Q stringlengths 18 13.7k | A stringlengths 1 16.1k | meta dict |
|---|---|---|
Does the Lorentz transformation necessary follow from the two postulates of relativity? The two postulates of special relativity are:
The choice of what inertial frame to use is arbitrary: all laws of physics are invariant. (the principle of relativity)
The metric $$(\Delta s)^2 = (\displaystyle\sum_{\mu=1}^3 \Delta x... | In some sense it is not the only possibility. And that's ignoring the obvious typos like missing signs or inconsistent use of superscripts and subscripts, and the fact that your equations require velocities to be dimensionless to even be dimensionally correct.
In particular the first principle tells you next to nothing... | {
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What happens to a body if it rotates extremely fast? I am thinking on a object, e.g. ball or planet that starts rotating with increasing speed. Let's assume that his speed get's closer to the speed of light, what happens to this object? There are several forces acting. But I always get caught thinking that it will get ... | Note that "c" means linear velocity, not angular. Then, you would refer to tangential velocity.
If an object rotated at relativistic (tangential) velocity, then each "shell" will have a different space and time compression. By contraction of the tangent lengthes, the perceived length of large circles would be smaller t... | {
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Prospects for detection of gravitons? With the announcement of the detection of gravitational waves, questions about the implications proliferate. Some relate to the possible existence of gravitons. The analogous relationship between gravitons/gravitational waves and photons/electromagnetic waves is frequently mentio... | Well, phenomenologists never give up. Here is a paper peer reviewed which explores the discovery of gravitons in future, but not too far future, colliders.
All one needs is large extra dimensions in a string theoretical model, to give predictions.
Two birds with one stone, graviton and extra dimensions.
Edit with new ... | {
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What actually is the event that we think we have detected with gravitational waves? This answer shows the "event" that is creating excitement. It looks to the untrained eye like a single "blip" on a detector. It appears to last less than a second.
It is, later in the answer, referred to as a "black hole merger".
Are ... | The signal was fit to that produced by two black holes merging, with each having a mass of roughly 30 times that of our sun. For a solar mass the Schwarzschild radius is about 3 km. So that means the black holes, if off by themselves, would have an event horizon radius of about 90 km.
Only right near the end of their... | {
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Would you hear a gravitational wave, if its amplitude and frequency were suitable? If there was a source of a continuous gravitational wave at (say) 50hz, and amplitude of say a micrometer (a typical sound wave displacement, I think), and you were nearby (standing happily on a planet in an atmosphere), with your ear po... | I don't see how you could hear gravity waves even if they were of the appropriate frequency and amplitude. Hearing depends on the motion of hairs in the vestibular system, specifically the relative motion between the hair and its attachment in the cochlea. If a gravitational wave were to pass, all parts of the organ wo... | {
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Is the Landauer limit reversible As I understand it, the Landauer limit, $kTln(2)$, is the minimum amount of energy to erase a bit. Is it also the minimum amount to create a bit? I'm asking statistical, like Avogadro's number of bits, i.e., $RTln(2)$.
My thinking: $RTln(2)$ is the work required, probably both ways (... | To create a bit in some defined state like 0 takes energy $kT\ln(2)+W$, where $W$ is the work required to create whatever the bit is made of (a flip-flop, a particle with spin, etc.). The first factor is just the Landauer cost of setting it in a definite state. As you say for a mole of bits you will have to pay at leas... | {
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Somewhat unusual projectile motion question
A stone must fly over two walls of height $h_1$ and $h_2$ $(h_2~ > ~h_1)$ from the side of the lower wall. The distance between the upper points of the two walls near which the stone's trajectory lies is $L$. Find the minimum velocity of the stone. (source: AN Matveev's Mech... | The problem is kind of hard to solve if one is not careful. One can write the satisfying equations but still might not be able to find the answer. I will outline a way to this.
The idea is that at the minimum required velocity the projectile just touches the top of the walls. Let the velocity and angle of projection at... | {
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Vacuum is not really empty Vacuum should contain something in it. Because nothing is perfectly empty that's what I feel, but what is there left in it? Is there any matter or its just enegry. Can energy be pulled out of some space?
| In quantum field theory, the vacuum is the state containing exactly zero particles anywhere in space and at all times. Since it is an eigenstate of the number operator, there is no uncertainty at all about this.
On the other hand, empty space between matter (i.e., what is informally called a vacuum) is never completely... | {
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Homogenuous Maxwell Equations in the Language of Differential Forms
*
*I understand that if I define electric field to be $E=E_i dx^i$, magnetic field to be
$B=B_1 dx^2 \wedge dx^3 + B_2 dx^3 \wedge dx^1 + B_3 dx^1 \wedge dx^2 $, and field strength to be $F= dx^0 \wedge E + B$, I would get the two homogenuous Maxwel... | *
*Yes, written in terms of the gauge potential $A_{\mu}$, the source-free Maxwell equations become trivially satisfied.
*It seems OP is using the electrostatic definition of $E_i$. In full electromagnetism, besides the $\partial_i A_0$ term, there is also a $\partial_0 A_i$ term in the definition of $E_i$.
See als... | {
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If pencil tip is heated why doesn't it write? Why doesn't a pencil write if its tip is heated in a candle flame?
| The reason must come from the hardening it experiments under fire.
Pencils' leads (the writing core) are made today of a mixture that contains clay (see for example this patent) which hardens under the heat, but mose importantly, the compound will loose the softness because of the separation of salts under the heat.
Th... | {
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What is the dielectric constant of a pure conductor? Dielectric constant is the ratio of permittivity of a medium to the permittivity of free space. How to find dielectric constant of a conductor?
| The permittivity of a conductor is infinite.
Let the value of an external electric field in free space (relative permittivity = 1) be $E$.
If this is applied to a material of relative permittivity $\epsilon_r$ then the electric field in the material is $\dfrac {E}{\epsilon_r}$
Inside a conductor the electric field i... | {
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Why absorption spectum is not identical to emission spectrum? Hydrogen emission and absorption spectral lines are typically depicted as the same:
(source)
However, in more complex systems, the emission and absorption spectra are significantly different. For example:
Absorption and photoluminescence spectra of DCJTB d... | As @MikaelKuisma mentioned, the reason for this difference is the contribution of nuclear vibrational overlap to the transition moment. When an electron is excited from a ground state $S_0$ to the first excited state $S_1$, the bond is stretched and the internuclear separation increases:
(source: Martin Pope and Charl... | {
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Practical time travel: time dilation above the event horizon Imagine there is a huge black hole with very small gravity gradient so that one doesn't get killed by spaghettification after even nearing the event horizon.
Now imagine a very curious creature wanting to know how the universe would evolve. Even though it is... | time travel between horizon and sigularity = $\pi G M/c^3$.
i.e. a 100th of second for M = 1000 solar mass.
| {
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Confusion on Time and Ensemble Averages of Classical Harmonic Oscillator Assume we have a classical harmonic oscillator
$$ \ddot{x} = -k^2x.$$
Then the general solutions are of the form
$x(t) = x_0cos(kt) + \frac{v_0}{k}sin(kt)$ where $x_0$ and $v_0$ are initial conditions. Lets assume that $x_0=0$. The time average of... | First, your Hamiltonian is wrong; you should be getting $(\beta~k)^{-1}$ for the force $k x$.
Second, your definitions of $k$ are going to be slightly off; the Hamiltonian $\frac12 m v^2 + \frac12 k x^2$ corresponds to the dynamics $\ddot x = -\omega^2 x$ only for $\omega^2 = k/m.$ Best then to write $\frac12 m (v^2 +... | {
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Why does LIGO have an arm length of few kilometers? Is the distance dependent on Gravitational Wave wavelength? Antennas for capturing radio waves need to have $\frac{\lambda}{2}$ length for optimum reception of signal. Does it imply LIGO arm length is $\frac{\lambda}{2}$ of Gravitational Wave it is trying to capture?... | Pretty close. The effective LIGO arm length is 1600km (the light beam is reflected forth and back 400 times). LIGO is most sensitive at approx. 150Hz (advancedligo.mit.edu/summary.html), which would be a wavelength of 2000km... so the LIGO arms are approx. $\lambda /2$. The noise minimum depends on the noise spectrum, ... | {
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How does gravitational wave compress space time? My question came from the talk of how gravitational wave stretches and compresses space time.
Say there are two protons that are 1 centimeters apart, as a G-wave passes through them, would the electrostatic force experienced by the protons change?
What about Plank's cons... | Suppose we choose our coordinates so both protons are on the $x$ axis, at $x = -0.5$cm and $x = +0.5$cm:
The distance $d$ between the protons is obviously 1cm - well, that may seem obvious but actually it's only true in flat spacetime. More generally the geometry of spacetime is described by a quantity called the metr... | {
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Is it wrong to say that an electron can be a wave? In QM it is sometimes said that electrons are not waves but they behave like waves or that waves are a property of electrons. Perhaps it is better to speak of a wave function representing a particular quantum state.
But in the slit experiment it is obvious to see that... | The rules of how electrons move are analogous to waves because an internal state is cyclic and different possible paths are summed showing an interference pattern.
That's not the same as saying that electrons themselves are waves. The formulas for waves are used to explain where to find an electron.
| {
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Force on current carrying square loop I'm asked to find force on square loop (side a) carrying current $I$, flowing counter clockwise, when we look down x-axis, lying in yz plane. the loop is centered at the origin. The magnetic field is given as:
$\vec{B} = kz\hat{x}$
Its solution states that force on left an right ca... | You are correct, and the "solution" is apparently in error. The force on the top leg is equal and opposite to the force on the bottom leg. They cancel just as the forces on the left and right legs do. There is no net force on the loop.
| {
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Question about source terms in scalar quantum field theory I'm having a bit of a mental block when trying to interpret the inhomogeneous Klein-Gordon equation $$(\Box +m^{2})\phi(x,t)=j(x,t)$$
In particular, how does one interpret the term on the right-hand side of the equation, $j(x,t)$ as a source term for the scalar... | Generally, source terms are what stands in the rhs of the differential equation $$\hat{\Theta}_x f(x) = j(x),$$ where $\hat{\Theta}_x$ is some linear differential operator (in your case $\hat{\Theta}_x = \Box_x + m^2$).
A generic solution of this equation is a sum of any solution of the homogeneous equation $\hat{\Thet... | {
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Is the local Lorentz transformation a general coordinate transformation? There is a saying in Nakahara's Geometry, Topology and Physics P371 about principal bundles and associated vector bundles:
In general relativity, the right action corresponds to the local Lorentz transformation while the left action corresponds t... | Here I answer on the question from the title.
There is some feature which is related to the spinor representation of the proper Lorentz group. In fact, there is homomorphism $SL(2, C) \to SO(3,1)$, whose core contains two elements - unity and minus unity. The second one corresponds to representation
$$
T(N)= -T(-N), \q... | {
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Gravitational waves induce changes in the $h_{00}$ (time) component of the metric? I'm rather stumped by a subtle point regarding metric perturbations of GW. I'm well aware the GW are able to produce changes in the flat space metric, They are transverse and have planes of polarizations (namely $\times$ and $+$). Howeve... | Group theoretically you can split the graviton $h_{\mu \nu}$, where as usual $g_{\mu \nu}=\eta_{\mu \nu}+h_{\mu \nu}$, in 3 irreducible representations of $SO(3)$:
$$h_{00} \rightarrow Spin \, 0 \; (Scalar)$$
$$h_{i0}\rightarrow Spin \, 1 \; (Vector)$$
$$h_{\mu \nu}\rightarrow Spin \, 2\; (Tensor)$$
Before choosing a... | {
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Is there a theory where there are (recursively) infinitely smaller particles? So I read that electrons are just points, with no mass, and furthermore, protons look like they have some "size" but that's really 3 "point-like" quarks. We first thought atoms were the smallest possible particle. Then we thought the same abo... | There is no such popular theory now, but I understand a somewhat similar idea was kicked around in the 70's, before the Standard Model was worked out. This was associated with the "Bootstrap model" of Geoffrey Chew. I am both too young and in the wrong subfield to give you a very detailed account of how this works, but... | {
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Why do charged particles follow magnetic field lines? This may seem like a dumb question, but I can't think of the answer. The context I am curious about is the solar wind. Specifically particles flowing out of coronal holes and following the magnetic field lines arching out into space. Why do both the positive and neg... | Background
In the absence of an electric field, a charged particle experiences a force that is perpendicular to the magnetic field and its velocity relative to that field, called the Lorentz force. This is given by:
$$
\mathbf{F}_{s} = q_{s} \ \mathbf{v}_{s} \times \mathbf{B} \tag{1}
$$
where $q_{s}$ is the charge of ... | {
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How does the drift velocity of electrons in a conductor depend on the temperature? How does the drift velocity of electrons in a conductor depend on the temperature?
I have two contradicting views for this.
*
*First, we can say that increasing the temperature of the conductor will increase the kinetic energy of the... | Let us consider the following equation:
$$i=ev_dAn$$
where $i$ is the current passing through the material, $e$ the amount of charge on the charge carrier (here it's the charge on an electron), $v_d$ is the drift velocity, $A$ is the area of cross section of the material and $n$ is the number of charge carriers per uni... | {
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Ammeter range and shunt resistance Its said that for an ammeter to give good reading, the full current in the circuit must pass through it. But if I am right, the ammeter is basically a galvanometer connected parallel to a very low resistance called a shunt. I am aware that connecting a low resistance in parallel wil... | An Ammeter which is a current measuring device has some limitations. If the instrument is designed as a moving coil galvanometer -it can measure small currents and the maximum limit may be about 30 micro amperes.
Therefore one uses a shunt resistor to share larger part of the current and limited(within range ) curre... | {
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In solids, is it phonons, or is it the oscillations of electrons in bands, that emit most of the blackbody radiation? In solids (most any object we see), which tends to emit most of the blackbody radiation: phonons (atomic, or molecular dipole, lattice vibrations) or oscillating electrons in their energy bands?
| Excellent question. The excitations involved are from occupied conduction (metals) or valence states (insulators, semiconductors) to unoccupied conduction band states. These form a continuum so can emit a continuous black body spectrum. These excitations are also responsible for the dielectric response.
| {
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How is a human voice unique? Well, I am quite new to concepts of vocal sounds. From the physics point of view I believe a sound has two basic parameters i.e, frequency and amplitude.
Considering the end sound wave produced by human voice it must have frequency and amplitude as parameters. Well, when a human can speak i... | A "pure tone" is a sound that has a single sine function as its pressure profile. The human voice is not a pure tone; it is a superposition of many different sine waves with different frequencies and different amplitudes. Here is an image illustrating how many sine waves of different frequencies can combine to make a m... | {
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Holonomic and Topological Quantum Computing In topological quantum computation, anyons are braided in spacetime, performing non-trivial evolutions of some degenerate groundstate.
In holonomic quantum computation, the system is braided in parameter space, performing non-trivial evolutions of some degenerate groundstate ... | In brief, the holonomy depends on the area enclosed by the path in parameter space, and is therefore sensitive to perturbations of the path, e.g. its length. In contrast, a topological evolution is largely independent of the path geometry, and depends only on topological data, specifically homotopy (e.g. how many times... | {
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A counterexample to the law of stable equilibrium? This is the law of stable equilibrium, according to Hatsopoulos and Keenan:
A system having specified allowed states and an upper bound in volume can reach from any given state one and only one stable state and leave no net effect on its environment.
Consider the fol... | The system is not in a stable state as long as the temperature in the two containers is different.
It might take some time for the heat to flow through the string.
| {
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What is the difference between gravitational force and gravitational field? I see two different formulas describing gravity:
$$F=\frac{GMm}{r^{2}}$$
$$g=\frac{F}{m}$$
But I don't understand the difference between gravity as a force and its field as a vector.
| Gravitational force depends on both the source mass and the test mass while the field is purely a property of the source mass.
For concreteness, consider the gravitational force acting on a person of mass $m$ due to the Earth having mass $M$. The gravitational force on the person is then given by \begin{equation}F=\fra... | {
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Voltage Drop and Current Flow Assume we have a source @100 DC volts in series with a 200 ohm resistor. According to Ohm's Law, current flow in 0.5 amps. Voltage drop across this resistor is 100 volts and equal to the source voltage. If voltage drop is 100 volts(meaning none is left on the "outflow" or neg. side of the... | This problem is an idealization; real batteries have an internal resistance, and so do the wires.
In this idealized circuit the wires have no resistance, nor do the connections. You can logically collapse them to points -- and this brings the battery terminal into contact with the resistor; the current has obeyed Kirc... | {
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How can we define a velocity for quantum objects? I have a question about quantum mechanics: I know that velocity is defined as the change of position with time, $v = \frac{\mathrm{d}x}{\mathrm{d}t}$.
In quantum mechanics, the position of a particle is not certain, but of a statistical nature. How can we define a veloc... | In the Heisenberg picture of quantum mechanics, the position operator is itself time-dependent, and you may just define the "velocity operator" $\dot{x}$ as in classical mechanics. However, the Heisenberg equation of motion says
$$ \dot{x} = \mathrm{i}[H,x]$$
and e.g. for a free particle with $H= \frac{p^2}{2m}$, we ha... | {
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Rayleigh equation as explanation for sky being blue I've been reading up on the internet as to why the sky is blue. The answer usually cites Rayleigh scattering that I've checked on wikipedia: https://en.wikipedia.org/wiki/Rayleigh_scattering:
$$
I=I_0 \frac{1+\cos^2\theta}{2R^2}\left(\frac{2\pi}{\lambda}\right)^4\left... | Rayleigh Scattering was calculated using classical theories of EM radiation.
Perhaps you should also look at Quantum Spectroscopy explanations. Scattering is different from absorption, at dawn and dusk water vapour has a greater effect, hence "Red sky at Morning/Night'.
Also consider the sky colour on Mars, where ve... | {
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Semiconductors, Solid-State Physics We know, that conductors, conduct because their valence energy band is "half" full, and k ("wave vector") can increase and therefore the electrons under the influence of a electric field can "move", and similarly insulators wont conduct, because ther valence band is full, and we have... | You said it here:
we have a "big" energy gap between the valence and conductivity band.
If you supply enough energy, electrons will jump to the conduction band (become excited). Semiconductors and insulators do not have many differences, it is simply called insulators when the gab is big, and semiconductors when smal... | {
"language": "en",
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"timestamp": "2023-03-29T00:00:00",
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What is this optical phenomenon, as looked from outer space? I just saw a photo from NASA. This is it.
This is beautiful. But i am not being able to understand, what are those red and green lines above the earth surface? These cannot be due to Rayleigh scattering of course as there are no particles to do that.
Moreo... | This optical phenomenon is called "airglow". A couple of other images, both also taken from the ISS:
(source: nasa.gov)
The blue band just next to the Earth in the second image is caused by Rayleigh scattering, which occurs primarily in the troposphere. The blue band is just barely visible in the first image, which wa... | {
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Can a coffee cup really jump off the table? I've been reading Nassim Nicholas Taleb's book The Black Swan which largely concerns the uncertainty of social and economic systems (and the futility of predicting outcome); the Black Swan being the rare event.
But in one of the chapters Taleb talks about the motion of atoms ... | I have seen some wet plastic coffee cups with very hot coffee poured inside moves horizontally. This happens not during the coffee is being poured but after a minute or two.
I theorized this is possibly due to trapped air between cup base and smooth table surface get expanded and create air cushion on which the cup sli... | {
"language": "en",
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"source": "stackexchange",
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What is time dilation really? Please will someone explain what time dilation really is and how it occurs? There are lots of questions and answers going into how to calculate time dilation, but none that give an intuitive feel for how it happens.
|
Asked by lucas:
I know nothing about relativity but I cannot accept that there is a phenomenon called time dilation. However I have no problem with it because of mathematics behind it. I have no problem if time is dilated, because I don't know what time is. But I wonder when they say a clock will work slowly with resp... | {
"language": "en",
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"source": "stackexchange",
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How much energy does proton - carbon 12 fusion produce? Page 25 of this document from the California Institute of Technology says that proton-carbon 12 fusion releases 7.54 MeV, while Wikipedia says it releases 1.95 MeV. Which one is correct?
| OK, you are referring to the fusion reaction
$^{12}$C + $^{1}$H $\rightarrow$ $^{13}$N + $\gamma$.
Let's neglect the $\gamma$ and insert the atomic masses
$12\cdot u + 1.00782503223\cdot u = 13.005738609\cdot u + x$,
where $x$ is an upper boundary for the released energy (since we neglected the $\gamma$). The data for ... | {
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Impulse Equations A solid sphere of mass $m$ rolls without slipping on a horizontal surface and collides with a vertical wall, elastically. The coefficient of friction between the sphere and wall is $\mu$. After the collision, the sphere follows a parabolic trajectory, with range $R$. What is the value of $\mu$ to maxi... |
only thing you left was the fact that friction stops acting when slipping stops. Range is maximised when upward velocity is max as horizontal is fixed
| {
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Gauss law in gravitation Is it possible to use Gauss's law of electromagnetism, (The net electric flux through any closed surface is equal to $1⁄\epsilon$ times the net electric charge enclosed within that surface.) to calculate the gravitational field at point by making certain changes, i.e, by replacing electric flux... | Yes, you can use Gauss's law for gravity.
$$\nabla\cdot\vec{g} = 4 \pi\, G\, \rho $$
or
$$ \oint \vec{g}\cdot\mathrm{d}\vec{a} = 4 \pi\, G\, M_\mathrm{enc} $$
where $\vec{g}$ is the gravitational field (equivalently, acceleration due to gravity), $\rho$ is mass density, and $M_\mathrm{enc}$ is the total mass enclosed b... | {
"language": "en",
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Can a qubit have an imaginary component? My knowledge of linear algebra is limited and my physics knowledge mostly comes from high school and Youtube so please bear with me.
In the equation $$|x\rangle = a|0\rangle+b|1\rangle,$$ I read that $a$ and $b$ can be complex. Does that mean that they can be imaginary? If so, d... | A complex number is equivalent to a vector in $\mathbb{R}^2$. Therefore you can visualize these vectors very easily. Of course, once you want to visualize a two-dimensional vector of complex numbers, you'd need four real dimensions, which is hard to "visualize" in three dimensions. However, for qubits, you don't really... | {
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Merging and Splitting of Black Holes We know that two black holes can merge to form a single black hole with the release of vast amounts of energy. Can the reverse happen? That is can it happen that large energy is supplied to a black hole and it splits into two?
| Given that as far as anyone knows there is only one black hole in the centre of every galaxy, if it were to split into two it would split the galaxy. We know that galaxies often collide and can see one feeding into another, but surely there is no evidence of a split galaxy. It would look rather like a cell dividing wou... | {
"language": "en",
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Integral of a velocity profile? Part of my fluid mechanics homework asks me to solve:
$${\partial u\over \partial x} = 0$$
Which represents how the velocity profile, u, changes in the x. I'm not sure whether you can integrate partial derivatives but my intuition says that you just integrate and get:
$$u=C$$
Is this lo... | Velocity u could be a a function of time AND space in general. From the first relation mentioned in the problem, all you can infer is that velocity does not depend on space. All remains would be its time-dependency. You can also show all this in partial-derivative notation.
| {
"language": "en",
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Is there a maximum energy for a relativistic particle? So I was told today that the Standard Model breaks down at really, really high energies. The lecturer mentioned particles such as electrons hypothetically having energies equivalent to that of entire stars and it got me thinking, surely the maximum theoretical ener... | There is no maximum energy of a freely moving massive particle in special relativity.
The relativistic energy of a particle of rest mass $m$ moving in your frame at speed $v$ is given by $E=\gamma m c^2$ where $\gamma = \frac{1}{\sqrt{1-(v/c)^2}}$. If you look closely at $\gamma$ you will see that it is not defined at ... | {
"language": "en",
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Does increasing the width of the slit increase the intensity of the light passing through it considering the slit as a source I did an experiment in which I tried to show that the visibility of the interference fringes is related to the relative slit width in a double slit interferometer. In other words if one slit had... | The fringe pattern is simply the fourier transform of the slit aperture, in 1 or two dimensions.
The fourier transform of a single slit ~ $sinc(x/a)$ where a is the width of the slit.
The fourier transform of a double (equal) slit ~ $cos(x/a)$ eqn.(1)
The fourier transform of two slits , one twice the width of the ... | {
"language": "en",
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Why fuse needs to be slightly more able to bear current than the appliance? if I have a bulb with rated current of $4 A$ then why I need to connect an $5A$ fuse?( which has slightly more ability to bear current.)
| The actual amount of current that will cause a fuse with a given rating to open is a random variable that depends on random variables in the manufacturing process. Same goes for the light bulb: The actual amount of current that the light bulb will draw from a given supply voltage is variable.
In order to prevent blown ... | {
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Does the rotational form of Newton's second law always hold? Does the equation,
$$\vec \tau=I\vec \alpha$$
(rotational form of the second law) always hold? If not, in what conditions does it hold true?
|
Does the equation,$$\vec \tau = \mathrm I \vec\alpha$$(rotational form of the second law) always hold?
No. This assumes a rigid body, that the body is rotating about one of the principal axes of the rigid body, and that the external torque is parallel (or anti-parallel) to the body's rotation axis.
| {
"language": "en",
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Putting a capacitor into a strong magnetic field, will this change the capacity? I'm wondering, does a magnetic field change the number of electrons, placed and displaced on the two plates of a capacitor. To prove or disprove this, I think the capacitor could be connected to an other capacitor outside the magnetic fie... |
does a magnetic field change the number of electrons, stored on a capacitor.
No, because ...
*
*The purpose of a capacitor is not to store electrons but to store energy. A "charged" capacitor contains the same number of electrons as an "uncharged" capacitor.
*Electrons don't easily disappear or appear, they have ... | {
"language": "en",
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Why so much electric charge? I'm working on the Millikan experiment using the following apparatus:
http://www.unitedsci.com/product-catalog/millikan-oil-drop-apparatus-0
when I compute the value of charge of the oil drops, the vast majority is around 200 times the charge of the electron, but according to the manual and... | I'm not sure how this manufactured device looks from the inside. During my undergraduate my friend and I built our own device. But I can give you some possible explanations.
First of all there is a slight chance that the mercury lamp causes this due to the emission of UV. Is it build in? Because it also generates a lot... | {
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Invariant polynomials of the Landau theory of phase transitions (crystal symmetry?) I'm convinced I'm missing something so obvious but here goes
Typically, one can define something like a "general" expansion of an order parameter, ${\boldsymbol \Gamma}$, up to 6th order as follows
$$F = \frac{1}{2} A_{ij} \Gamma_i \Gam... | The brute-force method to find the symmetric polynomials of a point group is to start with the generic polynomial and perform a symmetrization over group elements. This can be done for small finite groups and does not require much knowledge about the representation theory.
Let $G$ be the point group (can be $O_h$, $T_d... | {
"language": "en",
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Can the quantum mechanical current density be imaginary? I am dealing with a situation where I get an imaginary transmission current density.
Is this possible?
Does it imply a zero transmission probability?
| The formula for the probability current is
$$
\boldsymbol j=\frac{1}{2m}(\psi^*\hat{\boldsymbol p} \psi-\psi\hat{\boldsymbol p}\psi^*) \tag{1}
$$
which is manifestly real. As a cross-check, if you write $\psi=R(x)\mathrm e^{iS(x)}$, then the current is given by
$$
\boldsymbol j=\frac{R^2}{m}\nabla S \tag{2}
$$
yet agai... | {
"language": "en",
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Lead shielding very close to the Sun I understand that eventually lead would melt when it nears the sun. In a liquid state how effective would lead be in blocking radiation? Would it still be as effective as solid state of lead? What about lead in a gas state?
| All that really matters is the column density of the lead - how much mass per unit area you have. What this means is that if you change the state or density of lead then so long as you arrange it so that $\rho x$ is the same, where $x$ is the path traversed by the radiation, then the absorption due to the lead will be ... | {
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Vierbeins in General Relativty; degrees of freedom? I am self-learning GR.
I want to ask if vierbeins $e^b_{\ \ \nu}$ need to satisfy any relations or if I am free to choose any type of vierbein I like
So I have been looking into tetrads again. I understand I can calculate $g_{\mu \nu}=e^a_{\ \ \mu}e^b_{\ \ \nu}\eta_{a... | Yes. You are free to choose any such vierbein. Note that any two choices of vierbeins are related by a local Lorentz transformation. This appears then as a gauge symmetry in tetrad formalism. By choosing a particular veilbein, you have essentially fixed the gauge.
| {
"language": "en",
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When does the principle of superposition apply? I assumed from my general physics courses that the principle of superposition was just an empirical fact about forces. Then I could understand that derived quantities like the $E$ and $B$ fields would also obey it because, for instance: $$F_1 + F_2 = qE_1 + qE_2 = q(E_1+... | The principle of superposition is not obvious in any sense. However, it is an experimentally verified fact to a certain accuracy. If you look at Newton's law or Coulomb's law, it does not say anything about the fact that the net force is the sum of individual forces as if all other particles were absent. There is no re... | {
"language": "en",
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Help! An 8 year old asked me how to build a nuclear power plant I would really like to give an explanation similar to this one.
Here's my current recipe:
(i) Mine uranium, for example take a rock from here (picture of uranium mine in Kazakhstan).
(ii) Put the rock in water. Then the water gets hot.
(iii) [Efficient way... | You may need to explain the concept of a chain reaction, at least enough to explain why the rocks don't explode. Every fission event in Uranium generates neutrons. This occurs naturally at a slow rate, or can also be triggered by a Uranium atom getting hit by a neutron. The more densely packed the Uranium is, the mo... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/244158",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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Neutron population growth in a reactor In nuclear reactors physics, the effective constant $k_{eff}$ is defined as
$$k_\text{eff} \equiv {\text{number of neutrons in one generation}\over \text{number of neutrons in the preceding genereation}}$$
And the equation that describes the change of the neutron population, the p... | It's okay if the two results are equal only at first order. The implicit assumption is that the length $\ell$ of the "neutron cycle time" is short enough that the higher-order terms are negligible. This is the standard calculus technique for deriving the exponential function; it shows up all over the place.
Note that... | {
"language": "en",
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Could an asteroid land slowly on Earth's surface? The concept in my mind is that an asteroid is on a vector similar to Earth's, but slightly slower (e.g., 50kmh slower). As Earth passes it, it enters the atmosphere at a sharp angle, and since Earth was passing it, it just barely touches down due to Earth's gravity and ... | If the asteroid is in parallel to the orbit of the earth and at rest it will feel the gravitational attraction and will fall with velocity growing as $g\cdot t^2.$ This force will be there whatever the angle and velocity of the asteroid, centrifugal forces may make it miss the earth in a parabolic orbit, or be caught i... | {
"language": "en",
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Units don't match in the torsional spring energy! According to Wikipedia's description of torsion springs and according to my understanding of physics the energy of a torsional spring can be written as
$$U=\frac{1}{2}k \varphi^2$$
where $k$ is a constant with units of $\rm N\,m/rad$.
I am freaking here because if the... | Let's see how the units work out if we convert a linear spring (where we know everything) to a torsion spring, by attaching our linear spring to a stiff rod some distance $R$ from a pivot:
The (linear) force due to the spring is $\vec F = -k\Delta \vec x$, for spring constant $k$ having units of newtons per meter. Th... | {
"language": "en",
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Why does the kinetic energy work theorem apply to inclined surfaces?
Work is supposed to be force x distance, how did we end up with work equaling the difference of hights x gravitational acceleration ?
Sorry for my poor understanding :D
| Look at the forces in your system:
*
*In the y-direction, you have gravitation force.
*In the x-direction, there is no force.
Edit:
Suppose you have vectors for the force and the displacement:
$F=(F_x,F_y)$ and $d=(d_x,d_y)$, now to get the work W, you calculate the dot product* of these two:
$W=F*d=F_x*d_x + F_... | {
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How does one calculate how big something has to be, to be seen at a given distance? Ignoring curvature of the Earth.
How do I calculate the size an object would need to be in order to appear to be approx 1cm tall at a given distance?
| Let $w$ be the actual size of the object, $d$ be the distance to the object, $w_r$ be the size of a reference object, and $d_r$ be the distance to the reference object.
If you want your object to appear to be the same size at some distance $d$ as a reference object at a reference distance $d_r$, then using the properti... | {
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Is acceleration relative in relativity? Suppose a box A is moving relative to a Box B, then by time dilation equation if I take 1 sec passed for an observer in A then for an observer in B will be little longer. Now if I suppose that the box B is moving while A is stationary under the same condition, then by the time di... | Are you familiar with the concept of the relativity of simultaneity? Because simultaneity is relative, when they move apart they will disagree about which pairs of readings on each of their clocks are simultaneous. For example, suppose they move apart inertially at 0.6c, with each clock set to read a time of 0 seconds ... | {
"language": "en",
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Why does the temperature of the gas in a container moving with constant velocity not change?
Systematic changes do not affect thermodynamic equilibrium.
What does this mean? And what kind of systematic changes are allowed?
The container with gas is stationary till some time then it's given a constant velocity and the... | This means that changes that happen to the whole of the gas won't affect its temperature.
This is because the temperature of a gas is proportional to the average kinetic energy of the particles.
$ T \alpha KE_{average}$
Since in an ideal gas all particles move in straight random paths, an increase in velocity in one ... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/245123",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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How to write BdG Hamiltonian in graphene? In Beenakker's paper:Specular Andreev Reflection in Graphene, the BdG Hamiltonian is written as:
$$
H_{BdG}=\begin{pmatrix}H-E_F&\Delta\\ \Delta^*& E_F-H\end{pmatrix}
$$
from equation (1).
Where $H$ is the Hamiltonian of pure graphene and it is:
$$
H=\begin{pmatrix}H_+&0\\ 0& H... | According to @Bercioux answer, if we choose the basis:
$$
\phi_1=(\Psi_{A+},\Psi_{B+},\Psi_{A-}，\Psi_{B-},\Psi_{A+}^\dagger,\Psi_{B+}^\dagger,\Psi_{A-}^\dagger,\Psi_{B-}^\dagger)
$$
The BdG Hamiltonian should be written like this:
$$
H_{BdG}^1=\begin{pmatrix}H_+-E_F&0&0&\Delta_2\\0&H_--E_F&-\Delta_2&0\\
0&-\Delta^*_2&E... | {
"language": "en",
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In a waveguide, where does the energy in attenuated waves go? In an electromagnetic waveguide, there is generally a "cutoff frequency." Electromagnetic waves with a frequency that is lower than this cutoff frequency will not propagate at all -- i.e., they will be exponentially attenuated.
Suppose that there is a sourc... | I believe energy will be reflected from all sides in this case, which will not be much different from a case of a source in a cavity. The amplitude of the electromagnetic field will grow until losses in the walls of the waveguide become comparable to the power radiated by the source.
| {
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Synthetic Photometry - Calculating a colour index I have a theoretical black body spectrum as described by plancks law. I also have the bandpass sensitivity function for various filters. I would like to calculate a colour index from this information, so I can compare it to an experimental result.
My proposed method is ... | In the link, the spectrum is very noisy (possibly by the way of absorption peaks). Then, convolving it by a band-pass filter is simulating the integration - or average - over the band, resulting in a smooth curve, that you can then sample (i.e. pick up discrete values) without suffering aliasing artifact (as you would ... | {
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Which properties control the strength of strong interactions? Does the strong nuclear force depend on mass, charge or spin? Accordingly, can we order neutron-neutron, proton-proton and neutron-proton pairs by the strength of the strong force between them?
| The picture is basically "upside-down" or rather "inside-out":
According to our most current understanding, mass, charge and spin for the particles you are asking about, are actually the by-product of the elementary constituents of the Proton,Neutron and other baryons/mesons.
All particles mentioned are actually combi... | {
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Is the electric field strength along an equipotential surface constant? I'm trying to determine whether or not the electric field strength $|\vec{\mathcal{E}}|$ is constant everywhere on an equipotential surface. I know an equipotential surface is defined as
$$
S = \{\mathbf{x}\in\Bbb{R}^3\text{ s.t. } V_{\mathbf{x}} ... | Consider the symmetry plane between two equal magnitude but opposite sign charges. It has the same potential everywhere (zero Volts in the usual gauge). Does it have the same electric field strength everywhere?
For simplicity we'll place a $+1 \,\mathrm{C}$ charge at $+1\,\mathrm{m}$ on the x-axis and a $-1 \,\mathrm{... | {
"language": "en",
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Are black holes very dense matter or empty? The popular description of black holes, especially outside the academia, is that they are highly dense objects; so dense that even light (as particle or as waves) cannot escape it once it falls inside the event horizon.
But then we hear things like black holes are really empt... | (fellow amateur here) I believe that the notion that black holes are empty comes from that fact that all the matter that gets sucked past the event horizon is packed into an infinitival small ball of infinite density, thus it would be the same as if you had a hollow sphere the size of earth, and one particle in the cen... | {
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Wave intensity and superposition Let us say we have 2 point sources of sound. My question is how do we consider the intensity to vary according to position?
Let's say both have same amplitude, frequency and speed, just different phase.
Does intensity add up individually or do we calculate the net displacement in pressu... | Any physics problem regarding waves, to my knowledge, will need you to compute the amplitude dependance in time and space before anything.
Waves superposition can be constructive or destructive depending on the sum of the amplitudes of the superposing waves. Intensity is defined as the product of the sound velocity by ... | {
"language": "en",
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What would be the minimum fissile material needed to start fusion within a pulse unit? I am trying to calculate the weight of the pulse unit and composition and the approximate fallout, for a ground launch in regards to Project Orion`s nuclear pulse propulsion for a 0.03 kiloton and 0.35 kiloton detonation. The fusion ... | Basically, you are asking for the minimum fissile material needed to build a nuclear bomb. This site might help with some of that. However, it seems likely that the real answers are classified. I have heard that a nuke can be created using as little as 1kg of Plutonium. I also saw a reference to a Polish paper during ... | {
"language": "en",
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Why is the cut off mass for massive stars 8 solar masses? Why can't it be 10-11 solar masses or so? I know that stars having a mass greater than or equal to 8 solar masses are termed "massive stars". But why is the cut-off 8 solar masses?
| The division is conventionally made at the boundary between where stars end their lives as white dwarf stars and where more massive stars will end their lives in core collapse supernovae.
The boundary is set both empirically, by observations of white dwarfs in star clusters, where their initial masses can be estimated,... | {
"language": "en",
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DNA breaks with particles or photons (Radiation therapy) When protons (or other particles) or photons are used in radiation therapy to treat cancer patients, the main effect is for it to make DNA breaks that hopefully will make the cancer cell die eventually (At least that is the very easy explanation. There are a lot ... | Yes, it is essentially just the Coloumb interaction.
Sometimes, this will strip electrons from atoms. However, those electrons might have been responsible for a bond in a molecule, so this will have effectively destroyed the molecule.
Other mechanisms include having a nucleus recoil from a proton (perhaps imparting en... | {
"language": "en",
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Driven harmonic oscillator Given the Hamiltonian of a loaded particle
$$\hat H = \frac{\hat p^2}{2m}+eE(t) \hat x + \frac{1}{2}m\omega^2 \hat x^2$$
show that
*
*The time dependent expected values $\langle \hat p\rangle$ and $\langle \hat x\rangle$ satisfy the classical laws of motion
*Discuss the time dependence of... | Ehrenfest's theorem proves that expectation values of $\hat{x}$ and $\hat{p}$ obey classical equations of motion in general. This is true regardless of whether the system you are considering is that of a driven harmonic oscillator or not.
The difference in the case of a driven harmonic oscillator, is that solutions to ... | {
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Why do I get two different answers? Using Calculus and Using Newton for Distance/Velocity Why do I get two different answers?
QUESTION: How long does it take to slow down from 8000 m/s to 6000 m/s with an acceleration of -400 m/s^2 ?
GIVENS
D distance
V velocity
T time
V initial velocity 8000 m/s
V** final velocit... | The formula 2 is correct and it gives correct answer t=5s. But formula 1 is wrong. The correct formula is $D=\frac {1}{2}at^2+vt$. If you differentiate $D=at^2+vt$, you will get $v=v_0+2at$, where $v_0$ is initial velocity. That is wrong.
So the correct answer is t=5s.
| {
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How do temporary dipole-dipole interactions work in quantum mechanics? The standard presentation of temporary dipole-dipole interactions (in high school at least) is classical: the electrons in an atom/molecule 'orbit' around its nucleus/nuclei. As a direct result of this orbital motion, at any particular time there wi... | Consider two atoms at some distance $R$ from each other. The Hamiltonian of this system is then the sum of the Hamiltonians of the two atoms plus interaction terms involving the electrostatic interaction between the electrons of one atom with the electron and nucleus of the other atom. You can then calculate what the s... | {
"language": "en",
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Why don't all the gluon's get converted into energy in an uranium atom undergoing fission? I have following questions and arguments.
*
*why do only gluons get converted into energy in an uranium atom undergoing fission?
*why don't all the gluons get converted into energy?
*which conditions lead to such process?
| In general an atom undergoing fission breaks up into other, smaller nuclei and stable particles: photons (x rays and gamma rays), electrons(beta decays) , alpha particles an other lower mass nuclei.
Gluons are never free, because of QCD, and always inside a proton or a neutron. Their spill over attractive force is due... | {
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Why does force cause acceleration? Consider a ball placed on a smooth plane. If you take a plank made out of wood and whack it (apply a force on it), does it accelerate because
*
*First, the force compresses the part of the ball in contact and hence the ball is now like a compressed spring with potential energy
2.N... | I am not sure that i understand your question 100%
If your question is - as mentioned in the title 'why does force cause acceleration '- then the answer is
simple: the Newton's second law of motion (the net force on an object is equal to the rate of change
of its linear momentum p in an inertial reference frame) whi... | {
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Difference between scattering and refraction? I while back I learnt that when light is incident on a dipole the dipole will scatter the light, and when it is incident on a material of a different refractive index then the light refracts. From the Ewald-Oseen extinction theorem, it seems that refraction is caused by sca... | Refraction occurs when a large number of dipoles scatter coherently. Each individual dipole scatters light in response to the incident radiation in (almost) all directions, but when you have a large collection of scatterers, each one scattering in many directions, you have to sum the contributions of each one in order... | {
"language": "en",
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Link between energy per unit frequency and derivative of the energy in regard of frequency I take a simple example to illustrate my question. I consider $\frac{du}{d \omega}$.
It physically represents the volumic energy per unit interval of frequencies (imagine a system with electromagnetic fields inside).
If I take $\... | They are the same thing. That is the reason "energy per unit frequency" is written the same was as the "derivative of energy with respect to frequency."
When we ask how energy changes with respect to frequency (the derivative) it is the same as asking "for every unit change in frequency, how does the energy change".
T... | {
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How Are Quantum Computers Able to Store Any Data at all? So if qubits can have more than two states, and according to this video,
https://www.youtube.com/watch?v=T2DXrs0OpHU
you don't know what you get until you actually "open the box", if its all randomness and probability,then how can it store anything?
Like, if you... | With quantum computers, as with classical computers, the initial states (variables) are set at the beginning of the process.
Suppose you write an ordinary computer program to find the largest prime number less than $N$; you might use the Sieve of Eratosthenes. At the end of the process your computer program has many n... | {
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What is uppercase ${\cal O}$ in electrodynamics? I'm a bit puzzled as to what the symbol ${\cal O}$ means in electrodynamics, I'm reading this paper here http://arxiv.org/abs/astro-ph/0404512.
See equation 43 which is in page 12, what is this uppercase ${\cal O}$? I can't find its definition anywhere.
| This symbol means that there's an error of aproximation, an example is the equation you mentioned:
$f(r) \sim \frac{1}{4r} + \mathcal{O}(\frac{ln(r)}{r^2})$
Here, the function $f(r)$ is being aproximated by the first term, it means that you can aproximate the actual value of the function $f(r)$ by computing the term $\... | {
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What is the difference between emu and esu? My textbook contains the following two statements:
*
*In the CGS system the unit of charge is electrostatic unit of charge (E.S.U). It is also called Stat Coulomb (StatC).
*In the CGS system, the unit of charge is electromagnetic unit (E.M.U).
How can e.m.u and e.s.u bo... | Quoting from the Wikipedia page on the CGS system:
*
*The e.s.u of charge, also called the franklin or statcoulomb, is the charge such that two equal $q=1\:\mathrm{statC}$ charges at a distance of $1\:\mathrm{cm}$ from each other exert an electrostatic force of $1\:\mathrm{dyn}$ on each other.
*The e.m.u. of curren... | {
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Bifundamental representations Can someone give me explicit examples (in matrix form) of bifundamental representations? Illustrative would be for instance:
a) SU(3) x SU(2)
b) SO(4) x U(1)
c) E6 x U(1)
but other you may have ready would also work. A reference would also be great.
| I will talk about $SU(3) \times SU(2)$.
First, a matrix $T_3 \in SU(3)$ acts in the fundamental representation on $\mathbb C^3$ in the following way: A vector $\vec v \in \mathbb C^3$ with components $v_i$ is mapped to $v'_i = (T_3)_{ij} v_j$. Similarly, a $T_2 \in SU(2)$ acts on $\vec w \in \mathbb C^2$ as $w'k = (T_2... | {
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Question about aircraft/rockets Lets say that you're sitting an inverted airplane. How do you determine how fast the plane must accelerate in order for you to not fall out?
| That depends on two things: The coefficient of friction between the pilot and his seat and the direction of acceleration.
First case: The aircraft accelerates along its flight path. The pilot is pressed against the seat by the acceleration, and if that pressure is sufficient, friction will keep him in place. Since the ... | {
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How Fermi momentum and Fermi energy are related? The Fermi momentum is defined as $\sqrt{2mE_F}$, where $E_F$ is the Fermi energy. Does this equation mean that the Fermi momentum depends only on the kinetic part of the Fermi energy?
Is it correct to say that turning on an external field for a spin-half system affects o... | The energy and momentum are related by the "dispersion relation." For a classical free particle, the kinetic energy of a particle is the total energy and so
$$ E=\frac{p^2}{2m} \rightarrow p = \sqrt{2mE}.$$
That is the origin of the relation you mentioned. For a relativistic free particle, you have the Einstein disper... | {
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What is the moment of inertia really? Is moment of inertia or second moment of inertia, simply the resistance of a body to rotate it over an axis? What is radius of gyration? What if the axis is via the center of mass or somewhere different? can you give me please an overview of these issues with SIMPLE words, and with... | The radius of gyration is roughly the proportion of the moment of inertia of a body to its mass. A higher gyradius means that one body will have a larger moment of inertia than a body with a lower gyradius, if both bodies have equal mass.
| {
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Which coordinate is to be considered for the energy of simple pendulum? For an simple harmonic oscillator energy can be represented as in picture. Consider in particular picture (b) with the energy as a function of the coordinate $x$.
Consider now a simple pendulum. The coordinate $x$ in (b) is the coordinate of an ho... | The equation of motion for a simple pendulum is actually not the same as for a simple harmonic oscillator. In fact, the pendulum motion can is described by the differential equation
$$\frac{d^2\theta}{dt^2}+\frac{g}{l} \sin{\theta}=0$$
It is only in the small angle approximation (where $\sin{\theta} \approx \theta$) th... | {
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Why does a ceiling fan start up slowly? I think it probably has something to do with the capacitor inside but I don't get it why doesn't it just Start spinning instantly when we push the button why does it slowly start to spin and gradually gets faster?
| The fan motor provides a torque $\tau$ which has to accelerate $\alpha$ the fan blades whose moment of inertia is $I$:
$$\tau=I\alpha$$
Given how long it takes for the fan blades to stop the frictional torques must be fairly low and so the torque applied by the motor to keep them going must also be low. With the relat... | {
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Physical meaning of partition function in QFT When we have the generating functional $Z$ for a scalar field
\begin{equation}
Z(J,J^{\dagger}) = \int{D\phi^{\dagger}D\phi \; \exp\left[{\int L+\phi^{\dagger}J(x)+J^{\dagger}(x)}\phi\right]},
\end{equation}
the partition function is $Z(0,0)$. We know that the derivatives o... | In terms of Feynman diagrams, the partition is represented by the sum over so-called vacuum bubbles - diagrams with no external legs. In formulae and in terms of the interaction picture and the free vacuum $\lvert 0 \rangle$ and the interacting vacuum $\lvert \Omega \rangle$, we have that
$$ \lvert \Omega\rangle = \lim... | {
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Deviation of free falling objects (Coriolis effect) using conservation of angular momentum I read this pdf on non inertial frame, in particular I have a question on the deviation of free falling object due to Coriolis effect.
Consider a ball let go from a tower at height $h$. The displacement due to Coriolis effect, ... | You're right about the wrong average velocity. But you can indeed use the conversation of angular momentum to calculate the right displacement. In order to do that let $\omega_0$ be the angular velocity of the earth and $h_0$ be the initial height of the ball. Then it follows from the conservation of angular momentum t... | {
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Atmospheric Pressure inside a closed room
Even though they’re too tiny to see, all the molecules of air in the atmosphere above your head weigh something. And the combined weight of these molecules causes a pressure pressing down on your body of 10,000 kg per square metre. This means that the mass of the air above the... | "Closed room" word is ambiguos. If first the room was open , then was closed, without pumping all of air out(creating a vacuum), the pressure conditions would remain same, because there will be still air inside the room.However, had we pumped all air out, our blood capillaries would collapse, since our internal pressur... | {
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Why is Kinetic Energy = (-) Total Energy and Potential Energy = 2 $\times$ Total Energy? I came across this relation while reading on the Bohr atomic model. Are there any other forces for which these relations hold good?
| This is true for central potential problems. Because in that case, both potential energy and kinetic energy are in (1/r) terms. Also, Potential energy is negative and its magnitude is twice that of Kinetic energy . Thus we conclude that only the mathematics of this problem allows it to be expressed as the formula u pro... | {
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How does a tranverse wave propagate? Sound waves can be understood as particles hitting each other and to conserve momentum the vibration travels in air. Each particle transfering it's momentum to the other until it reaches our ears. Atleast we can think of a mental picture of why they propagate. But what about transve... | You pull a small piece of a rope up, and as that piece goes up it pulls the piece adjacent to it up and as that piece goes up... When you move your hand back to it's original position you're applying a force to the piece again and it pulls the adjacent piece down, etc... Model of displacement as a function of position ... | {
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Meaning of a certain value at Fourier Transform Define the Fourier Transform of a certain signal in the time domain FT[$x(t)$]=$X(j\omega)$
$X(j\omega)$ = $\int$ $x(t)$ $e$^($j\omega$$t$)$ $dt
I'd like to ask what is the meaning of the value obtained from $X(j\omega)$ with certain frequency $\omega$
for example if w... | *
*Your Fourier transform eq. is incorrect. it should be $e^{-jwt}$ not $e^{jwt}$
*Physical meaning: Split your integral into real and imaginary parts, the Fourier transform equation is split into integral with sine and cosines instead of $e^{jwt}$, but with same frequency.
$F = \int \Re{x(t)} cos(wt) dt + j \int \I... | {
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Is power still consumed when we switch off the lights? I was having heated discussion with one of my friends. We were discussing Earth Hour and its role in saving electricity, and creating awareness.
He stated that even if you turn off the lights, the load from the transmission lines is there at you home, so power is s... | First answer this: does it take more power to run one light bulb or two?
Transmission lines are designed to be low loss, but they run a long way. Lightbulbs are designed to be "lossy" because that's how they work. Let's say for the sake of argument that the whole transmission circuit loses 100 watts and you're talking ... | {
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Submerged water jet I am trying to calculate at what pressure and speed water from a high pressure water jet will hit an object 100 millimeters away from the nozzle opening, but i can't figure it out.
The nozzle will be used at approximately 100 meter below sea level in salt water. Its a circular nozzle with a diamete... | The formula to use for the nozzle velocity is:
V = (gpm * .321) / A where: gpm = gallons per minute
V = Velocity in ft/sec
A = Area of nozzle in sq. inches.
A 2mm nozzle = 0.0787 inches. Area A = .785(0.0787^2) = 0.00486 in^2
Flow of 60 L/M = 15.7 gpm.
Noz... | {
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Why do X-rays go through things? I always heard that the smaller the wavelength, the more interactions take place. The sky is blue because the blue light scatters. So why is this not true for X-rays, which go through objects so readily that we need often use lead to absorb it?
| Light is composed out of a large ensemble of photons, and photons are quantum mechanical elementary particles. Matter is composed out of atoms and molecules , which have small dimensions and are in the quantum mechanical range.
The quantum mechanical "size of interaction region" is given by the Heisenberg uncertainty r... | {
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Wavefunction Collapse I believe my Lecturer and the textbook have contradicted one another. My lecturer gave the example that if the spatial part of the wavefunction of a particle is given by
$\psi(x) = c_1\psi_1(x) + c_2\psi_2(x)$
for the infinite square well potential (where $\psi_1$ and $\psi_2$ are the ground and f... | Both are correct, actually. If you measure an observable for that wave function you'll either find the eigenvalue corresponding to state 1 with probability $|c_1|^2$ (similarly for state 2), subject to the condition $|c_1|^2 + |c_2|^2 = 1$.
Edit: What Griffiths is saying is that before you perform the measurement, the ... | {
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What is the temperature of compress air entering the atmosphere? Hi to all of you enthusiasts,
I have a 1 liter compressed air tank with around 207 bar of air pressure inside. It has been sitting out for a while and I am assuming its temperature has almost reached the surrounding temperature which is 40 degrees Celsius... | Your mistake: the volume is not 207 times greater.
This would be only true for constant temperature; so it's no wonder if you get constant temperature :)
The volume increases more than this. It is governed by the laws for adiabatic expansion. See wikipedia. The relevant equation is $$T^\kappa p^{1-\kappa} = const.$$ ... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/251322",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "1",
"answer_count": 1,
"answer_id": 0
} |
How, if at all, does the behavior of a parallel plate capacitor change in the presence of a magnetic field? I'm an AP physics student curious about magnetism and my teacher couldn't answer this question. We already learned about velocity selectors, so I know that, when the plates of the capacitor are in the XZ plane an... | What 'behaviour' are you asking about?
Magnetic fields only affect moving charges. If the charge on the capacitor is not changing, the magnetic field has no effect, regardless of whatever direction it is in. No charges cross the space between the capacitor plates. Perhaps you are thinking of a situation where charge... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/251519",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "1",
"answer_count": 1,
"answer_id": 0
} |
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