrete atomic positions,... | {
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CPT and event horizon Is the example of neutrino entering the event horizon of BH quoted from this article a valid possible example of CPT violation due to the presence of event horizon in BH ?
Please, note that there is a very similar previous Question here .
I don't think this is a duplicate, meaning that I have spec... | ok, dear user: You are probably confused by the long, correct but superficial and naive discussion of the blogger you quote above that disagrees with Hawking. Of course, in most of the cases I agree with the blogger, or, better said, I would agree with him if it happened to have the same biases and beliefs about nature... | {
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Temperature: Why a Fundamental Quantity? Temperature is just an indication of a combined property of the masses of the molecules and their random motion. In principle, we can explain "no effective energy transfer between two conducting solid bodies in contact" via a condition in terms of the masses of the molecules and... | A quantity is called as fundamental quantity if it can't be explained in terms of other fundamental quantities:
*
*we know temperature is the vibrations and collision of constituent atoms and molecules and
*vibration can be explained by other known fundamental quantities.
Hence temperature is not a fundamental qu... | {
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"url": "https://physics.stackexchange.com/questions/96448",
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Can stress be observed directly? Strain can be directly observed using e.g. a ruler. Can (internal) stress be directly observed?
| Strain is difficult to observe with the naked eye. Many material either plastically deform or break instead of showing visible strain. With the help of polarization filters it is no problem to visualize strain in transparent materials.
This is an image of a plastic ruler under strain viewed through polarization filter... | {
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Calculate work done in an inclined plane How can you calculate the work done by a force (of unknown quantity) exerted on a 10kg block on an inclined plane. The force is pointing upwards and parallel to the incline (which is inclined 30 degrees with respect to the horizontal).
a. frctionless plane
b. coefficient of fric... | OK, I'll help you this far. Here's the diagram you should be able to make, and figure out everything else from that. I purposely put in ?? so you can't just hand it in and pretend you did it.
| {
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Why does a picture of a person seem to be looking in the same direction irrespective of the angle of observation? If you observe a picture of a person hanging on a wall who seems to be looking directly towards you always seems to be looking at you even though you change your angle of observation to the extremes.
The s... | Seeing an object is seeing the light reflected from the surface. When we change the lighting on the object then we observe a different image.
When we observe an object from different angles we see different images. This is because the reflected light goes in different directions and we see a particular ray only in on... | {
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$1.7\cdot 10^{-24}$ mole apples a day As the title suggests I was wondering why the International Bureau of Weights and Measures
decided a mole to be a standard (SI-)unit. After some research I found I was not alone with this problem.
The core of my question is:
*
*How is the unit “mole” necessary as a standard un... | The kilogram is the only kg-m-sec physical standard: a 35 mm film can-sized cylinder of Pt-Ir alloy whose mass measurably drifts (possibly trace atmospheric hydrogen chemistry) at different rates for the primary standard and its secondary standards. A silicon-28 single crystal solid sphere machined precise to a couple... | {
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Which electron gets which energy level? Electrons sit in different energy levels of an atom, the farther the higher energy is. Every electrons have the same structure, they can gain energy from environment, electrons which gained energy could jump to a higher energy level and will finally fall back again.
I'm wonderin... | The electron is not who "wins" energy. The increase in energy corresponds to the system electron-nucleus. The "incoming" energy is stored in the system, by increasing the distance from the nucleus to the electron.
The configuration of the atom, is such that always "looking" the lowest energy state for the system.
| {
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Do black holes exert an infinite amount of energy at the event horizon? An interesting thought crossed my mind when reading about Hawkings' apparent horizon theory.
If we assume that event horizons do actually exist, it would seem that black holes violate basic laws of physics. My (limited) understanding is that in tr... | Look into the sky through all 4(pi) steradians. Every direction is equidistant from the same Big Bang. There is no visible direction, no path to escape this universe. There is no energy expended in enforcing this. It is a consequence of geometry.
Exactly how black holes are structured, "surface" and center, remains... | {
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Admixtures of longitudinal and timelike photons! In the quantization of electromagnetic field the physical states $|\psi\rangle$ are found to obey the following relation:
$[a^{(0)}(k)-a^{(3)}(k)]|\psi\rangle=0$
It is explained as the physical states are admixtures of longitudinal and timelike photons. What do longitudi... | When you change the free field $A_\mu$ by means of a gauge transformation, you can easily see that it affects longitudinal and timelike degrees of feedom. Since observables are gauge invariant, those degrees of freedom cannot be physical.
| {
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What are the correct initial conditions for the moon (in a simulation)? So I've modeled the interactions between the sun and all the planets (and the interactions between the planets) using Verlet integration.
I've used data from Wikipedia for masses, distance from the sun etc.
I initialized the initial velocities of ... | You may have noticed that if you start with the sun at rest, and put Jupiter into the system with an initial velocity to (say) the left, then over time the whole system moves left. (If you haven't noticed this is it worth setting the system up that way and letting it run long enough that you do notice it.)
The trick is... | {
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Does there exist a single plate capacitor(conductor)? Does there exist a single plate capacitor(conductor)? if yes
How will you define the capacitance and potential(difference)
of such conductor?
| A simple example is that of a sphere. One way to find its capacitance is to take the limit of a nested sphere capacitor with radii $a,b$:
$$C = \lim_{b\to\infty}\frac{4\pi\epsilon_0}{\frac{1}{a}-\frac{1}{b}} = 4\pi a\epsilon_0\text{.}$$
A van de Graaff generator is a commonly discussed in physics classes, and involves ... | {
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Twin Paradox, calculating spacetime intervals from both perspectives I've very recently started to try to understand special relativity. I'm want to get a decent understanding of the twin paradox. I'll post what I've done so far and highlight what's gone wrong for me.
The situation is that Alice and Bob both begin at p... | There are just 3 events that need be considered here: (a) the initial event that Alice and Bob are co-located, (b) the event that Bob turns around and (c) the final event that Alice and Bob are again co-located.
If, according to Alice, Bob's speed on both legs is $v$, and the distance to the turnaround point is $r$, t... | {
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Would a considerably big asteroid be disintegrated by the Earth's Roche limit? If there was a big asteroid with a diameter of say 50km+ in a collision course with the Earth (not orbiting), would it disintegrate into smaller chunks due to the Earth's Roche limit, or the time it will spend in the Roche radius won't be en... | When an object comes within the Roche limit, it breaks up because of tidal stresses - the part closest to the earth feels a stronger gravitational attraction than the furthest part. Hence, the closest part will fall a little faster than the trailing parts.
As a result, "disintegration" does not mean that the body will ... | {
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What's the dimensionality of a solid angle? I haven't seen this explained clearly anywhere. Solid angles are described usually as a fraction of the surface area of a unit sphere, similar to how angles are the fraction of the circumference of a unit circle. However, I don't know how solid angles are actually quantified.... | John Rennie's answer seems fine to me (+1). I'll only add the relevant pieces of the BIPM brochure (PDF, p. 118). BIPM rules.
| {
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Is crystal momentum an operator? My teacher has for Bloch waves the notation $\langle \vec{r}|\vec{k} \rangle = e^{i\vec{k}\cdot \vec{r}}u_{\vec{k}}(r)$ and uses it consistently. However, does this not assume that there is an operator that has eigenstates $|\vec{k} \rangle$? If so, how would such an operator be defined... | It turns out the Bloch states are eigenstates of the translational operator, $T(\vec{R}_{j})$, namely, $T(\vec{R}_{j})\left\vert\vec{k}\right\rangle=e^{i\vec{R}_{j}\cdot\vec{k}}\left\vert \vec{k}\right\rangle$, where $\vec{R}_{j}$'s are lattice vectors. The translation group element $T(\vec{R}_{j})$ has a unitary repre... | {
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Ferromagnets and magnets tend to align in the center. Why is that? When you bring a large iron plate and a magnet, the magnet attracts the iron plate and it tends to slide itself to the center. When I place it on the edge, it always aligns at the center why is that?
| The magnet is attracted to the whole of the plate, so it will be at equilibrium when all the attractive forces from the plate to the magnet are balanced. In the case of a symmetric plate, the point where the magnetic forces between the magnet and the plate are in equilibrium would be the geometric center of the plate. ... | {
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Double slit experiment and representation of light waves Consider the following image from Wikipedia and based on it I have a doubt.
I do not understand why are the light waves represented like the waves in water. Shouldn't the waves be like sine waves. Why is the slit part the starting of a new wave. Secondly, Why do... |
Shouldn't the waves be like sine waves.
That depends on what you want to show. In this particular case, what is shown is the propagation of a particular ray of light.
Why is the slit part the starting of a new wave.
A slit acts as a source of spherical waves. This is the Huygens-Fresnel principle.
This is done to p... | {
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Why does gravity decrease as we go down into the Earth? We all know that gravity decreases as the distance between the two increases. Hence
$$ F = G \frac{Mm}{r^2}. $$
Hence the acceleration due to gravity
$$ g =\frac{F}{m}= G \frac{M}{r^2} $$
increases as $r$ decreases. Then why does it decrease as we go deep into t... | That equation applies for point sources, which the Earth technically is not. We can, however, treat the Earth as a point source as long as its internal structure is irrelevant (i.e. as long as we are outside of it). Once we enter the surface of the Earth, we can no longer simplify it by pretending it's a point and we h... | {
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Definition of quantum anharmonicity I have been reading research papers in mathematical physics for some months now, and I've seen the the term "anharmonic oscillator" quite frequently. At first I assumed that given a Schrodinger equation
$$\frac{d^2u}{dx^2}+(E-V(x))u=0$$
where $E$ is the energy, and $V(x)$ is the pote... | One has to be careful with the given potential. To start with it must be shown that
$$h=-(d/dx)^2+V(x),$$
defines a unique self-adjoint operator $H$, i.e., is essentially self-adjoint. In case
$$V(x)=ax^2+bx^3+cx^4$$
with $c>0$ this is indeed the case. In fact the resolvent of $H$ is compact (these matters are discuss... | {
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Definition of Ohm in SI basic units in words One way Wikipedia defines Ohm is (this is also teached in school):
$$1\Omega =1{\dfrac {{\mbox{V}}}{{\mbox{A}}}}$$
They describe this definition in words, too:
The ohm is defined as a resistance between two points of a conductor when a constant potential difference of 1.0 ... | I would describe it as (example) 120 joules per coulomb (120 volts) divided by 60 coulombs per second (60 amps) equals 2 (ohms) of resistance "which means you have 1/2 or 2 times less the amperes then voltage". so maybe an ohm can be n of VpA (# of volts[SI] per amp[SI] or in this case, # of N Kg per charge for every ... | {
"language": "en",
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The physics of breaking eggs I have to to write an 4000 word research paper for my IB diploma in high school. It is called the extended essay. I was thinking about writing on the physics of breaking eggs. I came up with the idea that their might be some experiments I could do and find the best way to crack an egg. I'm... | I think jinawee's list (among the comments) is a great starting point. There was one interesting series of experiments that I didn't find in that list (at least not in the first 5 pages of the list that I looked through), which were reported in this PRL paper. (If you don't have access to PRL, check out the arXiv versi... | {
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Formation of meniscus If molecules at the surface of a liquid have higher energy and want to minimise the surface area, then why is a mensicus formed which of course increases the surface area?
| The reason is that the gas-liquid surface area is not the only surface area that is minimized. The total energy of the system (including only surface energies) is given by:
$$E=\gamma_{lg} A_{lg}+\gamma_{sg} A_{sg} + \gamma_{sl} A_{sl} $$
Formation of a meniscus as opposed to a flat surface indeed increases $A_{lg}$, b... | {
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While holding an object, no work done but costs energy (in response to a similar question) I read the answer to Why does holding something up cost energy while no work is being done?
and wanting to know more, I asked my teacher about it without telling him what I read here. Instead of referring to muscle cells and biop... | Your teacher's explanation is incorrect. A simple counterexample can be constructed to illustrate this by considering what happens when the role of your arm is replaced by that of a rubber band.
When a weight is suspended from the ceiling by a rubber band, the band stretches and its polymer chains become more ordered,... | {
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Expansion of ideal gas Consider an ideal gas in a chamber (A), separated from another chamber (B) by a diaphragm, in the following two situations:
(1) Instantaneously burst the diaphragm
(2) Plug in an isentropic nozzle so that the gas escapes gradually
Are the two cases identical? I believe there should be some work d... | Assuming the walls of the container are perfect insulators the final steady states must be indentical, as they are determined only by the gas's volume, internal energy and particle number, all of which are the same in both cases. (Internal energy is the same as no energy is transfered to the gas from outside.)
I think ... | {
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The question about Lorentz invariance of the helicity quantum number for the massless particles I need to show that helicity is Lorentz invariant (under the proper Lorentz transformation) for the massless particles. I heard about most frequently used argument which contains an idea of impossibility to "outrun" the mass... | Rotational invariance follows easily from the Poincare algebra. The non-trivial part is the invariance under boosts. Using the Poincare algebra one finds:
$[\frac{J\cdot P}{H},K_i]=i\bigg(\frac{\epsilon_{ijk}K_jP_k}{H}+J_i-\frac{P_i}{H^2}J\cdot P\bigg)\qquad(1)$
So it does not follow from the Poincare algebra that $\fr... | {
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How to get a function for the voltage across a capacitor connected to an AC voltage source? I am looking for the way of obtaining a solution for $V_{c}$ ,as a function of $t$ depending of $\omega$, of the following differential equation related to an electrical circuit involving a low-pass filter : $ \frac{ d V_{c}(t)}... | If you just plug in your suggested solution, you get $$\frac d{dt} A\cos(\omega t + \phi)+\frac 1{\tau}A\cos(\omega t + \phi)=\frac{V_{in}}\tau\sin(\omega t)\\ -A\omega \sin(\omega t + \phi)+\frac 1{\tau}A\cos(\omega t + \phi)=\frac{V_{in}}\tau\sin(\omega t)$$ Now you should be able to use the function sum formulas t... | {
"language": "en",
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The relationship between the energy and amplitude of a wave? Derivation? From multiple online sources I read that
$$E \propto A^2$$
but when I mentioned this in class, my teacher told me I was wrong and that it was directly proportional to amplitude instead.
As far as I know, every website I stumbled upon concerning ... | The poster from that link is saying that the work done by the spring (that's Hooke's law there: $F=-kx$) is equal to the potential energy (PE) at maximum displacement, $A$; this PE comes from the kinetic energy (KE) and is equal to the integral of Hooke's law over the range 0 (minimum displacement) to $A$ (maximum disp... | {
"language": "en",
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The physics of sound boards As a kid I was bemused at why soundboards worked. A small sound could be demonstrably amplified simply by attaching the source to a surface that is rigid and not too thick. How could the volume increase so much given that there was no extra energy added?
As an adult I kind-of-think I know, b... | The soundboard resonates with the same frequencies as the source. It takes it energy form the vibrating source. As the soundboard distributes this energy over a larger volume of air, the sound is louder, but the energy is depleted quicker, limiting the time you hear the sound.
Try this with a tuning fork. Hold it by yo... | {
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Hydrogen atom: potential well and orbit radii I happened to open up an old solid-state electronics book by Sah, and in it he says:
"it is evident that the electron orbit radius is half the well radius at the energy level En"
The orbit radius is $r_n=\frac{4\pi\epsilon_0 ℏ^2 n^2}{mq^2}$ and the potential well $V(r_n)=\f... |
Of course the orbit has to be confined in the well, but it's not obvious to me why it should be exactly half the well radius? This isn't something I recall seeing before either in any other text.
Please keep in mind that when people are speaking of orbits in the microcosm of particles and nuclei, they are speaking ab... | {
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Radiation and absorption Can thermal radiation from a cooler object (B, which emits longer wavelength radiation) ever ADD to the overall thermal energy level of a warmer object (A, which emits shorter wavelength radiation)? Subsidiary question: What exactly happens - at the molecular level - to the longer wavelength r... | The thermal radiation from B does indeed heat object A. The trouble is that A loses energy by thermal radiation faster than the thermal radiation from B can heat it, so the end result is that A cools down.
You can show this very easily. The Stefan-Boltzmann law tells us that the energy flux per unit area is proportiona... | {
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Does electron in wave form have mass? I heard from my lecturer that electron has dual nature. For that instance in young's double slit experiment electron exhibits as a particle at ends but it acts as a wave in between the ends. It under goes diffraction and bends. But we don't see a rise in energy. It has to produce 5... | The so called Copenhagen Interpretation avoids the question about whether the electron is a particle or a wave. This question is directly not allowed. In fact, the wave function is an instrument of the theory with not physical meaning. Acording to CI, the goal of the theory is only to make predictions about the result... | {
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Non-symmetric Lorentz Matrix I was working out a relatively simple problem, where one has three inertial systems $S_1$, $S_2$ and $S_3$. $S_2$ moves with a velocity $v$ relative to $S_1$ along it's $x$-axis, while $S_3$ moves with a velocity $v'$ along $S_2$s $y$-axis.
So I constructed the Lorentz transformation by mul... | Yes, your intuition is correct: two different boosts do contain one rotation, and precisely two boosts along two orthogonal axes contain one rotation around the third orthogonal axis --- the most direct way to see that is by considering that the commutator of two different boosts is one rotation, and more completely th... | {
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What are functions of a complex variable used for in physics? Whenever someone asks "Why are complex numbers important?" the answer, at least in the context of physics, usually includes things like quantum mechanics, oscillators and AC circuits. This is all very fine, but I've never seen anyone talk about functions of ... |
This is all very fine, but I've never seen anyone talk about functions
of a complex variable.
Laplace transform:
The Laplace transform is a widely used integral transform in
mathematics with many applications in physics and engineering. It is a
linear operator of a function f(t) with a real argument t (t ≥ 0) ... | {
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What determines how much electrical charge an object can hold? What determines how much electrical charge an object can hold? Does increase voltage force more electrical charge to be store in an object (Van de Graaff generator), since electric field increase as voltage increase. I don't think it is about relative permi... | It should be associated with the work function, which is the minimum thermodynamic work (i.e. energy) needed to remove an electron from a solid to a point in the vacuum immediately outside the solid surface, and different materials have different work functions.
Consider a very simple case, that a spherical electrical ... | {
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Enthalpy Change in Reversible, Isothermal Expansion of Ideal Gas For the reversible isothermal expansion of an ideal gas:
$${∆H}={∆U}=0 \tag1$$
This is obvious for the case of internal energy because
$${∆U} = \frac {3}{2} n R {∆T} = 0 \tag2$$
and
$${∆U} = -C_P n {∆T} = 0 \tag3$$
For the case of enthalpy it is easy to ... | $$PV =nRT$$
So, for constant temperature, $dU=0$.
$H=U+PV$
The term $d(PV) = 0$ because $PV$=constant
So, $dH=0$
| {
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Bulk flow of air in a long tube between Antarctica and Australia? I have a 5km diameter clear plastic tube which is open at each end and runs from the center of Antarctica to Lake Eyre in Australia. The tube is on the ground where it can be and at sea level on the ocean.
Will there be bulk flow of the air in the tube? ... | I would think the air in the tube will generally flow from Australia to Antarctica: what we have is actually a "smoke stack": the air is hot in Australia, cold in Antarctica, and the altitude in the center of Antarctica is a couple of kilometers higher than the altitude of Lake Eyre (which is below the sea level).
| {
"language": "en",
"url": "https://physics.stackexchange.com/questions/100920",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "6",
"answer_count": 4,
"answer_id": 2
} |
Physical Interpretation of the Bloch vector In the expression of the density matrix of a (Electron-Spin) Qubit
$$
\rho=\frac{1}{2}(I + x \sigma_x + y \sigma_y + z \sigma_z)
$$
where $\tau=(x,y,z)$ is unit vector in the Bloch sphere, which is the physical Interpretation of $\tau$? Can it be interpreted as the direction ... | Performing explicit but trivial computations, it turns out that (assuming $\hbar=1$): $$\tau/2 = (\langle S_x\rangle_\rho, \langle S_y\rangle_\rho, \langle S_z\rangle_\rho)$$
So $\tau/2$ describes the expectation values of the three components of the spin
when the system is in the, generally, mixed, state $\rho$.
Ind... | {
"language": "en",
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"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "2",
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Taking pivot about an accelerating point Given this question:
A small ball of mass $m$ and radius $r$ rolls without slipping on the inside surface of a fixed hemispherical bowl of radius $R>r$. What is the frequency of small oscillations?
The standard solution is to write Newton's second law for the ball and then t... |
My question is since both pivots that we have chosen are accelerating, why are not fictitious forces considered?
Pivot is accelerating if it is a geometric point defined as the point of contact. Pivot is not accelerating if it is the material point of the small ball; it stands still and has zero acceleration. The des... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/101110",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "6",
"answer_count": 2,
"answer_id": 1
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Confused about Impulse Encountered a problem that involves impulse while studying for my exam and I'm not sure how to even approach it. I know that momentum is conserved, but I'm not sure how to relate that to avg force. Maybe someone can help point me in the right direction? I know that it's in quadrant III, through i... | The total impulse is the change in momentum (note that this is a vector equation):
$$ \vec{I} = \vec{p}_{final} - \vec{p}_{initial} $$
You know the momentum before and after the collision so you can calculate the total impulse, both magnitude and direction. Impulse if force times time, so the direction of the force wil... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/101226",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "1",
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Fermi-Dirac distribution derivation? I am trying to derive the Fermi-Dirac statistics using density matrix formalism.
I know that
$$<A>= Tr \rho A.$$
So I started from
$$<n(\epsilon_i)>= Tr \rho n(\epsilon_i)=\frac {1}{Z} \sum e^{-\beta \epsilon_i n_i}n_i=\frac {1}{Z} e^{-\beta \epsilon_i}. $$
In the last passage I u... | The derivation of the Fermi-Dirac distribution using the density matrix formalism proceeds as follows:
The setup.
We assume that the single-particle hamiltonian has a discrete spectrum, so the single-particle energy eigenstates are labeled by an index $i$ which runs over some finite or countably infinite index set $I$.... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/101408",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "3",
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Does the equation of continuity hold for turbulent flows? My textbook mainly deals with laminar flows. The book derives the equation of continuity, which states that the cross-sectional area times the velocity of a flow is always constant. But nowhere in the derivation does the textbook explicitly assumes that the flow... | Continuity is just the principle of conservation of mass in differential form.
The full continuity equation is (in index notation):
$\frac{\partial \rho}{\partial t} = -\frac{\partial }{\partial x_i}(\rho u_i)$
For example, consider an infinitesimal control volume (CV). The equation says that the local $\rho$ (inside t... | {
"language": "en",
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"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "3",
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Does a mirror help a near-sighted persion see at a distance clearer? A near-sighted person without eye-glasses can not clearly see things at distance.
If he takes a photo of the things at distance, he can see the things from the photo much clearer, because he can place the photo much closer to his eyes.
If he turns his... | does a flat transparent glass make near-sighted people see farther? the answer to this question is the answer to yours.
| {
"language": "en",
"url": "https://physics.stackexchange.com/questions/101627",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "22",
"answer_count": 8,
"answer_id": 3
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Wrong positioned Ampere-meter and Voltmeter I'm dealing with a problem here and even that I'm trying to solve it i can't
It says:
In what figures the voltmeter and ampere-meter are wrong positioned?
I think that all the the others are correct except the second one.
Can anyone help me?
| It's quite opposite. All are correct except the second one. Ampere-meter should be positioned in series configuration and voltmeter should be positioned in parallel configuration to the measured element. Notice that voltmeters should have very high resistance, so that most of the current will flow through the measured ... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/101701",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "1",
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x-ray in oil droplets experment In oil droplet experiment, x-ray makes the air molecules negatively charged. How does that work? X-ray carries high energy and ionizes air, doesn't that make air positively charged?
| I recently did this lab and the answer I got to this question was:
The x-rays ionize the air molecules or gas in between the capacitors. The free electrons then fly off and attach them selves to the oil drops. Alternatively, you could use an electron beam (same effect).
| {
"language": "en",
"url": "https://physics.stackexchange.com/questions/101811",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "2",
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Does putting color filters make the sources incoherent? In Young's double slit experiment a single source is used to illuminate two slits which then acts as two coherent sources to produce interference pattern. But, what if I put color filters on the two slits. Will it make the slits incoherent?
I myself think yes beca... | This will not happen because color filters don't work like this.
A red color filter does not convert blue photons to red photons. It absorbs photons that are not red (most of them) and lets red photons pass unaffected. If you use a red filter for one slit then a blue photon will not go through that slit at all, so you ... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/101867",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "2",
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The best way to cool the teapot My professor today in the class made us a question:
"Lets say we have a teapot with water in it.The water is hot.Now we want to cool the water.
Will it cool faster if we put an ice cube above the teapot or under the teapot."
My answer was the it will cool faster if we put the ice cube ab... | Open or not open, touching or not touching, ice cube above is better than ice cube below where cooling of the pot is concerned.
Your choice is correct but it is more accurate to say that air cooled by the ice cube sinks onto the teapot thereby cooling it (note that this mechanism cannot occur if the cube was under the... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/101915",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "1",
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Why doesn't diamond glow when hot? In an answer to this SE question, the respondent explains that heating a perfect diamond will not cause it to glow with thermal blackbody radiation. I don't quite follow his explanation. I think it comes down to: there is no mechanism for diamond to generate light in the visible re... | I bet that diamond will glow. you may not have heard of quenching before, but Soviet opticians love to tell the story of Vavilov. he studied luminescence, and before photomultipliers were invented, he used sit in the dark room for hours. the eye would get used to darkness, and become very sensitive. the observer would ... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/101960",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "11",
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Unusual observation in photoelectric effect simulation I was studying a photoelectric simulation (http://phet.colorado.edu/en/simulation/photoelectric) and I observed a really unusual thing. When I held intensity and potential at a constant value and then varied the frequency I observed that there was peak in photocurr... | You are increasing the energy of each photon, but holding the intensity constant. If you do this, fewer and fewer photons are leaving the lamp, so fewer and fewer are hitting the metal. This is probably the effect you are seeing.
| {
"language": "en",
"url": "https://physics.stackexchange.com/questions/102044",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "1",
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Can Information Travel Faster Than The Speed Of Light? Many believe that nothing can travel faster than speed of light, not even information. Personally, i think theoretically information can. Consider this following imaginary experiment:
Imagine we are living on a planet that is big enough for a, let's say, 10-light-s... | The idea that the pendulum would drop instantly isn't even true of short, Earth-bound pendula: c.f. various Internet videos about dropping slinkies (toy springs).
The reason why slinkies drop in this way is essentially the same reason why an idealised pendulum (strong enough to hold itself together, albeit maybe not as... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/102106",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "4",
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Energy in a Solenoid?
Consider a circuit consisting of a battery, a resistor and a solenoid inductor. Then, the emf $\mathcal{E}$, is defined as:
$$\mathcal{E} = L\frac{di}{dt} + iR$$
Multiplying both sides by $i$ gives:
$$\mathcal{E}i = Li\frac{di}{dt} + i^2R$$
The term on the left side gives the rate at which the ba... | 1) With a constant and DC power source eventually the solenoid will become fully 'charged'. At that point its 'resistance' term vanishes because it no longer produces an emf against the battery. At this point, the $\frac{di}{dt}$ term will be zero, because the current isn't changing.
2) When you cut power, the magnetic... | {
"language": "en",
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"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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How does a half-life work? Carbon-14 has a half-life of 5,730 years. That means that after 5,730 years, half of that sample decays. After another 5,730 years, a quarter of the original sample decays (and the cycle goes on and on, and one could use virtually any radioactive isotope). Why is this so? Logically, shoul... | I think you're confused simply by the language. Remember that it's a quarter of the original sample. So it's like compounding interest in the bank. You start with initial principal, once the interest is compounded, you might say that the percentage of that principal is ADDED TO the "principal", and then a percentage of... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/102222",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "33",
"answer_count": 13,
"answer_id": 8
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Prove identity of partial derivatives I can not do the following problem:
Prove the identity:
$$\left( \frac{\partial x}{\partial y} \right)_{z}\left( \frac{\partial y}{\partial z} \right)_{x}\left( \frac{\partial z}{\partial x} \right)_{y}=-1$$
State the properties that must be $x=x(y,z)$, $y=y(x,z)$, $z=(x,y)$.
The t... | $x=x(y,z)$, $y=y(x,z)$, $z=(x,y)$
$$dx= (\frac{\partial x}{\partial y})_z dy + (\frac{\partial x}{\partial z})_y dz$$
$$dy= (\frac{\partial y}{\partial x})_z dx + (\frac{\partial y}{\partial z})_x dz$$
$$\therefore dx= (\frac{\partial x}{\partial y})_z [(\frac{\partial y}{\partial x})_z dx + (\frac{\partial y}{\partial... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/102278",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "3",
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Why are free electrons free? This is what I understand so far: in a conductor, the ions have a weak pull on the valence electrons. So when an electric field is applied, the free electrons are able to easily move about. Makes sense.
In a neutral conductor with no electric field, the free electrons aren't bound to any io... | In a single free atom, electrons have well defined energy levels and are somewhat bound to atom. Consider the following quantum mechanical model of atom to get an idea about an isolated atom.
When all this isolated atoms come together to form the crystal, the atoms do not have well defined energy levels. There will b... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/102345",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "3",
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"answer_id": 1
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A paradox to Lenz's law I have read that in simple words, Lenz's law states that:
The direction of current induced in a conductor is in such a fashion, that it opposes its cause.
This validates law of conservation of mass-energy.
I arranged the following thought experiment:
Let there be a pendulum with its bob being ... | Actually pendulum wont oscillate forever.Its energy turns into heat in resistor.In other word it's domain would be something like this figure.
| {
"language": "en",
"url": "https://physics.stackexchange.com/questions/102556",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "5",
"answer_count": 7,
"answer_id": 3
} |
Some questions about Dirac spinor transformation law I have perhaps meaningless question about Dirac spinors, but I'm at a loss.
The transformation laws for for left-handed and right-handed 2-spinors are
$$
\tag 1 \psi_{a} \to \psi_{a}' = N_{a}^{\quad b} \psi_{b} = \left(e^{\frac{1}{2}\omega^{\mu \nu}\sigma_{\mu \nu}}\... | I think it is convention to write the conjugate Weyl fermion in,
\begin{equation}
\left( \begin{array}{c}
\phi _\alpha \\
\bar{\kappa} ^{\dot{\beta }}
\end{array} \right)
\end{equation}
(it is common to put a bar over the conjugate representation), with a raised index in order to comply with the ${} _{ \dot{\... | {
"language": "en",
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"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "3",
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Understanding fields and their correlation to forces I seem to be confused between the concept of a "force", and a field.
Now let's assume there is a magnetic field of $1$ $\mathrm{Tesla}$, what does that mean in relation to force?
Finally, if field is $1$ $\mathrm{Tesla}$ does that always mean, the force at that field... | A force is experimented by a charge when you put in in presence of a field. The strength of the force is a function not only of the strength of the field, but also of the strength of the charge. So, in a given electric field, a larger charge will experience a larger force. The classical concept of a field is more usef... | {
"language": "en",
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"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "1",
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Schrödinger's Equation and its complex conjugate I would like to know why there is a minus sign on the right-hand side of the Schrödinger's complex conjugate equation, whereas in the Schrödinger's equation there isn't. I know it is a simple question, but I don't know where this comes from.
$$
-\frac{\hbar^2 }{2m}\frac{... | It is the definition of complex number. Let's say
$z=x+iy\quad \Rightarrow z^*=x-iy$
$z=x-iy\quad \Rightarrow z^*=x+iy$
In simple words, you just have to change the sign of the Imaginary part. The thing is that $\psi(x)$ it's a imaginary number, so it's conjugate it's just $\psi^*(x)$. If you have the $\psi(x)$ functio... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/102838",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "4",
"answer_count": 3,
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Bogoliubov transformation with a slight twist Given a Hamiltonian of the form
$$H=\sum_k \begin{pmatrix}a_k^\dagger & b_k^\dagger \end{pmatrix}
\begin{pmatrix}\omega_0 & \Omega f_k \\ \Omega f_k^* & \omega_0\end{pmatrix} \begin{pmatrix}a_k \\ b_k\end{pmatrix}, $$
where $a_k$ and $b_k$ are bosonic annihilation operators... | I would just like to point out that the given Hamiltonian does not require a Bogoliubov transformation to be diagonalized, since it is of the form of a single-particle operator (nevertheless in second quantization) i.e. does not contain 'off-diagonal' terms of the form $a a$,...
You can simply diagonalize it by diagona... | {
"language": "en",
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"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "7",
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Charge distribution on conductors?
You have seen that the excess charge on an isolated conductor moves entirely to the conductor’s surface. However, unless the conductor is spherical, the charge does not distribute itself uniformly. Put another way, the surface charge density s (charge per unit area) varies over the s... | The fact that the static charge does not spread uniformly is the basis for things like lightning rods. Sharp edges are places that static charges, particularly higher voltage ones, like to reside. This design also aids in dissipating dangerous voltages via the coronal (ionized air) discharge mechanism.
Sometimes, the... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/103048",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "10",
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Prove EM Waves Are Transverse In Nature Why we say that EM waves are transverse in nature? I have seen some proofs regarding my question but they all calculate flux through imaginary cube. Here is My REAL problem that I can't here imagine infinitesimal area for calculating flux because em line of force will intersect (... | An EM wave is generated by the oscillation of an electron. Near the electron we have the near field and here all the wave components are non-zero. Far away from the source we have the far field and it is in the form of a spherical surface wave advancing along the radius of a sphere with centre at the source. If we take... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/103171",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "3",
"answer_count": 4,
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Can geodesics in a Lorentzian manifold change their character? From a physics perspective, it's pretty easy to see why a a massive particle will be restricted to timelike paths, etc. but does the math guarantee that on its own or do we have to impose it? More specifically, given an arbitrary smooth Lorentzian manifold,... | There is a conserved quantity for geodesics which comes from the fact that the metric $g_{ab}$ is (trivially) a Killing tensor, i.e.
$$\nabla_{(c}g_{ab)} = 0.$$
Any tensor $\xi_{ab}$ that satisfies $\nabla_{(c}\xi_{ab)}=0$ gives rise to the conserved quantity $\epsilon = u^a u^b\xi_{ab}$, which is preserved along geode... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/103215",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "3",
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Effect of linear terms on a QFT I was told when first learning QFT that linear terms in the Lagrangian are harmless and we can essentially just ignore them. However, I've recently seen in the linear sigma model,
\begin{equation}
{\cal L} = \frac{1}{2} \partial _\mu \phi _i \partial ^\mu \phi _i - \frac{m ^2 }{2} \phi ... | Adam's answer from a slightly different perspective. Linear terms are source terms, which are essentially equivalent to boundary conditions. Allowing nontrivial boundary conditions considerably enriches the mathematical behavior these models exhibit. In particular, you shouldn't be surprised that boundary conditions... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/103328",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "19",
"answer_count": 3,
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what determines the wavelength of waves on the open ocean? Looking at the picture below, you can totally see that these are tiny boats.
The water is practically washing over the hull of these boat models.
But the water has boundaries that are very far away, and even if the water is very deep, it would (at least in my... | This is really just a footnote to Ross' answer as Ross is quite correct and the link he provided contains the information you asked for.
In the open sea waves are normally produced by the wind. When the wind hits the sea surface it creates essentially random patterns of pressure variation and these lift some parts of t... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/103395",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "6",
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How does one exert greater force on the ground by jumping? When one jumps, how does he/she manage to exert greater force on their ground than their weight?
Also, what is normal force and the reaction force (are they the same thing?) and by newton's third law, shouldn't the reaction(weight) when we are standing on the ... | There's still something missing from all the answers so far. When you drop something on the ground, say, a rock of mass $m$, by the time it makes contact with the ground it's traveling at a velocity $v$ and thus has momentum $p = mv$. To be stopped completely, its momentum has to equal $0$ at the end. So you have a tot... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/103473",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "3",
"answer_count": 6,
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Why don't the leaves of an electrometer repel each other in water? A normal electrometer filled with air will repel like it should do for electrostatic demonstration, but what if it is filled with water instead or even oil, what will happen?
My guess is that the water is charged too, making the net repelling force equ... | If the electrometer leaves are wetted by the liquid, capillary forces (wicking) will pull them together and not allow them to easily separate.
DOI: 10.1021/la902779g
DOI: 10.1109/84.232594
DOI: 10.1021/ja983882z
http://web.mst.edu/~numbere/cp/chapter%203.htm
3.1.4 Application to Parallel Plates
Take two clean mi... | {
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"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "1",
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What is the exact relation between $\mathrm{SU(3)}$ flavour symmetry and the Gell-Mann–Nishijima relation I'm trying to understand how the Gell-Mann–Nishijima relation has been derived:
\begin{equation}
Q = I_3 + \frac{Y}{2}
\end{equation}
where $Q$ is the electric charge of the quarks, $I_3$ is the isospin quantum num... | Indeed, the formula only appeared empirically in 1956, before the eightfold way, for hadrons, long before quarks; and was seen to be such a basic fact that it informed the way flavor SU(3) was put together; and was subsequently spatchcocked into the gauge sector of the EW theory a decade after that--hence the alarming ... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/103717",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "7",
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Should theory be the appropriate term? Should theory be the appropriate term? I mean, for example, because of the quantum field theory we have been able to find the subatomic particles that it theorized and make the Standard Model. Why then is is labeled as a theory? Also wave-particle duality is widely accepted fact y... | From http://en.wikipedia.org/wiki/Scientific_theory:
"Scientific theories are testable and make falsifiable predictions. They describe the causal elements responsible for a particular natural phenomenon, and are used to explain and predict aspects of the physical universe or specific areas of inquiry[...]. Scientists u... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/103813",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "1",
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Should water cool faster if is inserted metal canister with ice inside either mix only with ice? Let's say that we have two canister first bigger (metal canister 2l) with 1l of water at 100C, and second smaller (metal canister 1l) with 1l of ice. And we want to cool down boiled water to 50C. So we will insert ice (only... | Ice absorbs heat from the boiling water by melting. That means, if you put ICE in water, it increases the volume of liquid and their by its mass. if you are considering only the temperature(Not volume) initially and finally, the ice dropped in the canister will be faster, because even after melting of ice, cool water +... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/103861",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "3",
"answer_count": 2,
"answer_id": 1
} |
Creating electricity from mains water pressure. Could someone cleverer than me help me out?
I had a crazy thought going through my head the other day and I can't lay my mind to rest until I get an answer.
Q. How much energy could be produced by using mains water pressure to turn a generator? And would it be feasible ... | You could certainly make electricity this way, it just wouldn't be cost effective. 3-4bar would be the same pressure as a 30-40 meter hydroelectric dam. The energy per time unit depends upon the flow rate (which depends upon the 4th power of pipe diameter).
potential energy = pressure X volume
I wouldn't want to se... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/103949",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "3",
"answer_count": 5,
"answer_id": 0
} |
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