Q stringlengths 18 13.7k | A stringlengths 1 16.1k | meta dict |
|---|---|---|
How would the Aurora light on Earth look like if there wasn't a magnetic field? Here are some pictures of the aurora light.
The beautiful phenomenon of Aurora is a well-known one, seen in the northern (Aurora Borealis) and southern parts (Aurora Australis) of the globe. Here is another short but easy readable article ... | We wouldn't have a magnetosphere if we didn't have a magnetic field. Therefore the solar wind wouldn't be able to interact with it and cause an aurora.
Once the solar wind strips away our atmosphere the sky would probably look a lot like the moon's sky (black with stars), or mars. https://en.wikipedia.org/wiki/Extrate... | {
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Evaluating Potential Energy Integral in Quantum Chemical Calculations My question is what are the steps for taking an integral of the following form?
$$\int e^{-\alpha|\mathbf r- \mathbf R_a|^2} {1\over|\mathbf r- \mathbf R_b|} e^{-\beta|\mathbf r- \mathbf R_b|^2} dV$$
This integral is commonly seen when attempting to ... | Since the integral is over all space, it makes sense to shift the origin of your coordinate system to $\mathbf{R}_b$. Then your integral becomes $$I = \int e^{-\alpha|\mathbf{r}'-\Delta\mathbf{R}|^2}\frac{1}{|\mathbf{r}'|}e^{-\beta|\mathbf{r}'|^2}dV',$$ where $\Delta\mathbf{R}\equiv\mathbf{R}_a-\mathbf{R}_b$.
The ne... | {
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If atoms were held by gravitational (instead of electrical) forces
"If atoms were held together by gravitational (instead of electrical) forces, a single hydrogen atom would be much larger than the known universe."
- from Grifffith's Introduction to Electrodynamics
I don't understand this. If the atoms were held to... | At first sight, you would indeed expect that the electron has to be much closer to the nucleus, so the force needed to keep the electron in a circular orbit will be the same as that in the case of the electric force.
But for the centripetal force (directed inwards and provided by the gravitational force or the electri... | {
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Fourier series analysis of string vibration In case of a plucked string,the amplitudes of successive frequencies fall by 1/n^2.
In case of a string which is struck so that say at x=a only the string has a velocity,say v,initially,then the amplitudes of successive frequencies fall by 1/n which implies that it is more en... | Sine waves are absolutely continuous, so they are good at approximating functions that are also absolutely continuous. By this I mean that a Fourier series for an absolutely continuous function will generally converge fast.
If the function is continuous but has discontinuities in the gradient, like a triangle wave, the... | {
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Why do different letters sound different? If one sings the letter "A" and "M" at the same volume and pitch, the two letters are still differentiable. If both pitch and volume are the same however, shouldn't the sound be the exact same?
| Here's something different to note. Let's say I would tell a band to play the musical note "C3". The bass, the guitar, the piano, the voice, the banjo, all of them sound different and yet we perceive them as the same note that has been played.
Similar, think of a sung "A" and a sung "B" (as in "bee") as an instrument r... | {
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Schwarzschild coordinates beyond the event horizon We can write down the metric of the Schwarzschild black hole in Schwarzschild coordinates.
On page 6 of the notes by Leonard Susskind of a course given at the Perimeter Institute titled 'Black Holes and Holography.' we find the following:
However, note that the Schwar... | I think the coordinates are valid inside the horizon as well, albeit inside the horizon $r$ is timelike and $t$ is spacelike. They are not valid at the horizon since both $r$ and $t$ have zero coefficients in the metric there. That means you need some other coordinate system there to connect the exterior and interior... | {
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Find the speed of the block in this question
The figure shows a block (assumed to be a point) being pulled by an ideal string across an elevated pulley. At any time $t$, let the horizontal distance of the block be $x$ from the pulley. The length of the string is $l$ and the height of the pulley is $h$ from the ground.... | Cosθ=(length of X/length of L). You need to find (delta length X/delta length L) or dx/dl. One is a relationship between lengths, the other is a relationship between changes in length. The two are just different.
| {
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What am I failing to understand about a light in a material? In a material, a photon's velocity becomes slower, photon's wavelength becomes shorter, but photon's frequency doesn't change.
If there is a material that makes low frequency photons have very short wavelength photons, and if I stick my finger in the material... | The energy of a photon is related to its frequency. In vacuum you can convert freely between frequency and wavelength - but once you have a material with a high refractive index, it's not so simple.
Your question about "radiation burn" is assuming that the energy of a short wavelength photon is always higher. That's no... | {
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Why are springs shaped the way they are? Why are springs coiled the way they are? Why not some other shape? Is the shape due to its elasticity or something?
| Well, metals can bend easily. If a length of metal is in the shape of a coil, then this bending can occur over the entire spring at once. Perhaps minimal temporary deformation at each point prevents permanent deformation. In any case, it maximizes lengthening ability while minimizing "effort" by the spring. I don't kno... | {
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Simultaneity in Newtonian mechanics How would Newtonian mechanics answer the train and moving light question?
The setup is:
A train is moving in the positive x_axis with speed c/2. A person stands in the middle of the train. There are two light bulbs at both ends of the train. The light goes off at the same time (ab... | Under C19th Newtonian theory, light was usually treated using the ballistic emission theory of light, which would say that the speed of light generated by bulbs inside the train would by default be cTRAIN and not cPLATFORM.
So if the central observer sends a trigger signal to cut the lights, that signal travels at cTRA... | {
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Dirac's quantization of electric charge I was following Nakahara's book Geometry, Topology and Physics, specifically subsection 10.5.2. I do understand how he obtains the equality,
$$ \Delta \varphi = \int \mathrm d\varphi = \int \limits^{2\pi}_{0} 2g \, \mathrm d\phi = 4\pi g$$
and that therefore this has to be a mult... | It is just a matter of convention. Nakahara uses the gauge covariant derivative $D_\mu \phi = ( \partial_\mu + \mathcal{A}_\mu ) \phi$ in the chapter. This is equivalent to the common definition $D_\mu \phi = ( \partial_\mu + i e/\hbar A_\mu ) \phi$ if $$\mathcal{A}_\mu = i e/\hbar A_\mu \,.$$ Nakahara's definition of ... | {
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Flat metric induced from Schwarzschild The task is to find a function $f(r)$ such that the induced metric from the Schwarzschild metric
$$ds^2 = -\left(1-\frac{2m}{r}\right) dt^2 + \frac{1}{1-\frac{2m}{r}} dr^2 + r^2 d\Omega^2 $$
on the level set $\{t=f(r)\}$ is flat. My first attempt was to guess
$$ dt=0 = f'(r)dr$$
b... | You have $dt=f'dr$ so $ds^2=(\varphi^{-1}-f'^2\varphi)dr^2+r^2d\Omega^2$ with $\varphi:=1-\frac{2m}{r}$. We want the $dr^2$ coefficient to be $1$, so $f'^2=\frac{1-\varphi}{\varphi^2}$. You can take the rest from there.
| {
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Biot-Savart law and magnetic field of a ring I have to calculate the magnetic field along the axis of a ring of radius $R$ on which circulates a current $I$ using the Biot-Savart law. The Biot-Savart law as given in my (really bad) course states
$$\mathbf{B}=\frac{\mu_0}{4\pi}\oint_{C}\frac{\mathbf{I}\times \mathbf{r}}... | I usually approach these problems less mathematical. Griffiths uses the following figure:
The part $dl'$ yields a piece of the magnetic field $dB$. All the horizontal components cancel so we only have to account for the vertical components. The integral becomes:
$$ B(z) = \frac{\mu_0}{4\pi} I \int \frac{d\textbf{l'}\ti... | {
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Why is light bent but not accelerated? Light is bent near a mass (for example when passing close to the sun as demonstrated in the famous sun eclipse of 1919). I interpret this as an effect of gravity on the light.
However, it seems (to me, at least) that light is not accelerated when it travels directly toward the (ba... | One thing that the previous answers are missing -- the light is accelerated; it just is accelerated according to the rules of special relativity, which says that it cannot pick up speed when already travelling at the speed of light.
Instead, it gains kinetic energy the way a photon gains kinetic energy -- by being blue... | {
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Charging current of capacitor In one of my books there is a figure
where G is a neon lamp. Basically the capacitor gets charged once the switch is closed up to a certain spark-current $U_Z$ where the neon lamp gets switched on so the capacitor can discharge to a certain charge-current $U_L$. Further it says that from ... | The time to get from zero to $U_L$ is obtained by solving (putting $RC=\tau$)
$$U_L=U_0\left(1-e^{-t/\tau}\right)\\
U_0-U_L = U_0 e^{-t/\tau}\\
\log(U_0-U_L) = \log(U_0)-t/\tau\\
t = \tau \log\frac{U_0}{U_0-U_L}$$
The time to get from $U_0$ to $U_H$ is similarly obtained. When you take the difference between these numb... | {
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Equation of motion for a falling slender bar
I have a few question about equations of the uniform slender bar motion.
The bar is released from rest on a horizontal surface as shown in the figure and falls to the left. The surface is rough so friction forces are applied at bottom end of the bar. The coefficient of fric... | Take this diagram as a hint:
Take torques by considering the center of mass as the pivot. The torque due to friction must equal the torque due to the normal reaction for the rod to not slip.
I think you'll arrive then at the answer for the coefficient of friction.
| {
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Canonical Momenta and gauge invariance Suppose there is a charged particle moving in an Electromagnetic field for which the vector potential is A.
Now we change A by gradient of some scalar(which is time independent) Hence, the scalar potential remains unchanged.
Now, I want to investigate the effects of such a gauge... | You are correct on both counts. Mechanical momentum is a gauge invariant physical quantity, but canonical momentum isn't. That means that canonical momentum is as measurable a quantity as the vector potential - which is to say, not at all unless you further specify what gauge you want it in.
| {
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Non-constant tension in rope Could somebody explain to me intuitively how tension is not the same in a rope with mass? My physics teacher (when regarding a massless string) told me that the tension is always equal because if you pull at one side more then the other side has to pull just as much to keep it in equilibriu... | If you pull on a massless rope from both ends, the tension at every point must be the same. Why?
Because the net force on any segment of the string must be zero, because it's a massless object and hence, tension must be same at every point.
In a string with mass, we can apply two different forces at the two ends of the... | {
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Insulated box of air at temperature $T$, is dropped from height $H$, what is the temperature of the air inside box on the ground? In an effort to understand more about the first law I was wondering about the potential energy term and how it would influence the gas inside the box I made this question and tried to answer... | Exactly, $dU=\delta Q -\delta W$, and here $\delta W=mgh$ and $\delta Q=0$. You can run some numbers to see that the value is very small for realistic settings.
| {
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Energy contributions of Hamiltonian density In Lancaster and Blundell, Quantum Field Theory for the Gifted Amateur, p.99, the Hamiltonian density is
\begin{equation}
\mathcal{H}=\frac{1}{2}[\partial_0\phi(x)]^2+\frac{1}{2}[\nabla\phi(x)]^2+\frac{1}{2}m^2[\phi(x)]^2,\tag{11.5}
\end{equation}
and it tells us that the ene... | Actually the first two terms are kinetic part, and the last term is the potential energy.
To get a correspondence to the classical mechanics, just consider the vibration of a string. When the string is displaced from equilibrium, a segment associated with the interval dx has a length:
$$dl = \sqrt{dx^2+d\psi^2}=dx\sqr... | {
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Does current run forever in water? (assuming the supply voltage is there forever) Suppose pH of water is $6$, I think this means there is one $\text{H}^{+}$ ion for every $10^6$ water molecules.
When we plug in the battery, I believe we see a current as the $\text{H}^{+}$ ions drift to the $-ve$ side of the battery a... | The ions are converted into gases $H_2$ and $O_2$ at the electrodes, so water is gradually being removed from the container - but it requires a very very large amount of charge to flow in order to convert all of the water into gases.
The $H^+$ ions exist as hydronium ions $H_3 O^+$. There is a reversible equilibrium in... | {
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Why large excavated holes can create air currents? My friend shared this post on my wall, but I got doubt: How can a hole like this create air currents which suck helicopterss also? I didn't really understand.
| The text seems to be very sensationalist. If this was the case then there would be a no fly zone over the grand canyon.
The one explanation I can think of is a draft due to the temperature difference at the top and bottom of the hole. The temperature at a great depth is much higher than that at the surface, and this ca... | {
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If the universe is constantly expanding, shouldn't we go away from other planets? I also saw that every point in the universe is the center. So what does it mean that the universe is expanding? It depends on the repository?
| I think, as far as I understand it, the expansion of the universe is overshadowed by other factors at smaller scales.
The gravity between the earth and the sun is strong enough that even as the universe expands, the distance between the earth and the sun is not affected.
Gravity continues to affect structure more than ... | {
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Help in an integration step in QFT by Lewis H. Ryder There is an integration step I can not figure out and is frustrating.
We start from the equality
$$ \dfrac{\partial^2\phi}{\partial x^2} = \dfrac{\partial V}{\partial \phi} $$
and by integration process we are supposed to get (eq. 10.8 in the textbook):
$$ \... | Just think about it as classical mechanics. Relabel $\phi$ to $x$ and $x$ to $t$ for
$$\frac{d^2 x}{dt^2} = \frac{dV}{dx}.$$
This is Newton's second law with $m = 1$ and an extra minus sign. Then the result is energy conservation with an extra minus sign,
$$\frac12 v^2 - V(x) = E$$
and is proved the same way. Presuma... | {
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Stationary waves and transfer of energy I have seen a question posted similar to this, but I am not sure if it answers what I was wondering about.
Essentially, we are taught that there is no average energy transfer of a wave to its surroundings. I understand that it intuitive for a mehanical wave on a rope, or even an ... | In a empty microwave oven, you create standing wave. And if it's empty, there is no transfer of energy to anything.
Now let's say you put a glass of water right in the middle of your MW oven, The molecules of the water (H20) have resonancies due to their internal structure : vibration, rotation etc... When the frequen... | {
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Why does a massless, frictionless piston move from high pressure to low pressure? Consider an ideal gas kept in a rigid cylinder with a movable massless, frictionless piston at the top. Let the pressure inside the cylinder be $P$ at pressure exerted by the surrounding on the cylinder be $p$. Let $$ P>p $$
Now since the... | If you had a massless, frictionless piston, it would oscillate infinitely fast. There will be an outward force initially, so it will accelerate outward (acceleration = infinity).
I'm not entirely sure how you have deduced that the force is 0. I'm quite sure it is not, if the pressures are different.
| {
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How is the Falcon 9 aerodynamically stable while ascending? How is the Falcon 9 aerodynamically stable while ascending? The rocket doesn't look like it should be able to fly straight. With the large, largely empty fairing at the top and the heavy engines at the bottom and no fins, it looks like it would want to flip ar... | It isn't.
Stabilisation is achieved by gyros which command the rocket nozzles to swivel so a sideways component of thrust can be used to balance the rocket. This has been true since the days of the A-4, which used moveable graphite fins sticking into the rocket exhaust to stabilise the device.
Before, rockets used much... | {
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Magnetic force on open circuit? Let's say we have a straight horizontal wire and we let it drop inside a magnetic field which will be parallel to the ground(coming out of the screen). Charges inside the wire feel a force due to their movement inside the magnetic field .
Let's say the field is coming out of the screen. ... |
So I'll have to ask again, does this ever stop? Is equilibrium ever
reached?
Prompted by the comments to reexamine the question, I now better understand the question.
Essentially, this is the canonical rod moving in a perpendicular magnetic field extended to the case that there is a constant external applied force.... | {
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Bounds of Integration (with respect to something that is not time) I have been reading Richard Feynman's lectures and came across an interesting proof regarding the Earth's gravitational force. At one point in the proof, Feynman uses the following the integral:
$\int_{R+a}^{R-a} dr$
(13.18 on http://www.feynmanlectures... | Reading through the proof, it seems like he actually starts by working in $x$, then proves the relationship between $x$ and $r$ (which includes the negative sign): $2r~dr = -2R~dx$.
Keeping the direction of the integration the same, you can see that the natural order for $r$ is from larger ($r=R+a$) to smaller ($r=R-a... | {
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Neutron stars - only neutrons? I was at a museum recently, and there was a display on neutron stars. It said that neutron stars are made only of neutrons, which honestly didn't make much sense to me - neutrons decay very quickly on their own, so how do neutron stars "last", so to speak?
So naturally, I checked wikiped... | Neutrons are stable in the neutron star because there is such high pressures that neutrons are unable to decay. The states for protons and electrons make sure that the neutrons do not decay. Neutrons do decay but not enough to make a dent on the neutron star. Also any neutrons that do manage to decay to protons most li... | {
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Time Constant of a circuit - capacitors in parallel or series?
When I charge the circuit as shown where the switch is at A, the p.d. across C1 is 10V, which is correct.
When I discharge the circuit, however, by changing the switch S from A to B, the total capacitance of the circuit is 200μF as C1 and C2 are in parall... |
the total capacitance of the circuit is 200μF as C1 and C2 are in
parallel.
They're not in parallel for either switch position.
When the switch is in position A, C2 and the 100k resistor are in series but one end of the resistor is 'dangling' so there is no path for current through the series combination.
When the ... | {
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Velocity of a Mechanical Wave on a String I recently read a derivation for an equation which governs how quickly a wave is transmitted along a string, $v = \sqrt{\frac{T}{\mu}} $, where T is the tension in the string, and $\mu$ is the mass per unit length along the string. The derivation makes sense but gives a more ma... | If you assume that tension and density are the only factors then dimensional analysis will lead you straight to that formula except for an undetermined constant. If you want an answer without such an assumption, then maybe you have to accept that the math is needed after all.
| {
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Derivative with respect to the radius of a moving particle on a non-frictional surface Basically I was just wondering about the following framing of question:
How can one determine the derivative of the velocity of the particle with respect to the radius when decreasing the force F on the string - (the particle is att... | How much of a quantitative answer do you expect? Because it kind of an abstract question.
First of all, you say "I've realized that when decreasing the force F, the radius R will be bigger." This is not true in a case where the force pulling on the string is bigger than the centrifugal force. The only thing you can be... | {
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How to choose the best Gaussian surface? Are there some basic rules so that I could choose a Gaussian surface according to my physics problem? Are there any guidelines for how to choose an appropriate Gaussian surface for the system of charges you are analysing?
| Choose the Gaussian surface in such that the electric field at every point on it is constant. Ultimately, you should be looking for symmetries, since it would simplify calculations a lot.
For example, consider finding the magnitude of the electric field due to an infinite thin sheet of charge, having a uniform positive... | {
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Why does a surface always exert force normal to it? In whichever angle an object is thrown at a surface, the surface always exert force normal to it. But why? According to Newton's third law, if an object hits a surface at an angle, the reaction force provided by the surface must be equal and opposite to the applied fo... | The force is normal to the surface only if no friction is present. If we have some sort of sticking between the thrown object (e.g. ball) and the surface (e.g. earth), there will be a non-normal component of the force.
Just think of an ball which slides (w/o friction) on the surface of the earth. As there is no frictio... | {
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What produces an electromagnetic field? A charge that moves, or a charge that changes over time? I've learnt an electromagnetic field is produced by moving charges, i.e. a current.
Is it the case, or is it actually the fact that the charge is changing at a given location?
I mean: imagine I have a charge $q_1$ locat... | Regarding a change in the charge, when you say
this is probably impossible? but let's imagine
─ let's not. Electric charge is conserved, both globally and locally, i.e. it obeys the continuity equation
$$
\frac{\partial \rho}{\partial t}+\nabla\cdot\mathbf j=0,
$$
and this is absolutely critical for Maxwell's equatio... | {
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Why is the spring force equal to the external force? So we are studying about springs, as of now, the assumption is that they are massless.
My teacher told me that when we extend a spring, or compress it, there is a force called the spring force which tries to reform the spring back it its original form. This force act... | Well, think of it this way: as you push into a spring the more it gets deformed and the more it gets deformed the more it pushes back. Eventually, you reach a position when the applied force is just equal to the force of the spring and at that moment you cannot push further and the spring is at rest now. The spring wil... | {
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First law of thermodynamics as conservation of energy We have that $\Delta U = Q + W$. What I don't see is how this formula relates to the law of conservation of energy. Can someone please clarify?
Does this mean that $\frac{dU}{dt}=\frac{dQ}{dt}+\frac{dW}{dt}=0$, so that $\frac{dQ}{dt}=-\frac{dW}{dt}$?
| Since your second question has been answered in the comments, I will answer your first question.
Let's examine in words what $\Delta U=Q+W$ means: "Any change in internal energy arises from a flow of heat into/out of the system and/or work done by/on the system." Put differently: "The only two ways internal energy can ... | {
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Scalar Field Theory for Gravity While reading the book Gravitation Foundation and Frontiers by Padmanabhan, I came across the Lagrangian for a scalar theory of gravity. But the coupling term consist of trace of the Energy Momentum Tensor. If we change the coupling term to $F(\phi)T_{ab}T^{ab}$, what prevents it from be... | If we linearize the equations of motion about a $\phi = 0$ background (and assume the usual sort of kinetic term), we will find a non-relativistic limit of something like $\nabla^2 \phi \propto \rho^2$, which is inconsistent with Newtonian gravity.
| {
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How to shift AGN x-ray spectrum to rest frame I have limited information to shift a spectrum (in the x-ray 0.5-10 keV bandpass) at redshift z=2 to rest frame. I have a plot of normalized (photon) counts s$^{-1}$ keV$^{-1}$ by energy (keV), and so I have no information to compute the flux density. Is there a way to shif... | The frequency is related to the redshift by $$\frac{\nu_{\rm obs}}{\nu_{\rm emit}} = \frac{1}{1+z}$$
Another useful relation is the fact that, for any redshift,
$$\frac{I_{\nu}}{\nu^3} = {\rm constant}$$
where $I_{\nu}$ is the specific radiative intensity.
The specific count rate (counts per area per time per energy in... | {
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Understanding the units of number density I understand that we can measure any general number density $n$ as,
$$ n = \frac{N}{V}$$
for total number $N$ and volume $V$. This puts the units of number density as $\text{length}^{-3}$ e.g. $\text{cm}^{-3}$
Now suppose the number density varies with radius as e.g.,
$$ n(r) =... | So $r$ has units of length, for example $\mathrm{m}$, so $r^{-2}$ has units $\mathrm{m}^{-2}$. to remain dimensionally consistent $N_{0}$ would have to have units $\mathrm{m}^{-1}$. Note that here, we have number density in 3 dimensions, giving a number per unit volume. We might imagine number density on the plane, or ... | {
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Time dilation and Transverse Doppler Effect – where does energy disappear? Kinematic effects of Special Relativity like time dilation and length
contraction are well known.
Article in Wikipedia makes it clear:
https://en.wikipedia.org/wiki/Time_dilation
“In the special theory of relativity, a moving clock is found to... | Let's say Sam has some light trapped in a box. According to Agibail that light in the box has momentum into the direction of motion of the box.
Transverse light according to Agibail is such that it has only transverse momentum.
If Sam opens the lid on the top of the box then according to Sam the out flowing light has n... | {
"language": "en",
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Two-point correlation function in Peskin's book I am reading Peskin's book on QFT and I reached a part (in chapter 4) where he is analyzing the two-point correlation function for $\phi^4$ theory. At a point he wants to find the evolution in time of $\phi$, under this Hamiltonian (which is basically the Klein-Gordon - $... | I am now very sure that Peskin made a mistake here. Please check the lecture Notes by Weigand
on page 43, where it is said clearly that The crucial difference to the free theory is, though,
that $\phi(x)$ cannot simply be written as a superposition of its Fourier amplitudes $a(\vec{p})$ and $a^{\dagger}(\vec{p})$ becau... | {
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Alternative form of scalar particle dynamics in the gravitational field I am interested in the dynamics of a single (classical) spin-0 particle in the General Relativistic spacetime of arbitrary signature and dimensionality. In the 1-st order (Palatini) formalism, this can be written as
$$ S[X] = -m \intop_{X} d\tau \s... | I think I just realized how to answer my own question.
The linear action is just a special case of the "length of the worldline" action in the
$$ e^0 \parallel dt;\quad e^{1,2,3}\perp dt $$
case. So this second action is obtained from the first one after gauge-fixing.
The whole point of the paragraph, though, is that i... | {
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On the average gas pressure over a pipeline This question stems from gas flow through pipelines, quoting this paper (link):
For the calculation of the $z$ factor one needs the average pressure
$p_{av}$. An obvious choice is the arithmetic average $$\tag{1}
p_{ava}=\frac{p_b+p_e}{2}$$
However the pressure over the ... | 1 and 2. To get the constant c, you treat the flow as fully developed locally, calculate the Reynolds number, represent the density in terms of the pressure (using the ideal gas law), determine the friction factor, and determine the local shear stress at the wall. This all then gives you the gradient of $ p^2$. You ... | {
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Is this an electromagnetic wave without the magnetic part? Jefimenko's Equations are:
$$
\begin{align}
&\mathbf{E}(\mathbf{r}, t) = \frac{1}{4 \pi \epsilon_0} \int \left[ \left(\frac{\rho(\mathbf{r}', t_r)}{|\mathbf{r}-\mathbf{r}'|^3} + \frac{1}{|\mathbf{r}-\mathbf{r}'|^2 c}\frac{\partial \rho(\mathbf{r}', t_r)}{\parti... | To add to Emilio Pisanty's answer: for the situation you are considering, Jefimenko's equations simplify to
$$
\begin{align}
\mathbf{E}(\mathbf{r}, t) &= \frac{1}{4 \pi \epsilon_0} \int \left[ \left(\frac{\rho(\mathbf{r}', t_r)}{|\mathbf{r}-\mathbf{r}'|^3} + \frac{1}{|\mathbf{r}-\mathbf{r}'|^2 c}\frac{\partial \rho(\ma... | {
"language": "en",
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"source": "stackexchange",
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How to evaluate the Lorentz force at a surface where the field is discontinuous? I'll take a simple case as an example. You have a constant and uniform magnetic field inside an ideal infinitely long solenoid, with currents circulating all around the thickless coils (so there's a surface current with a field discontinu... | It is indeed the average, as you suspect. To understand why, witness that the current is spread over a nonzero thickness. Begin with an azimuthal directed current density $J(r)$ (sketch this) and you get two equations:
$$\frac{\mathrm{d} \,B(r)}{\mathrm{d}\,r} = -\mu_0\,J(r)\quad\text{(}\vec{B}\text{ axially directed)}... | {
"language": "en",
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Deformation of a self-gravitating sphere from two forces I have a fluid sphere (say a gas or a liquid of uniform density, under its own gravity) on which forces is applied to its surface. I would like to find its approximate shape (most probably an oblate ellipsoid), from the forces applied on its (initialy) spherical... | The problem is to find $r(\theta, \phi) = r(\theta)$ with r the radius of the ellipsoide.
I think we can assume that the gravitationnal field created by the fluid is the same as the one from a sphere (weak deformation).
$$\mathbf{G}(r) = - \frac{\mathcal{G}M}{R^3}{r} \mathbf{e}_r$$
Where M is the mass of fluid, and R ... | {
"language": "en",
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Attenuation of radio frequency transmissions in space In a science fiction movie some aliens come to earth and when asked why, they say they received our radio transmission and came to investigate, the radio transmission being the first television broadcast (the Berlin Olympiad in 1936). So, the idea is that it took de... | What you are looking for is called free-space path loss.
Let's assume the signal is broadcast from a spherical source (e.g. the signal isn't sent with a directional antenna). Neglecting all other sources of loss (e.g. diffraction, reflection), the simplest way to calculate this loss is $\frac{1}{4\pi r^2}$.
The signal ... | {
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Why would a steel tube vibrate under high voltage? Can anyone explain why a vertical steel tube, standing with one end in contact with the ground under a $230 \space kV$ electric transmission tower, would physically vibrate at high frequency? I'm not well-grounded in electricity laws, but I suspect it may have to do w... | The high-voltage line is inducing eddy currents in the steel tube, and these are reacting against the cyclic magnetic field that surrounds the wire- and the steel tube becomes "microphonic". If the excitation frequency is close to one of the tube's fundamental (mechanical) harmonics, then the tube will "sing". This occ... | {
"language": "en",
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Are all correlation functions in a CFT non-zero? I am particulary interested in the Ising CFT. Is it clear/true that for any field $\phi$ and a large enough number $r \in \mathbb R^+$, we have that $\langle \phi(x) \phi(y) \rangle \neq 0$ if $|x-y| > r$?
In case such fields exist, are they expected to also be realized ... | For CFTs we actually know the precise functional form of the 2-point functions
\begin{equation}
\left\langle \phi(x)\phi(y) \right\rangle = \frac{C_\phi}{|x-y|^{2\Delta_\phi}}
\end{equation}
where $\Delta_\phi$ is the scaling dimension of your field and $C_\phi>0$ for non-trivial fields. You can look up the formula in ... | {
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When short circuits are not exactly short circuits?
Here $R1 = 2 \Omega$, $R2= 4 \Omega$ and $R3= 4 \Omega$
Though there looks to be a short circuit in this diagram, my teachers say that this circuit can easily be redrawn into simple parallel circuit. As far as I know a short circuit is an alternate way for current to... | It is best to label all the nodes.
$D$ and $F$ are in fact one node and are on one side of each resistor.
$A, \, B$ and $C$ are in fact one node and connected to the other side of each resistor so the three resistors are in parallel.
All the wires are doing is ensuring certain parts of the circuit are at the same pote... | {
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Why do opposite dipoles of same charge and equal magnitude cancel each other out?
In carbon dioxide, there are 2 dipoles of equal magnitude and charge pointing in opposite directions.
Why can't both oxygen atoms obtain a partially negative charge while the carbon atom contains a partially positive charge twice in mag... | Sean's answer is definitive, but I think it's worth adding a few comments.
Why can't both oxygen atoms obtain a partially negative charge while the carbon atom contains a partially positive charge twice in magnitude? Shouldn't two oxygen atoms pulling on a single carbon atom result in more positivity?
The oxygen atom... | {
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Why can a regular infrared camera not show temperature (thermography)? There are a lot of questions here dealing with infrared cameras and thermographic cameras. I think I understand the reason why a thermographic camera is able to retrieve the temperature values from any object and convert them to a falsecolor represe... | Partly a definition, thermographic means shows temperature - so any camera that shows temperature is thermographic and any that don't aren't !
To measure temperature a camera needs a couple of features. It needs to be sensitive to a wavelength that the object is emitting. A room temperature object has a peak emission a... | {
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Converting 1 Kelvin into eV I am using $E=\frac{3}{2} kT$ to find the equivalent of 1 K in eV using $k=1.38\times 10^{-23} \,\mathrm{\frac{J}{K}}$. I get $E= 1.29 \times 10^{-4} \,\mathrm{eV}$, but Wikipedia says it's $8.6\times 10^{-5} \,\mathrm{eV}$. Could anyone tell me what Wikipedia did different then me?
| It is easier to see when you use k in eV per K which is
$$
8.6173303(50)×10^{-5} \ \mathrm{\frac{eV}{K}}
$$
Wikipedia is simply using E = kT
You should always care about your units. Numbers have no physical meaning without them.
| {
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Why does sugar dissolve faster in hot water compared to cold water? Why does sugar dissolve faster in hot water compared to cold water?
| I will explain it with the help of Le Chatelier principle. It states that the rate of reaction depends on the temperature. If the reaction is exothermic, then decrease of temperature will increase the rate to compensate the effect caused by decrease of temperature. However the rate will decrease if the temperature is i... | {
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Buoyancy Force and Density I am doing a practice problem about buoyancy force. If there are two objects, (one made of wood and one made of metal), and we hold them underwater, will the buoyancy force of both objects stay the same? That's what I believe at least.
| Yes the buoyant force is the same. The buoyant force is defined as the weight of the water displaced or $\rho V g$, where $\rho$ is the fluid density and $V$ is the volume displaced. Because the amount of water displaced is the same for each object (I assume you are stating that they have the same volume), the buoyant... | {
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Why does Newton's Third Law actually work? My father explained to me how rockets work and he told me that Newton's Third Law of motion worked here. I asked him why it works and he didn't answer. I have wasted over a week thinking about this problem and now I am giving up.
Can anyone explain why Newton's Third Law works... | Newton's Third Law works because the universe tries to be fair. If you push against something it makes no sense not for it to push back against you. Your hand pushes on the table, and the table pushes back just as hard against your hand. If it didn't push back, your hand would go straight through the table. The world w... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/348514",
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"source": "stackexchange",
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Does phononic "Superconductivity" exist? Can solids be cooled to a sufficiently low temperature such that sound can travel through them without acoustic impedance?
It seems that if I had a solid in the shape of a torus, sitting in ambient vacuum, cooled to absolute zero, and then decided to introduce a compression alon... | I think there is an important difference between electrons and phonons that has to be considered here. The superconducting transition entails the formation of a many-particle state, where electrons attract each other and bind together through phonon-mediated interactions. In effect what is happening is that the motion ... | {
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Does gravity have anything to do with Van Der Waals forces? Does gravity have anything to do with Van Der Waals forces? Just throwing this out there, I was wondering if they do because gravity is such a weak force and the VdW forces at the molecular level could seem to be a good intermediary force between gravity and t... | No. Van der Waals forces are electromagnetic, not gravitational. "Van der Waals forces" are actually a family of different effects. Dipole-dipole Van der Waals falls off as $1/r^7$ (non-retarded) or $1/r^8$ (retarded). These forces can be understood using only electromagnetism and quantum mechanics. Gravity is unnecess... | {
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Why does battery generate less terminal voltage difference when current flows? The terminal voltage difference of a battery means the difference of voltage between the two termials of a battery. Now, a battery has a voltage at the positive terminal and a voltage at the negative terminal. Voltage means the work needed t... | Some reasons the voltage of a battery goes down under load:
*
*Internal resistance. A simplistic first-order model of a battery is a voltage source in series with a resistance. As you draw current, the current causes a voltage across the resistance. That voltage subtracts from the internal voltage source to give yo... | {
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What is the Planck scale magnetic field strength? Using the constants $\mu_0$ (or $\varepsilon_0$), $c$, $\hbar$, $e$ and $G$, it is possible to define two quantities with units of magnetic field :
\begin{align}
B_1 &= \sqrt{\frac{\mu_0 c^7}{\hbar G^2}} \equiv \sqrt{\frac{c^5}{\varepsilon_0 \hbar G^2}} \approx 8 \times... | A Planck magnetic field strength is not uniquely defined.
Actually you can construct many of them:
$$B= \frac{c^3}{Ge}\left(\frac{e^2}{4\pi\epsilon_0\hbar c} \right)^n$$
where $n$ is an arbitrary number, and the factor in brackets
is the dimension-less fine-structure constant $\alpha \approx \frac{1}{137}$.
| {
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How can a monochromatic X-Ray tube produce a spectrum in XPS? I thought that if we use monochromatic source, we can only get one peak, if it exists.
Because Photoelectric Effect allows only the electron that have the corresponding frequency(energy level) that can be excited.
appreciate your help to rectify my understan... | Monochromatic X-rays produce electrons from a multiplicity of orbitals,
producing a range of electron kinetic energies. One can analyze the outgoing electron
energy to produce a spectrum. It's a spectrum of Xray photon energy
minus binding energy of the electron, so for a fixed Xray energy, it's
the electron bindin... | {
"language": "en",
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Expression for angular friction Consider say a door rotating about its axis. Is there, in general, any expression for the frictional hindrance to its motion? I was thinking in line with the coefficient of friction for linear motion on a surface.
| Not in terms of dry (coulomb) friction. But in terms of damping, relating angular speed to torque $$\tau = c_\theta \,\omega$$
where $c_\theta : [\rm \frac{N m}{rad/s}]$
The source of this damping is a thin lubrication layer and the corresponding shearing of the lubricant. It is easy to estimate the damping coefficient... | {
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If someone were to put really small objects 10x spaced on a background, would they see the objects or the background? If someone were to put a sheet full of 1 micron x 1 micron black squares as a grid on a white piece of paper, and spaced them 10 microns apart (up-down, left-right, obviously diagonal doesn't count), wo... | What you describe is identical to the process called halftoning, which is used in print to give the illusion of greys with only black and white, or the illusion of full color with only 4 pigments. You describe a pattern which is 1% covered with black cubes, and 99% open space, so it would appear to be the "1% black" c... | {
"language": "en",
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Definition of symmetrically ordered operator for multi-mode case? As I know, Wigner function is useful for evaluating the expectation value of an operator. But first you have to write it in a symmetrically ordered form. For example:
$$a^\dagger a = \frac{a^\dagger a + a a^\dagger -1}{2}$$
For single mode case where the... | A quasiprobability distribution depends on the symbol/operator ordering prescription. E.g.:
*
*For Weyl/symmetric ordering of Hermitian operators, one uses the Wigner quasiprobability distribution.
*For Wick/normal ordering of creation & annihilation operators, one uses the Glauber–Sudarshan $P$ representation.
*... | {
"language": "en",
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How does a man inside bubble ball accelerate without an external force? As Newton's Laws states an object should be in rest or in constant velocity if no external force is applied. A man inside a stopped car cannot push the car as he is not giving any external force.But a man inside a bubble ball can make it move. What... | The simple answer is that there is an external force, that of friction towards the ground. The man and the ball can thus change their velocity by using the friction provided by the ground, much in the same way we can walk by using the frictions on the ground.
An important follow up question, that the OP touches upon, i... | {
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Conservation of energy problem with water hose? When we squeeze the end of the pipe while watering plants , the water speeds up , but the amount of water being released is the same ? From where does this excess kinetic energy come from ?
| Since mass=density×volume, m=dAx
Since the kinetic energy remains conserved
K.E=1/2mv^2=1/2(DAx)v^2.
As K.E is constant, as Area decreases velocity must increase.
A is area, v is velocity and x is length of water column.
| {
"language": "en",
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How could I measure the colour spectrum of a light bulb and investigate how closely it matches a black body radiation curve? Here is my research question:
What is the colour/spectrum produced by each globe type? What is the temperature equivalence? How closely does a globe match a black body radiation curve?
I will b... | You will need to use a spectrometer to measure the irradiance at various wavelengths. A camera will only measure three wavebands (R/G/B) so this will not give you the necessary resolution to make a meaningful comparison of spectral composition.
| {
"language": "en",
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Observing Two-Beam Interference at Home I want to know how difficult it would be for me to observe two-beam interference at home.
I have:
*
*A laser pointer.
*A non-polarizing beam-splitter.
*A mirror.
*Two concave lenses.
*An uneven shaky floor, some chairs, and tape.
*Patience that spans an entire day.
Thi... | The setup you describe is similar to the one used in creating holograms. All you would need to add would be the beam spreaders.
Unfortunately, this demands a level of stillness which is hard to achieve without a properly isolated optical bench. Red lasers are roughly 650nm, and if you want to see effects, you're goin... | {
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Different values for same integral calculated via contour integration Perhaps this question should be asked on the Math community, but I think that, because of the specific example that I will cite, I might get a better insight on my doubt here.
So, why can we get two different results (mathematically) according to wh... | This is simply a consequence of the Cauchy Goursat Theorem and Residue Theorem: the first tells you that an integral is invariant under an homotopy of a contour unless the the region between a contour and its homotopic image includes a new singularity; the second tells you that the integral changes by $2\,\pi\,i$ time... | {
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Shouldn't work be the same in all coordinates? We know that the work done by a force $\mathbf{F}$, along a path $\mathbf{x}$, is given by:
\begin{equation} W = \mathbf{F}^T \cdot \mathbf{x}
\end{equation}
However, suppose that i apply some change of basis, given by a matrix $A$. So, $\mathbf{F}$ will become $A\mathbf{... | Let us write the dot product like this:
$$\vec F^T \vec x$$
where the $T$ means transpose. If we now apply the change of coordinates we get:
$$\vec F'^T \vec x'=(A\vec F)^T A\vec x$$
$$=\vec F^T A^T A \vec x$$
Now a change of coordinates matrix must be orthogonal (in this case) so
$$A^TA=I$$
Hence we get:
$$\vec F'^T ... | {
"language": "en",
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How does one find the wavefunction of a particle in its rest frame? In classical mechanics, the orbital angular momentum of a particle is defined as $\textbf{L}=\textbf{r}\times\textbf{p}$. This is zero in the rest frame of the particle where $\textbf{p}=0$.
Quantum mechanically, $\textbf{p}$ is an operator. So puttin... | The rest-frame wavefunction $\psi(\boldsymbol x,t)$ is the one such that
$$
\boldsymbol 0\equiv\langle \boldsymbol p\rangle=\int_{\mathbb R^3}\psi^*(\boldsymbol x,t)(-i\boldsymbol \nabla)\psi(\boldsymbol x,t)\ \mathrm d\boldsymbol x
$$
If $\boldsymbol k\equiv\langle \boldsymbol p\rangle$ is non-zero, we just need to re... | {
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Can transverse sound waves be polarized? I know that polarization only occurs in transverse waves and polarization of light occurs as EM wave is a transverse wave. But sound waves are both transverse and longitudinal in solids. So can polarization occur for the transverse part? But we cannot stop the sound wave from pr... | These transverse waves are known as S-waves or shear waves and yes they can be polarized. Waves that are polarized in the horizontal direction are known as SH-waves and those in the vertical direction are known as SV-waves. These waves exhibit the property that when they meet a boundary between two mediums (say solid -... | {
"language": "en",
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Traveling Wave Equation $\sin(kx-wt)$ vs $\sin (wt-kx)$ In my textbook most if the times it uses $A\sin(wt-kx)$, but occasionally there is a problem using $A\sin(kx-wt)$
So i just changed it from $A\sin(kx-wt) \to -A\sin(wt-kx)$
but does the amplitude change to $-A$?
Is the wave going downwards first?(as negative ampli... |
Is the wave going downwards first?
That all depends an what you mean by downwards and what type of change you're interested in.
Let's investigate "downwards": The wave solution describes the disturbance of some quantity from its equilibrium solution. It may be a displacement of a section of string from its rest posit... | {
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Does amplitude affect time period for spring mass system? I know that with the formula $T=2\pi\sqrt{\frac{m}{k}}$ the time period is not related to the amplitude. However, would amplitude matter if i do this experiment in real life. Would a greater amplitude result in more friction of some sort?
| No, the amplitud does not affect to the period.
For a spring-mass system:
if you solve the differential equation $$m\ddot x +kx=0$$ you get a solution that looks like this
$$x(t)=A_0 \cos (\omega t -\delta)$$
Where both the amplitude ($A_0$) and the phase angle ($\delta$) are in fact arbitrary constants which could be ... | {
"language": "en",
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How many dimensions are there in the electric field? I am not a physicist. I am buying some polariser for my camera. Circular polariser intrigues me. Basically you pass light through a linear polariser, then through a waveplate, you get circular polarisation.
Wikipedia says the following:
By adjusting the thickness o... | Electromagnetic waves such as visible light are transverse waves. This means that the direction of oscillations of the fields is perpendicular to the direction of propagation of the wave. In general we can decompose the electrical field into two orthogonal components along the oscillation plane and the relative phase b... | {
"language": "en",
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Does a glass of water at room temperature emit (infrared?) radiation While reading the introduction to Feynman's lectures, it's mentioned how a glass of water cools down through evaporation, when some molecules get a bit extra energy and break free. If it's not a closed system, energy will be gradually taken away from ... | Yes, all matter above absolute zero emits radiation. To quote wiki:
When the temperature of a body is greater than absolute zero,
inter-atomic collisions cause the kinetic energy of the atoms or
molecules to change. This results in charge-acceleration and/or dipole
oscillation which produces electromagnetic radi... | {
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Why do objects feel heavier when held with an extended arm than with a bent arm? I do realise that this is due to torque and that torque is at maximum when the angle between the direction of the torque and the force acting on the object is 90 degrees. I would like to know if it is the angle between the forearm and the ... | You should always choose to calculate the torque with respect to the axis of rotation in each case.
In one of the cases, that point is your elbow and so the distance is elbow-hand, while in the other case it is the distance shoulder-hand=whoele arm.
Evidently a longer distance makes greater torque, and so more propens... | {
"language": "en",
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Total eclipses becoming rare soon? Given that the moon is receding from the earth and that the average angular size of the moon is approximately equal to the angular size of the sun at the moment, what is the current rate at which total eclipses of the sun are decreasing? ( let's say frequency rate in total eclipses / ... | In about 620Myr
The moon is receding at around 3,8 cm/yr and eclipses will stop (ie the shadow won't reach the Earth) when it has moved another 23500km
| {
"language": "en",
"url": "https://physics.stackexchange.com/questions/352892",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "4",
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What causes the phenomena of a ring appearing around the shadow of an airplane So I was sitting in an airplane and I saw a ring appearing around the shadow of the plane on the clouds. What causes this phenomena? I've added an edited image, so the effect is more pronounced.
| This phenomenon is called a Glory. It is caused by back scattering from individual water droplets. There is a lot more detail to be found on this site: http://www.atoptics.co.uk/droplets/gloab.htm
Wikipedia also has an article on it, which claims that the physics is not fully understood.
| {
"language": "en",
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"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "2",
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How do magnetic cores (ferrites) guide magnetic field? As far as I know, magnetic materials have magnetic dipole moments which align when they are under influence of the outside magnetic field.
Basically they increase the magnetic field strength. But people also say that they guide magnetic field. Does the magnetic fie... | A ferrous metal will attract the magnetic field lines around it to pass through it. Thus, it will decrease the density of magnetic field lines outside the magnet and increase the same inside itself.
So, yes the magnetic field strength decreases in area where a ferrous metal is introduced.
Ferrous metals attract the ma... | {
"language": "en",
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Does work done depend on the frame of reference? Suppose I am sitting on a bench and looking at a moving car. Force is applied on the car by its engine, and it makes it displace, hence some work is done on the car. But what if I am sitting in the car and looking at the bench? The bench covers some displacement, but who... | Let me address your scenario first. What you suggested is bad physics because it breaks the conservation of energy. It doesn't work because the car is not an inertial frame. An inertial frame is arguably defined as one in which newton's laws work. We know that the bench frame is inertial because momentum is conserved a... | {
"language": "en",
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"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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How much power in a lightning strike? The Biblical story of 1 Kings 18:20-40 relates how a lightning strike ignited a bulls carcass, as well as a wood pyre, both of which had been thoroughly wetted with abundant water. Is there enough power in a lightning strike to do this? Does the power of a mountain top lightning st... | In this link the following estimates are given
From articles in Windpower Engineering & Development, we learn that lightning bolts carry from 5 kA to 200 kA and voltages vary from 40 kV to 120 kV.
Here we find an average estimate :
An average bolt of lightning, striking from cloud to ground, contains roughly one bi... | {
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Is a lightening strike deterministic? This relates to a previous question: Is a dice roll deterministic?
Essentially, I'm trying to get a better understanding of how quantum indeterminacy interacts with the macro world.
It seems to me that lightening involves charge, and might be subject to quantum indeterminacy in te... | Quantum effects appear at the microscopic level, or at highly organized solids and fluids (superconductivity, superfluidity for example). This is due to the very small value of the Planck constant in the Heisenberg uncertainty, which is obeyed automatically macroscopically down to micron levels.
Lightning strikes fol... | {
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With respect to what we are saying space is homogeneous or space-time is isotropic? I don't really understand what we are talking about when we say space is homogeneous. What we are measuring? My notion is: it should depend on the entity and with respect to that entity one can decide space is homogeneous or not!
May b... | You are correct in the sense that there are physical quantities, observables, like scalar and vector fields that are, in general, varying in space.
However, that's not what the phrase "spacetime is isotropic" is meant to convey. What this means is that, in the absence of anything to break the symmetry, each point in s... | {
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Do charges move to the outer surface of a conductor to minimize the potential energy? We can think the charges go to the outer surface of a conductor to minimize the electrostatic potential energy of the system. We can check this using a simple calculation using a charged sphere.
A uniformly charged sphere would have ... | If you put two equal point charges, say two nuclei with $+|e|Z$, at the opposite points of the conducting sphere, they will stay there. The free electrons of the conductor will start to move due to attraction to these charges until the friction losses (=resistance) dissipate the extra energy into heat. Otherwise there ... | {
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How does one obtain observables from a wave function? I'm beginning to study the quantum chemistry (my background is computer science and computational mathematics) and I'm not sure if I understand well the basic concepts, like wave function and operators.
I've read questions
What is a wave function in simple language?... | $\hat{O}$ will have a set of eigenvectors $\phi_i$ and eigenvalues $o_i$.
You can expand your wave-function $\psi$ in terms of the basis set $\phi_i$, i.e. $\psi=\sum_i c_i\phi_i$.
If you make a single measurement then your wave-function $\psi$ will collapse to one of the eigenvectors $\phi_i$ with probability $|c_i|^2... | {
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Thermodynamics : Doubt in First Law I just started my study of thermodynamics. I am having problem in uderstanding a concept.
Suppose I drop an ice-cube and a rock of cube shape. Which one will reach the ground first? I know ratio of Work to Heat equals Joules Constant. Therefore any change in potential energy will res... | The falling process can be quite complex when we come to answer your with one word: stone or water.
When an object falls, it will be subjected to the following two forces: gravity force and air drag force. If the air drag force can be ignored, the gravity force acts on the object converting the potential energy to a k... | {
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Closed container buoyant force A closed container of water contains a Styrofoam block attached to the bottom of the container by a massless string. When the system is accelerated upwards, what happens to the tension in the string?
Background: I am an MCAT Physics teacher and this question was on an MCAT. Assuming the... | Buoyancy does not depend on compressibility. The variation of pressure with depth is linked to the weight of a cylinder of liquid having cross-section $A$ extending from depth $y=-D$ to the surface $y=0$. The density is $\rho(y)$ and the pressure is $p(y)$.This cylinder has a weight $$W=gA\int_{-D}^0\rho(y)dy$$ that m... | {
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Nature of Work done by Forces I am confused about the possible nature of work that a conservative and non conservative force can do.
*
*Do Non conservative forces like friction only do negative or zero work and not positive?
*Can conservative force also do negative work, I know Gravitational Force is conservative f... | Yes force of friction can do positive work
Work done by conservative forces may be positive.negative or zero
| {
"language": "en",
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"timestamp": "2023-03-29T00:00:00",
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Time dilation for non-physicists Apologies in advance, as I'm not a physicist, and may use terms incorrectly.
In the movie Interstellar, the planet Miller has a time dilation of one hour to seven Earth years. This has brought up several questions for me:
*
*At what point would someone (outside the gravitational forc... | It was a fictional story. It was not well researched. According to Newtonian physics, it would take about a year to accelerate to the speed of light at 1G. If the movie were more realistic, then once you're that deep in a gravitational potential well, it would probably take many years of apparent time on the ship to ac... | {
"language": "en",
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"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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How can the presence of a solvent be included in a polymer bead-spring model? I have a bead-spring model of a polymer melt and I would like to simulate what happens when a solvent is added to the system.
The most direct way to do this would be to add solvent particles into the system. But my simulations already take en... | I assume you are currently running a deterministic simulation which explicitly computes the time evolution of all degrees of freedom using Newton's equations. In order to implicitly simulate a solvent, what you want instead is a simulation that computes the time evolution of only a subset of relevant degrees of freedom... | {
"language": "en",
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Why is unit of pressure (psi) used to determine things like bite force of an animal? Whether in tv documentaries or journals, whenever they talk about an animal's bite force, it's measured in PSI anytime imperial units are used (ex: National Geographic, NIH Journal). Many even seem to highlight the fact that it's pound... | Thank you for asking this question! You are absolutely correct. Bite force (any force) should be reported in units of pounds-force or Newtons. Better yet, I would model the jaw as a hinge and report the torque around the hinge since the force would likely be higher closer to the back of the jaw. I suspect when bite fo... | {
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What do they mean when they say that it does not require any work to move a charge from one point to another in an equipotential surface? In the textbook it says that no work is required to move a charge from one point to another on an equipotential surface. Do they mean work by the electric field or work by anything? ... | "it takes no work" in the same sense it takes no work to move an object on a perfectly frictionless, flat surface. It is true and theory, but moving an object requires accelerating it at least a little bit, which requires some work, as you point out.
| {
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"source": "stackexchange",
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Direction of friction in complicated physics problems I want to ask how to determine direction of friction in complicated mechanical problems (for example 5 masses each over other and 3 forces on these masses in 3 different directions and friction between every masses)?
Is there a absolute way to find direction of fric... | If the block is moving, the direction of the frictional force is in the opposite of the relative motion of the block compared to the frictional surface.
If on the other hand it is a static situation the frictional force is in the direction opposite to the direction that the blocks would move if it were a friction-less ... | {
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Why does a calculation to count objects covering a certain area seem to give nonsensical units? Suppose you want to estimate the number of atoms in a rectangular sheet of graphene. You might estimate the sheet to have $10^{7}$ atoms along one edge and $2*10^{7}$ atoms along the other edge. Multiplying while keeping tra... | What is wrong with your calculation, is that you substituted a "count" for a dimension.
The correct way to do it, would be to determine the length of $10^7$ atoms. Assuming they take 1cm, then $1cm^2$ would have $1x10^{14}$ atoms, and the sheet (1 cm by 2 cm, or 2 $cm^2$) would contain ($1x10^{14}$ atoms/$cm^2$ x 2 $cm... | {
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"timestamp": "2023-03-29T00:00:00",
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"answer_id": 4
} |
Lorentz Transformations Vs Coordinate Transformations I'm really confused about Lorentz transformations at the moment. In most books on QFT, Special Relativity or Electrodynamics, people talk about Lorentz transformations as some kind of special coordinate transformation that leaves the metric invariant and then they d... | Looking at your question i guess i have a simple answer.if any two observers are in a specific type of coordinate frame (cartesian polar.....e.t.c)and they want to know the energy momentum position and velocity then they will use lorentz transform to find out each others position velocity energy momentum.but if one obs... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/356034",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "13",
"answer_count": 5,
"answer_id": 3
} |
What exactly happens in the basic QED Feynman diagram? When a photon is absorbed by an electron, I think that the following things happen:
*
*The electron changes in momentum, angular momentum and energy.
*The phase of the electron wave function changes by a fixed angle given by the coupling constant.
Is this cor... | As for the first point, any of the quantities by which the electron is characterized are changed due to conservation laws, which are the 4-momentum conservation law, angular momentum conservation law, charge conservation law. The photon doesn't carry electric charge but it definitely carries the 4-momentum and the angu... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/356269",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "1",
"answer_count": 2,
"answer_id": 1
} |
Sufficient conditions for a mapping to be canonical in Hamiltonian Mechanics My professor mentioned:
A simple way of testing whether a mapping $(q,p)$ to $(Q,P)$ is canonical is by examining:
$$P · dQ − p · dq$$
and if it equals to $dA$ (a differential) then it is canonical.
However, I'm wondering why is this the case,... | Be advised that there are different definitions of a canonical transformation (CT), cf. e.g. this Phys.SE post.
Your last definition of a CT agrees with the definition in e.g. Landau & Lifshitz and Goldstein, while your professor is listing a sufficient condition for a symplectomorphism, which is called a CT by e.g. A... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/356504",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "3",
"answer_count": 1,
"answer_id": 0
} |
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