Q stringlengths 18 13.7k | A stringlengths 1 16.1k | meta dict |
|---|---|---|
When does causation take time? I apologize in advance if this is an elementary question. I am a statistician and would like to use an assumption in a statistical method, but I don't know if the assumption usually holds in nature.
I would like to assume that, if $X$ causes $Y$, then the causal effect from $X$ to $Y$ tak... | There is a very simple answer to at least a part of your question. The minimum possible time for a causal effect to propagate where event $A$ is a cause of event $B$ is given by the spatial distance $\mathrm{d}_s(A,\,B)$ between the events in spacetime divided by the universal signal speed limit $c$, i.e. $\mathrm{d}_s... | {
"language": "en",
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How to find the null geodesics? The metric below was considered in [Spacetime perspective of Schwarzschild lensing]
$ds^{2}=2f du^{2}-\frac{2}{l^{2}} du dl-\frac{1}{2l^{2}}(d\theta^{2}+\sin^{2}\theta\, d\phi^{2})$
The authors gave null geodesics for this metric as
where $A,B,C$ are three first integrals of the null ge... | The equation you list
$$g_{\mu\nu}\partial_\tau x^\mu\partial_\tau x^\nu=0$$
is satisfied by all null-trajectories. However, a null geodesic must also satisfy the geodesic equation
$$\partial^2_\tau x^\mu +\Gamma^\mu_{\nu\rho}\partial_\tau x^\nu\partial_\tau x^\rho=0$$
These two equations, taken together, should suff... | {
"language": "en",
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What happens if a body jumps in the Moon? I need to know why on Earth (ha ha..!) this behaviour happens when a body jumps in the Moon (a celestial body without any atmosphere at all).
Video explanation: https://youtu.be/Qgs5E5gKO48
The steps I followed using Kerbal Space Program:
*
*Start in position A
*Perform a c... |
Should not the object end up in position A again?
No, it shouldn't, because of the Coriolis effect (assuming the moon is rotating about an axis with respect to the stars).
From the perspective of a frame rotating with the moon, the coriolis acceleration is $-2\,\vec\omega\times \vec v$, where $\vec w$ is the moon's a... | {
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What is the minimum number of collisions for photon required to lose all of its energy in an electron cloud? The electron cloud I refer to is a free electron cloud. Please help in this question. Is the answer infinite? If it is then it would take infinite time, which it doesn't.
| As you know that electron loses its energy in scattering with free electron via Compton scattering and the change in wavelength of the photon can be written as
$\lambda'-\lambda=\frac{h}{m_ec}(1-\cos\theta)$
after some manipulation the above equation can be written as
$\Delta E_{photon}=\frac{2E_{photon}^2}{m_ec^2}(1-... | {
"language": "en",
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When should you jump off a falling ladder? If you stand on the top of a falling ladder you will hit the ground at a higher speed (and therefore presumedly sustain more injury) if you hold on to the ladder than if you jump off it.
This was solved
here.
Where is the "break even" height on the ladder, from where you will ... | We can do this with a minor modification to the calculation described in the earlier question. As before we'll take the ladder length to be $\ell$, but now we'll take your height to be $\alpha\ell$, where $\alpha$ ranges from zero to one. Our reference point is if you let go, in which case your speed when you hit the g... | {
"language": "en",
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"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "30",
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How many arcseconds the light of a star unfolds in the vicinity of jupiter? One of the main demonstrations made to test the theory of relativity were the images of the solar eclipse of May 26, 1919, (causing a shift in the positions observed in celestial coordinates of its source stars 1.7 arcsec, the amount predicted ... | The correct simple formula that gives a VERY close approximation (in the 'weak field' approximation) is [4G/c^2][M/R]
... where M is the mass of the object, and R is the radius of closest approach of the light. Note that since the first term is a constant, the deflection varies as M/R.
See here for an incorrect and cor... | {
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Conductance of semiconductors at very high temperatures The restivity of typical conductors tends to increase as temperature increases. From what I understand, this is due to electron scattering.
Semiconductors tend to have their restivity decrease as temperature increases as more electrons are promoted to conductance ... | This DTIC Report (PDF) shows that the conductivity of silicon continues to increase as temperatures increase from 500K to close to silicon's melting point at 1,687K:
This is due to the rapid increase in the number of free electrons and holes with increasing temperature.
As temperatures increase, phonon scattering in... | {
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Deceptively simple mass-spring problem? This question is inspired by two other, similar, so far unanswered questions (posed by different OPs).
Mass $m_2$ sits on a incline with angle $\theta$ that provides just enough friction for it not to start sliding down. It is connected by a massless string $S$ and perfect sprin... | Got it.
As $m_1$ drops, gravitational potential energy is converted to spring potential energy:
$$m_1gy=\frac12 k\ell^2$$
Where $y=\ell$ because the string doesn't stretch.
The maximum drop is:
$$y_\textrm{max}=\frac{2m_1g}{k}$$
Maximum tension in the spring then is:
$$T_\textrm{max}=ky_\textrm{max}=2m_1g$$
For $m_2$ t... | {
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Transferring force through a string, including gravity I couldn't think of a better title to describe this confusion that I have.
Say you pick up a string and pull on both ends so that it is rigid. The string is a collection of an infinite number of objects. For simplicity, assume there are $n$ objects for some large ... | If you divide the string into $n$ parts then each part has mass $m/n$, where $m$ is mass of string. So beginning with one end of the string and proceeding with your argument, by the time you reach the other end the force will be $-\textbf{F}-n\times (m/n)\textbf{g}=-\textbf{F}-m\textbf{g}$, which is as it should becaus... | {
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Why image is blurry or focused with convex lenses? I have a few fundamental questions in optics about the focus and blurry images.
Each text book says that according to this picture the object image is the same.
1) If we move the screen to point further then the image will be blurry. What causes it to be blurry?
2) Why... | Thought I'd pop it into an answer for clarity - and more words:
Your picture answers these well. Look at those blue lines. These are light rays from the point at the top of the Object.
At the real image point, they are all together, in another nice sharp point. This is in focus.
Point 4 needs some clarification - the ... | {
"language": "en",
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Bohr / De Broglie postulate (what does $n λ= 2 π r$ imply) From the Bohr/De Broglie postulate we have n λ = 2πr where λ is the De-Broglie wavelength , r is the radius corresponding to n and n is the quantum number.
*
*An electron in the state n=2 has more energy than that at n=1
*That implies that the De- Broglie w... | Well if you go with Bohr's model of atom then,
since $mv^2/2 = K.E.= KZe/(2an^2)$
$= 2.18 *10^{-18} *Z^2/n^2$.
It means the total kinetic energy decreases with increase in n. This also means that velcity, $v$ of electron also decreases with n.
Now look at de Broglie's equation-
$\lambda = h/m_ev$
Since velocity decreas... | {
"language": "en",
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Does gravitational time dilation happen due to height or difference in the strength of the field? The reason why you have to tune differently the atomic clocks in GPS is because the GPS is higher or because there is less gravity there, or both? In other words in a constant gravitational field which doesn't differ with ... | Quite simply:
1) you know from special relativity that accelerated frames experiences a time dilation effect (time is slower for them), and that the more accelerated, the slower the time,
2) strong equivalence principle tells you that standing still on earth or at a constant height with respect to the ground means you'... | {
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How to measure the inner diameter of thin tube (0.5mm to 2mm) Does anybody know what method or equipment could be used to measure the inner diameter of capillary tubes? They would be in the region of 0.5-2mm in diameter.
Edit: the tube is made of plastic and I have standard lab equipment available.
| Some reasonable methods have already been proposed, but you might just measure the height of water column in the capillary (at least if the capillary is transparent) and calculate the diameter (https://en.wikipedia.org/wiki/Capillary_action#Height_of_a_meniscus)
| {
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Finding normal and tangential velocity and acceleration for motion along a 3D curve Basically, I have a major problem on my hands.
As part of an assignment, I have been given a set of 3D points, as well as the time between them, and nothing else, and I'm supposed to find the tangential and normal velocities and accele... | The velocity $\vec{v}$ can be obtained by computing the derivate of each position component with respect to time.
The acceleration $\vec{a}$ can similarly be obtained as the second derivative.
The tangential component of the acceleration is then $\vec{a_T} = \vec{a} \cdot \frac{\vec{v}}{v}$, and the normal component $\... | {
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Expressing the magnitude of a cross product in indicial notation I am trying to teach myself tensor calculus but have reached a stumbling block - expressing the magnitude of a cross product in indicial notation. I know that one can express a cross product of two vectors $\vec{A}$ and $\vec{B}$ in indicial notation as f... | You're right that
$$\mid \; \vec{A} \times \vec{B} \mid^2 \; = (\vec{A} \times \vec{B})_m(\vec{A} \times \vec{B})_m$$
We can write $(\vec{A} \times \vec{B})_m$ as
$$\epsilon_{mij}a_ib_j$$
and since we need to use different indices we'll write the second $(\vec{A} \times \vec{B})_m$ as
$$\epsilon_{mkl}a_kb_l$$
(by chan... | {
"language": "en",
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"source": "stackexchange",
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Neutron-Antineutron Annihilation Is the process $n + \bar{n} \rightarrow \pi^{+} + \pi^{-} + \pi^{0}$ possible?
| It might be suppressed for reasons I am too lazy to examine the process for (symmetry concerns, especially related to rotations), but energy is not a problem. If the two neutrinos have enough kinetic energy, it can be converted into the mass of the pions (among other possibilities, including electron-positron productio... | {
"language": "en",
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"source": "stackexchange",
"question_score": "3",
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Path integral approach to harmonic oscillation I've been trying to verify this result from Das' book "Field Theory: A Path Integral Approach",
Consider the action of a harmonic oscillator perturbed by a source $J$
$$ S=\frac{1}{2}m\dot{x}^2-\frac{1}{2}m\omega^2x^2+Jx. $$
The transition probability would be given by
$$... | You confused the action with lagrangian.
$$S[x]=\int dt L\Big(x(t),\dot{x}(t)\Big)$$
As $L$ contains only simultaneous $x$ and $\dot{x}$ you'll get,
$$\frac{\delta^2S}{\delta x(t_1)\delta x(t_2)}=\Big(\dots\Big)\cdot\delta(t_2-t_1)$$
$\delta$-function will eat double integration
| {
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Lorentz similarity transforms I am reading Peskin-Schröder, p. 36. Here is what I don't understand: They define a similarity transform in the coordinate space as:
$$x^{\mu} \rightarrow x'^{\mu} = \Lambda^{\mu}_{\nu} x^{\nu}$$
Then their field transform becomes:
$$\phi(x) \rightarrow \phi'(x) = \phi(\Lambda^{-1} x)$$
Ho... | The idea is that the transformation of fields
$$\phi \to \phi'\tag {1}$$
induced by a coordinate transformation
$$x \to x' = \Lambda x \tag {2}$$
is such that if we simultaneously change coordinates and fields, then nothing changes.
In other words, the right hand side of (1) must be defined in order to fulfill
$$\ph... | {
"language": "en",
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How are the spins of three quarks in a nucleon aligned? A proton is composed of uud. Are the two up quarks paired up to cancel each other's spin or are one up quark and one down quark paired up?
I know the three quarks may only carry a small proportion of the total proton spin. But they still need to be aligned somehow... | The wave function of a proton is $2|u\uparrow u\uparrow d\downarrow\rangle-|u\uparrow u\downarrow d\uparrow\rangle-|u\downarrow u\uparrow d\uparrow \rangle$... So the probability of having u paired up with d is 2/3, and that of having u paired up with u is 1/3.
| {
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Internal forces in an isolated system I did a weird activity and now I am trying to figure out the physics behind it:
While sitting on a chair I kept my feet above the ground and tried to move the chair forward. I was able to. Initially, I thought that perhaps the center of mass won't be changing as I was pushed backwa... | I respect MaxW's view. But the term that he is calling the forward energy is what I am calling inertia's role. The reason for me to answer again is that he has neglected inertia's role completely and is stating that friction is the only reason for such movements and is also stating that this movement is not possible wi... | {
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Why is imposing a symmetry on a theory considered more "natural" than fine-tuning its couplings? Theories whose behavior would qualitatively change if their couplings were not fine-tuned to particular values are often dismissed as "unnatural" (in high-energy physics) or "unrealistic" (in condensed-matter physics), whil... |
Why is imposing a symmetry on a theory considered more “natural” than fine-tuning its couplings?
Take a one carat diamond (200 milligrams ofcarbon). It can be described by a simple symmetry
Unit cell of the diamond cubic crystal structure
Which is "simpler" : imagining the build up of the crystal by using the sym... | {
"language": "en",
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For lattice, what are the Goldstone bosons for the broken rotation symmetries? In $1$ dimension, we know that lattice breaks continuous translational symmetry into discrete translational symmetry, which generates $1$ Goldstone boson, i.e. $1$ longitudinal phonons.
In $d$ dimensions, if there are only $1$ type of atoms... | For the case of translational symmetry, the gapless point of the phonon mode is understood as a uniform translation of the lattice, which of course costs zero energy. However, by saying that the phonon is gapless, we practically compute the energy $E(k)$ of a phonon of lattice momentum $k$, and take the limit $$\lim_{k... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/278249",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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What exactly is a 'quantum mechanical physical system'? I was reading the Wikipedia article about the Zero-point energy in which it states
Zero-point energy...is the lowest possible energy that a quantum mechanical physical system may have...
And I just wondered what it was referring to as a 'quantum mechanical physi... | It's certainly a rough term, which really doesn't mean much more than a system where you get a very wrong answer if you treat it with classical physics. Thus, if it's close to its "zero point energy", it's redundant to call it a quantum mechanical system, as that goes without saying! But one must certainly avoid equa... | {
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Why does increasing resistance decrease the heat produced in an electric circuit? If $H=\frac{V^2}{R}{t}$ ,then increasing resistance means decreasing the heat produced.
But, isnt it that the heat in a circuit is produced due to the presence of resistors? Moreover metals with high resistances are used as heating elem... | Yes, there are two separate issues that involve resistance to keep track of. The first is, what is the current that will run through the circuit, given the voltage. That depends on the resistance such that the lower the resistance, the higher the current, and that's where the counterintuitive behavior is coming into ... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/278530",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "6",
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Can Boyle's law be used to approximate energy storage? We know from Boyle's law that $PV=k$, where pressure $P$ has units of Pascals, volume $V$ has units of cubic meters, and $k$ is a constant. Multiplying and simplifying the units from the left side of this equation, we have
$$\mbox{Pa}\cdot\mbox{m}^3$$
$$=\frac{\mb... | It has the right units, but doesn't really work. If you want the internal energy available for doing useful work then that will depend on the technique used for extracting that work. For example, if the gas is expanded isothermally then $P = P_i V_i / V$ and the work the gas does in expanding is: $$\begin{align} W & = ... | {
"language": "en",
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Special Relativity: Length Contraction Confusion So here's a scenario I made up and I want to know if it is correct or not.
I'm was standing on the earth, l$_0$ meters away from a stationary rocket in space. The rocket then starts travelling towards me at a constant speed v. From my frame of reference the distance l$_0... | The length $l_0$ exists in your reference frame, so you may measure it without any length contraction. The rocket does not jump towards you due to length contraction when it starts moving quickly (it will move toward you, though). The length that exists in the rocket's moving frame is the length of the rocket itself. T... | {
"language": "en",
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"source": "stackexchange",
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If my car was a vacuum inside, would it get as hot parked in the summer sun? Okay, I've been wondering this one all summer. Whenever I open my car door, I'm greeted by a wall of very hot air, which takes a while to cool down, of course, with the air conditioning. So I was wondering, if when I parked my car, I could fli... | The same amount of energy would get through the car windows whether or not there was air inside the car. This heat would be absorbed by the interior surfaces, which would radiate in the infrared part of the spectrum. Unfortunately, the car windows are just as opaque to that IR radiation whether or not air is in the c... | {
"language": "en",
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Calculating relative distance covered Two balls 'A' and 'B' are thrown vertically upwards with the same velocity. The mass of A is greater than that of B. We need to find which of the balls reaches a greater height (assuming the effect of air resistence is negligible).
I personally feel that A would travel further sinc... | the thing you have missed to mention is effect of air resistance.If we include the effect of air resistance in this question then role of mass will come into play, but if you are not including air resistance then you will use s=ut+at^2/2, which is independent of mass so both bodies will traverse the same distance.Hope ... | {
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How do we prove or disprove that a particle has no internal structure? In many pop physics books I have read that an electron has no internal structure.
How do we know that and how can we rigorously prove that it has no such structure at all?
| You can't "prove" the electron has or has not internal structure. All you can do are collision experiments at the energies available to you. Along these lines the proposed ILC (International Linear Collider) - if build - will provide an unprecedented new look at the electron (and positron).
| {
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Why doesn't electric charge immediately leak off charged objects? I will focus my question with a particular example: a metal sphere, surrounded by vacuum, is given a negative charge. I know that when this charge is great enough, electrons will be emitted from the sphere, but why is the threshold for this so high? As I... | An electric field which would strip electrons from the metal would need to be strong enough to provide for a voltage difference of $4V$ over a distance related to the work function -- the distance between "electron is in the metal" and "electron is outside the metal". One should expect this distance to be on the order... | {
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Why can't I build a non-reversible optic setup which focuses the sun to higher temperatures? Following this question I would like to challenge one of the assumptions.
The standard answer is that thermodynamics prohibits focusing the sun to a spot such that the spot reaches a higher temperature than the sun itself, beca... | Don't forget the Lagrange Invariant. That's what it's all about. The sun has a finite size in object space and therefore has a field. Faster optical systems will provide smaller spot sizes of the sun but the angles will be larger. Longer focal length systems will provide larger images but the angles are smaller. As you... | {
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If you are vacuuming your carpet and you wrap the cord around your body do you become a magnet? If you wrap an active electric cord around your body, do you become an electromagnet?
| No. The power cord on a vacuum cleaner has both supply and return conductors, which produce opposing magnetic fields. The region of nonzero magnetic field is limited to a few cable diameters away from the cable.
Also the magnetic field due to an alternating current changes direction at 50-60 Hz, depending on your loc... | {
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Memory fading “striyers” in viscoelastics I was talking to a guy who does polymer moulding, and we were discussing a few industrial issues in melting, mixing and forming shapes, and with a few of my suggestions he rebutted with, "no that would create striyers". So for example, one mixing technique I suggested had the f... | Striation? ...Striations means a series of ridges, furrows or linear marks
| {
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Coaxial Rotor Helicopters From what I've read and watched it looks like in the coaxial setup the rotors are stacked and turn in opposite directions so as to counter the torque in the main rotor and eliminate the need for the rotor in the tail. It looks like this:
Now, I have problems understanding why would this setup... | As well as downward velocity the upper rotor imparts some rotation - this means the lower rotor will "hit the air faster". But the net result is less rotation of the air below the second rotor which in principle allows for greater efficiency.
As has been pointed out, the weight and complexity of the gearing mechanism n... | {
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Fourier's law and time taken for heat transfer? Fourier's law states that
"The time rate of heat transfer through a material is proportional to the negative gradient in the temperature and to the area."
A mathematical description of this law is given as
$$\frac{dQ}{dt}=-KA \frac{dT}{dL} \, . \tag{1}$$
where $K$ is t... | You are equating the temperature change of an object due to heat loss (or gain) to the heat current across an unrelated interface. You should have written the equation (2) with partial derivatives, on the left side with respect to time, on the right side with respect to the coordinate. Therefore you cannot simply cance... | {
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Is there a way to estimate fan capacity at altitude? Provided you know the capacity of a fan (flow rate) at constant speed and at sea level, is there an analytical way to predict what the flow rate would be at altitude? Or is this specific to the fan's design?
| Following answer is speculative.
Flow rate of air ($Q$) is determined once fan's geometry, its angular speed ($\omega$), and thermodynamic state of air (in particular its $\rho,\mu$) is specified. Since geometry of fan is not being changed, let us take any linear dimension associated with it (say, length of fan blade) ... | {
"language": "en",
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Static Equilibrium Problem with 3 Tension Forces
I had some trouble solving these.
For the first one I assumed there wasn't a tension force on the 2nd mass, which gave me:
$$FT_1.\cos A = FT_2.\cos D$$ and $$FT_1\sin A + FT_2\sin D = F.g$$
Not sure how to approach 2nd problem.
| These questions are to do with the equilibrium of a point mass (knot) subjected to three forces provided by three masses and transmitted via pulleys and strings to the knot.
There are many methods of solving such problems but drawing a force diagram, which will be a triangle in this case, might help?
Because you have a... | {
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Is there a Schrödinger equation for phase space? The Schrödinger equation is generally formulated in position space
$$
i \hbar \frac{\partial}{\partial t}\psi(x,t) = \hat H_x \psi(x,t) = \left [ \frac{-\hbar^2}{2m}\frac{\partial^2}{\partial x^2} + V(x,t)\right ]\psi(x,t)
$$
or in momentum space
$$
i \hbar \frac{\parti... | The answers given so far are correct, but I don't think they hit the core of the issue. Quantum mechanics has either a position or a momentum representation where this or is an exclusive or. In general quantum physics is described according to a complete set of commuting operators, and in the case of momentum and space... | {
"language": "en",
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For solids/liquids can $dP$ or $dV$ be assumed to be $0$ when calculating $\triangle H$ or $\triangle U$ by the following formulae? For solids/liquids can $dP$ or $dV$ be assumed to be $0$ when calculating $\triangle H$ or $\triangle U$ by the following formulae?
$$\triangle H=nC_p\triangle T + \int (\frac{\partial H}{... | Bulk modulus of a substance is a measure of its compressibility. It is given by $\beta$ = V.$\partial$P/$\partial$V where $\partial$V/V is the fractiaonal change in volume, for infinitesimal pressure change $\partial$P. For liquides, $\beta$ is very high having magnitudes of the order of $10^9$ Pa often. This means, th... | {
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Curved image in a miniscus Reflected in a coffee cup meniscus one commonly observes a tiny image of a straight horizontal florescent lamp behind the observer quite altered. It becomes curved and changes direction with a U-turn midway somewhat like $ <,\, >\, $ shapes.
Why does it turn backwards? What happens at the ... | I think that these are the patterns referred to in the question.
Quality is not great as I used water and not coffee and also lacked a third hand.
If one looks at near glancing incidence with the fluorescent light behind one then the pattern looks like image 1 below.
$AB$ is along the interface between the water and ... | {
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How did Maxwell's theory of electrodynamics contradict the Galilean principle of relativity? (Pre-special relativity) The Galilean principle of relativity:
The laws of classical mechanics apply in all inertial reference systems
OR
No experiment carried out in an inertial frame of reference can determine the absolut... | Imagine a stationary electron sitting next to a long length of wire with current flowing through it. Since the wire is neutrally charged, there is no electric force on the electron, and since the electron is stationary, there is no magnetic force.
Now imagine the whole system is moving lengthwise at a constant velocity... | {
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Force between proton in a conducting shell and electron outside of shell? There's a proton inside a conducting shell and an electron outside of it. Inside the shell, there is no field due to the electron, but the electron feels the field due to the proton. Therefore the electron should move towards the immobile proton,... | The whole shell moves because the electric field experienced by the outer electron has its origin in positive charges induced by the inner proton on the outer metal surface equivalent to the proton charge. The metal shell would even move without a proton inside because the electron induces positive charges on the surfa... | {
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Do we need a bounded domain for the Laplace equation to have a non-zero solution $u$? If we have the Laplace equation for electrostatics in free space, that is
$$\Delta u(x) = 0 \quad \quad x \in \mathbb{R}^3,$$
is the only solution $u = 0$? And also, we only get non-zero solutions for $u$ if we instead consider the La... | Since you are dealing with the whole space, you can take advantage of the so called Liouville theorem for harmonic functions.
Liouville theorem. Let $\phi : \mathbb R^n \to \mathbb R$ be a $C^2$ function such that $\Delta \phi =0$ everywhere. If $\phi$ is bounded (i.e., there is $k \in [0,+\infty)$ such that $|\phi(x)... | {
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Energy dissipated when two charged capacitors are connected in parallel The question at hand is:
"Two capacitors of capacitances $C_1$ and $C_1$ have charge $Q_1$ and $Q_2$. How much energy, $\Delta w$, is dissipated when they are connected in parallel. Show explicitly that $\Delta w$ is non-negative."
I'm confused abo... | I will show that the expression $\Delta U$ is in fact negative, rather than positive, since the system dissapates energy, rather than spontaneously gaining it. That is, we must have $\Delta U = - \Delta w$.
Starting from your expression for $\Delta U$,
$$\Delta U = \frac{(Q_1+Q_2)^2}{2(C_1+C_2)}-\frac{Q_1^2}{2 C_1} - ... | {
"language": "en",
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Time dilation in orbit When orbiting a massive object, perhaps a neutron star, you maintain your altitude while at the same time you are close to a very strong gravitational field. Being in orbit, and being in free fall is indistinguishable for the object in question. The object is not affected by gravity, locally.
Ano... | Yep! Still applies.
Set $c=1$ and use the Schwarzschild metric. This metric is the unique solution for any vacuum, spherically symmetric spacetime which behaves like a Newtonian $\frac{1}{r}$ potential in the large $r$ limit. If the Schwarzschild radius is $R$, we just have have:
$${d\tau }^{2}=\left(1-{\frac {R}{r}}\... | {
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Is measurement of coordinates possible near strong gravity? We know that Schwarzchild metric describes an asymptotically flat spacetime. This means that far away from the event horizon we can safely interpret the $r$ coordinate as distance from the center.
But when close enough to the event horizon the curvature becom... | The Schwarzschild $r$ coordinate at a point is defined as the circumference of the circle passing through that point and centred on the mass divided by $2\pi$. This definition applies at all distances even inside the event horizon.
To see this take the Schwarzschild metric:
$$ ds^2 = -\left(1-\frac{r_s}{r}\right)dt^2 +... | {
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Two balls A and B of the same size are dropped from the same point. If the mass of A is greater of the two, and if air resistance is the same on both, which ball will reach the ground first/simultaneously?
I thought that since the acceleration acting on them is same, both will reach the ground simultaneously. But the a... | The heavier one will reach the ground first. Note that saying that the air resistance is the same for both is a bit vague, and it is by no means the same thing as neglecting air resistance. The drag force depends on the shape of an object (surface area) and therefore it is the same for two identical balls with differen... | {
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Why is it that the change in internal energy always uses the formula with Cv in regards to pressure/volume/temperature changes on a gas? Normally I would associate the use of $C_v$ with finding the energy taken into or leaving a system when the volume is kept constant. However, the formula to find $\triangle E_i$ (chan... | I rationalize the use of $C_V$ for finding $\Delta U$ of ideal gases this way:
Internal energy is the measure of kinetic energy on a microscopic level. That is, the average velocity of all the individual particles that make up a system.
For ideal systems, the volume of a container which makes up the system will not h... | {
"language": "en",
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Is Physical Information Real My question is about physical information and whether or not it is something real or merely fancy math. My problem is that physicists seem to talk as if information is real - however when they describe what it is they make it sound like it's merely a mathematical abstraction.
For example, i... | From the point of view of quantum field theory, the only difference between you and complete vacuum is the arrangement of quantum fields. Namely, you and vacuum ("nothing" in a layman's language) are made of the same "things", the only difference is how you configure these "things". That's information.
| {
"language": "en",
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"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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Consequence of approaching infinite mass for near-light speed particles Considering that the inertial mass of an object approaches infinity as the speed of the object approaches $c$, and that inertial mass equals gravitational mass, does this not imply that particles nearing $c$ would have gravitational mass approachin... | the whole reason that the inertial mass increases as an object approaches C is that it requires an increasing amount of energy to be able to accelerate faster, hence to accelerate an object (that has mass) to C would require infinite energy (and break a LOT of physics)
| {
"language": "en",
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"source": "stackexchange",
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(SR) Lorentz low speed approximations In Special Relativity, the standard Lorentz transformations are:
$t' = \gamma (t - \frac{vx}{c^2}) \\
x' = \gamma (x - vt) \\
y' = y \\
z' = z$
However, if we make a low speed approximation where $v \ll c$, then $\gamma \approx 1$ and we get:
$t' = t - \frac{vx}{c^2} \\
x' = x - vt... | At flippiefanus's suggestion, I am converting this from a comment to an answer:
The physical significance of the term is exactly what it looks like --- when $v$ is small and $x$ is comparably large, $t\neq t'$ (even approximately). Thus when you and I pass each other even at very slow speeds, we will still disagree sub... | {
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Wave function in a semi infinite line How to normalize the wave function of a particle in a semi-infinite 1D interval $x\in [0, \infty],$ with boundary condition $\varphi(0)=0\,?$ Hamiltonian is $H=P^2/2M$ and wave function $\varphi(x)=C\sin(xp/ \hbar)\,.$
| The wave function:
$$\varphi(x)=C\sin(xp/ \hbar)$$
Isn't normalisable. Just try it:
$$1=\int_{-\infty}^{+\infty}[\varphi^*(x)\varphi(x)]dx=C^2\int_0^{+\infty}\big(\sin(xp/ \hbar)\big)^2dx=C^2\Bigg[\frac{x}{2}-\frac{\hbar}{4p}\sin(2xp/ \hbar)\Bigg]_0^{+\infty}$$
It has no Real solution for $C$.
| {
"language": "en",
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Why wave theory cannot explain photoelectric effect and provides evidence for particle nature of light? I am able to understand how light can be modeled to have wave characteristics from Young's double slit experiment.
But I am unable to comprehend how we can understand light to have particle characteristics from the p... | Take it by the other way, for the emission as well for the absorption of EM radiation photons are a good description. The photoelectric phenomenon is a good example for the point that EM radiation is made of photons.
The description of EM radiation as a wave has some weaknesses. For a thermic source of EM radiation one... | {
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Theoretically, could there be different types of protons and electrons? Me and my friend were arguing. I think there could theoretically be different types of protons, but he says not. He says that if you have a different type of proton, it isn't a proton, it's something else. That doesn't make sense to me! There are d... | There are two ways to distinguish particles: you can either measure a difference in the intrinsic physical properties of the particles - say mass, for example - or track the trajectory of each particle with infinite precision.
Since a proton is always formed by one d-quark and two u-quarks, every proton has the same ma... | {
"language": "en",
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"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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Could the gravitational field equations be formulated in term of the Riemann curvature tensor (as opposed to the Ricci curvature tensor)? The most symmetries and identities in Riemannian geometry are in term of the Riemann curvature tensor. One may ask why the gravitational field equations are not in term of this main ... | The Einstein field equations are in terms of the Riemann curvature tensor! It is just contracted with the metric once to give the Ricci curvature tensor. That then is contracted with the metric again to give the Ricci scalar. A combination of both tensor and scalar.
So you have the Ricci tensor (two indices) from the R... | {
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Working principle of inverter I got project on the working of inverter from school. I know this that DC inverter has an alternator switch which constantly changes its direction so that magnetic field is produced in primary coil due to which current is induced in secondary coil and we get output AC. So according to all ... | You are right. The alternator turns the DC of the battery into AC, which allows for changing magnetic fields in the primary. A transformer need a changing magnetic flux (which is why "DC doesn't work") - the alternating switch keeps changing the direction of the current, so the flux keeps changing. This induces e.m.f. ... | {
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What is the power output for an OPO pumped below threshold? I'm trying to figure out approximately how much power will be output from an OPO when pumped below threshold (ie Pin=0.1Pth). All the research I've done turned to the same basic equation which only works for above threshold (~(sqrt(Pin/Pth)-1) which is always ... | Below threshold operation means that the gain inside the optical parametric oscillator is smaller than the overall losses. Your gain medium effectively changes the intra-cavity losses. Below threshold, the net loss is (still) positive and the system is (still) similar to an ordinary cavity. How much light will be trans... | {
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Falling rotating object in higher order potential fields For which $n$ would an object with a non-zero rotation fall to the center of this field?
$$\alpha >0\\ V(r) = \frac{\alpha}{r^n}$$
(Apparently it should never touch the center if it has non-zero rotation and $n=1$). I am totally stumped, as I cant see why the ord... | Consider an object with non-zero rotation, and velocity vector $\bf{v}$. That it has a non-zero rotation means that, at least as long as $r \neq 0$, $\textbf{v}\times\textbf{r} = rv_\perp \neq 0$, where $\bf{r}$ is the radial position vector and $v_\perp$ is the component of $\bf v$ perpendicular to $\bf r$. As a simpl... | {
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If an Ideal Current Source has infinite resistance, how is current flow possible? Where does current come from if an ideal current source has infinite resistance? Current can't move through the current source because of the resistance, so I don't really understand how and why an ideal current source has infinite resist... | "Ideal" in this context means that no consideration is being given to how the ideal properties (constant current regardless of load, infinite resistance) can be achieved in practice. As freecharly puts it, it is an abstract concept.
The process of analysing electrical circuits starts with modelling real electrical com... | {
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Motion of one body with reference to another I studied that Galileo was punished by the church for teaching that the sun is stationary and the earth moves around it. His opponents held the view that earth is stationary and sun moves around it.
The question i want to ask is if the absolute motion has no meaning,are the ... | This is an interesting question. You say that "absolute motion has no meaning." Can you explain that a little more? Suppose that I am in a spacecraft. For simplicity imagine that I am far from any other object, so I can neglect gravity (I don't think this restriction is necessary, but it simplifies things.) I can... | {
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Why is velocity inversely related to pressure in a flow? I've seen the equations that give this relationship, and I understand the math and have seen it worked out in problems. But I don't have a qualitative, conceptual grasp on the relationship.
Is the pressure that which is exerted by a small element of the flow, or ... | You say "if you speed it up".
Who speeds it up?
The only thing that can speed it up is a pressure difference.
(Let's do it horizontally, so we can ignore gravity.)
That's why less pressure means higher velocity, and vice-versa.
| {
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"source": "stackexchange",
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Why is direct current needed to produce an electromagnetic field using a solenoid? I am performing an experiment for school investigating the magnetic force of a solenoid. While doing this experiment I realized that I needed to connect the solenoid to the DC output of the power supply instead of the AC.
I am perplexed ... | To produce a steady magnetic field by a current in a coil you need a direct current. If you use an ac current the magnetic field would change with time and change direction every half period of the ac current.
| {
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"url": "https://physics.stackexchange.com/questions/284864",
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If a system is deterministic, will it still be deterministic if time is reversed? If you were to drop a ball, it would be easy to calculate when it will hit the ground and how much energy will be absorbed by the ground (let's assume there's no air resistance and the ball does not bounce).
If you were to then reverse ti... | If the equations in whatever deterministic theory you are using are reversible in time, then you can use the current state to predict both the future and the past your system just as easily, because it's all in the mathematics. However, deterministic equations can suffer from sensitivity to initial conditions. Genera... | {
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What is the prevailing opinion in scientific community about Hans C. Ohanian's description of spin? In the paper What is spin?, Am. J. Phys. 54 (1986) 500, by Hans C. Ohanian, spin is described as a circulating flow of energy in the wave-field of a particle. Is this the generally agreed upon explanation of intrinsic a... | Ohanian's paper shows that spin can be understood as a circulating flow of energy, and is a wave property, valid in both classical and quantum mechanical formulations, rather than inherently and mysteriously "quantum mechanical" in nature. A fine point not needed for calculations that can be ignored by the pragmatic e... | {
"language": "en",
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Correlating lattice time to physical time in Lattice boltzmann Method In LBM literature, more often the time-dependent behavior is plotted with respect to the number of time-step(lattice time $\Delta t$), I also read this note from Jonas Latt, however it stills seems unclear to me how to correlate $\Delta t$ to physica... | In those notes, it is stated that time $t_p$ is divided by some reference time-scale $t_{0,p}$. And the time step in the discretised system is $\delta_t=t_{0,p}/N_\mathrm{iter}$. So if you perform $N_t$ time-steps then this corresponds to a time interval of $\Delta t_p=N_tt_{0,p}/N_\mathrm{iter}$.
| {
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Is there a notion of causality in physical laws? I was reading "A Few Useful Things to Know about Machine Learning" by Pedro Domingos and towards the end of the paper he makes this statement:
"Many researchers believe that causality is only a convenient fiction. For example, there is no notion of causality in physical ... | All answers are good; I would like to add something missed though: Newtonian Mechanics is not exactly a deterministic theory. In other words, sometimes, even if there is not a cause, an effect can just occur. SeeNorton's dome.
In short, determinism (uniqueness theorem in Newton Mechanics) is a mathematical consequence ... | {
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What actually oscillates in quantum harmonic oscillator with given frequency? Quantum harmonic oscillator is said to be describing motion of microscopic stuff (like atoms in molecules). But unless one keeps on measuring the position on the atom, it doesn't exist at all. It's in superposition of several possible positio... | First of all, I would agree that the particle "is in superposition of several possible positions (position eigenstates)" but I would strongly disagree that "it doesn't exist at all." But anyway: if the quantum harmonic oscillator is in an energy eigenstate, then nothing oscillates at all; this is true for any energy e... | {
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Do circular wheels maximize mechanical efficiency?
I recently wondered whether there is a simple proof that circular wheels maximise mechanical efficiency. By this I mean:
Show that for a wheel with a given width and cross-sectional area, the
circular wheel reaches the bottom of an incline faster than a wheel
wit... | When it is coming down the motion of the wheel of any shape is one dimensional. Degree of freedom of two dimensional object is one when no torque is acting . In this case of if we consider free fall then only acceleration is gravitational acceleration which will not apply torque here. By using the two dimensional objec... | {
"language": "en",
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Why Objects still move under the effect of fictitious force? As I read in many books and websites, An inertial force is a force that resists a change in velocity of an object. It is equal to—and in the opposite direction of—an applied force.
If the inertial force (P) is equal to the applied force (F), then the net forc... | Real forces are always interactions between two objects. If we think that a force, such as your inertial force, is acting on an object, we should try to identify the other object. If we can't, then we were wrong; there is no force.
The inertial force in your hypothetical problem does not pass that test. You have ... | {
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What is the difference between conventional current and electronic current? what is the difference between conventional current and electronic current?
How are they linked to one another?
| The conventional current is defined as charge per unit time transported in a certain direction. The current direction is the direction of positive charge movement. A positive current is also negative charge per unit time moving in opposite direction to the corresponding positive charge. In conventional current, the typ... | {
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Generalized version of work-energy theorem I know that for rigid bodies only the work-energy theorem states that the net work done on the body equals the change in kinetic energy of the body since a rigid body has no internal degrees of freedom and hence no other forms of energy such as potential energy.
Is there a mos... | The "generalized work energy theorem" is extremely simple:
The work done on or performed by the system equals the difference in energy of the system. The energy of the system is the sum of all different kinds of energies of your system: kinetic, potential, chemical, etc.
How does the work split across different types... | {
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Gravity between two Photons (I searched for an answer online already but I couldn't quite find what I was looking for...)
I thought about this for a long time now. If two Photons fly in the same direction, one behind the other one, for my understanding the one behind the other one should be pulled towards the photon in... | The speed of gravity is also only c, so the photon in front never gets overtaken by the gravity of the photon in the back. The photon in the back travels through the gravitational field of the one in the front, but since the direction of pull is to the front while the back photon is already travelling with c in the dir... | {
"language": "en",
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Why does the bicycle move forward after I give it an impulse with the help of brakes? Whenever I need to slow down my bicycle I use brakes, momentarily pressing them and then releasing. For some reason, this momentarily halts the bicycle and when I release the brakes, the bicycle continues to move forward albeit with a... | When you tap the breaks, the bicycle stops but your body keeps moving. Almost immediately after you let go of the breaks you push/hit the front handlebars and the bike keeps going. Having your bike coming to a full stop (without your body slowing down) without problems is only possible at low speeds. At higher speeds t... | {
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Charged particle as observed from an inertial and a non-inertial frame of reference A charged particle fixed to a frame $S^\prime$ is accelerating w.r.t an inertial frame $S$. For an observer A in the $S$ frame, the charged particle is accelerating (being attached to frame $S^\prime$) and therefore, he observes it to r... | This is not complicated.
*
*The question of whether the particle radiates must be resolved in
its frame of reference.
*The question of whether the radiation is observed must be
resolved in the observer's frame of reference.
Changing the observer or adding more or different observers does not impact whether or not ... | {
"language": "en",
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How attitude indicator (gyro horizon) adjusts to the Earth's curvature? Image a plane is flying from North to South and is crossing equator. How gyro horizon would maintain correct pitch angle? (Or East-West?)
I assume that pitch angle is correct at takeoff, so the further plane flights, the more difference would be be... | The attitude indicators need to have devices in them to correct for precession in the gyros caused by turns. The system used in mechanical gyros is based on a collection of pendulous vanes. Basically, for short times the gyro controls the attitude indicator, for long term the pendulous vanes are pulled by gravity in th... | {
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Why don't light beams refract when they hit a curved surface I saw a diagram that showed a light beam hitting a curved glass block (half circle) and nothing happened until it hit the flat surface, in which it refracted. Why doesn't it also refract when it hit the curved surface. I also tried this in real life with the ... | Well, your light ray must have hit the curve at an exact point where the angle of incidence was zero, (the light ray was perpendicular to the exact point at which it hit the semi circle), which means there was no refraction.
But in general, a ray of light can bend when it hits a curved surface, it just depends at what ... | {
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Can "dressing" a qubit multiple times increase the dephasing time more than dressing it once? A paper was recently published (arXiv pre-publication link; I've only read a more popular description of the content because of my lack of domain knowledge) describing how "dressing" a qubit in a microwave field consistently r... | Yes, it can. In particular, dressing an already dressed qubit can protect from the decoherence introduced by fluctuations of the microwave field used for the (first) dressing.
This is, eg, described here:
http://dx.doi.org/10.1088/1367-2630/14/11/113023
The principal idea of CCD is to provide a concatenated set of con... | {
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Could we specify that a quantum space-time (any) belongs to what mathematical spaces? e.g to discrete spaces? Apparently, there is not a unique and generally accepted definition for a quantum space-time yet. In any case, I'd like to know that, at this stage, could we specify that a quantum space-time (any) belongs to w... | The influence of mass on the space-time geometry can be described with quantum theory, where we can state the expected effect of mass on curvature of space-time.
Also it can be theorized that if mass has influence on space-time curvature, in quantum situations where mass does not curve space-time at measured coordinate... | {
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Operator functions: why is $f(A)$ uniquely defined? In Nielsen and Chuang, they write: Let $A = \sum_a a|a\rangle \langle a|$ be the spectral decomposition of $A$. Define $f(A) = \sum_a f(a) |a \rangle \langle a|$. Apparently this is uniquely defined. I'm having trouble seeing why this is.
If we used some other orthono... | It's a standard result of linear algebra that the spectral decomposition of an operator is unique (up to a trivial reordering of the eigenvalues/vectors). If you could write $A$ as both $\sum_a a | a \rangle \langle a |$ and $\sum_b b | b \rangle \langle b |$, with the $a$s and $b$s nontrivially related, then this woul... | {
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How many photons can exist in a cubic box of unit volume, simultaneously? Suppose that we have a cubic box of unit volume. Simultaneously, how many photons can exist in such box? Is there any limit?
| Photons are bosons so unlike fermions such as electrons there is no restriction on multiple photons occupying the same energy state. Consequently there is no limit on the number of photons you can put in your box.
There is an upper limit to the total energy density in the box since if you make it too high the box willc... | {
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Acceleration during collsion Okay so, this question is pretty simple. When two objects of constant velocity collide, is there a constant deceleration upon contact? or does it follow some unique function that can only be evaluated by testing it? Furthermore, if it is in fact constant, how do we know and how did we orig... | In general, Newtonian mechanics, that is taught at high school and at university in introductory level, considers objects as point particles or at most uncompressible solids. Therefore, in most cases, collisions are considered as elastic, where both kinetic energy and momentum are conserved.
However, in reality this is... | {
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Two Cases Of Harmonic Motion Caused By Gravity I'm a highschool student and we learned not so long ago Simple Harmonic Motion, and I'm trying to analyse "similar" cases which I thought of.
Here we have a body (with mass $m$) being affected by the gravity of a body whose mass is $M$, yet it doesn't collide with it (it ... | The first case is very different from a harmonic oscillator. The speed of the moving body becomes infinite as passes through the center.
The second case could be analyzed by expanding $$\frac{x}{(d^2+x^2)^{3/2}}= \frac{x}{d^3}\left(1-\frac{3x^2}{2d^2} + \ldots\right)\tag 1$$
If $x\ll d$ you need only to retain the fir... | {
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Photons at the big bang Did photons exist at the singularity of the Big Bang? If they did not, then does that mean that it is impossible to see what happened at the big bang?
| Well, photons were at the Big Bang, but it wasn't light that we can now observe until the era known as recombination, about 378,000 years after the Big Bang, that photons had a practically infinite mean free path due to the majority of protons in the universe being bound up in neutral atoms, and the universe became tra... | {
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Since quantum mechanics give you that photons have (relativistic) mass $m=\frac{hf}{c^2}$, why gravity does not accelerate it? Since quantum mechanics give you that photons have (relativistic) mass $m=\frac{hf}{c^2}$ why gravity does not accelerate it?? I know it changes its energy hence its frequency hence its wave le... | "Accelerate" is not the right word since the velocity of a photon has to remain constant as a result of its being massless. The confusion I think comes from thinking of gravity as an instantaneous force that attracts things but this idea does not survive special relativity. What we call gravity is a result of curvature... | {
"language": "en",
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Work done by gravity on falling object does not seem to equal change in mechanical energy So I have some confusion here, I am sure I knew this at some point. Let's say an object of 10 kg is dropped from a height of 10 m. When it reaches the ground, the work done on the object should be the force ($mg$) x distance or ... | This is a common point of confusion that boils down to the fact that there are two physically equivalent but conceptually different ways of viewing this situation.
You can either look at gravitational potential energy (GPE) as an "internal" form of energy that your 10 kg object can have or you can look at the gravitati... | {
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Would there be no time in a universe with only light? It is sometimes said, that if you stand still (in space), you travel through time at the speed of light. On the other side light never stands still, so it always only travels through space (at the speed of light), but not through time. Does that mean, if our univers... | The time dimension would still exist. There just wouldn’t be any energy in it and nothing to experience the passage of time.
| {
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What do I actually see when I look at a laser? I have a green laser. Texts usually say you can only see visible light when it is reflected from another material. But you can clearly see a laser ray all the way from the device to the surface pointed at, what is that ray then? Is it a reflection off of air?
I can also se... | As well as lighting up dust particles along its path, the beam is also lighting up water droplets in the air, particularly when outdoors.
| {
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Why do we need wires to discharge a capacitor? I've been studying Capacitance and Dielectrics and I can't understand why the capacitor will only discharge if there is a wire connecting them. I understand that when the capacitor is charged up, there is an electric potential difference between the plates that makes the e... | The Coulomb force is there but in the ideal situation the air and the dielectric contain no free /mobile charge carries, that are insulators, so there is no mechanism for a current to flow between the two metal plates.
In the real world because the air and the dielectric are not perfect insulator the capacitor will dis... | {
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What happens when car's trunk pops open while driving? Yesterday my car's locking mechanism for the trunk malfunctioned and popped open while driving. Luckily I was cruising at very low speeds (around 15kph) and I just stopped and fastened it again.
What I'm wondering is what would happen if I were traveling at relativ... | Put simply, there is a pressure of air under the trunk. Consider the following crude diagrams:
The first is that of an average sedan. Now there is a certain effect known as the Coanda effect, which refers to the tendency of flowing fluids to follow the curvature of a surface, even when it deviates from its original fl... | {
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What does "point of application of force" mean in the given context? I faced a particular conceptual doubt while solving a textbook problem. I will initially write the complete question in my textbook and then try to boil it down to a single conceptual doubt so that it complies with the rules of Physics Stack Exchange.... | Best guess, the point of application is an average position weighted by how much force is applied.
If the force was uniform, then that point would be the center. Since it's not, it's stronger closer to the long wire, the point will be moved to the left of center a bit. This means that not only is there a net force on... | {
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Are there more causes besides Gravity and Velocity that cause time dilation? Albert Einstein discovered that both gravity and velocity alter time in a given reference frame relative to the time of an observer in a different reference frame. If gravity and velocity both alter the passage of time, is it possible that oth... | The answer is no, according to what we know today, there are no other causes.
For the answer you have to remember what is time dilation: time dilation is the dilation of the absolute proper time of particles from the point of view of an observer. That means that each particle/ each worldline consists of absolute spacet... | {
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acceleration and potential energy due to conservative force how can we find acceleration due to a conservative force as a function of time when potential energy due to the conservative force is given as function of position(e.g. U(x)=x^2)
| The force $F$ is minus the potential energy gradient $\frac{dU}{dx}$ for a conservative field.
$F =-\dfrac {dU}{dx}$
So if you know the mass you can use Newton's second law to find the acceleration.
| {
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Given that ice is less dense than water, why doesn't it sit completely atop water (rather than slightly submerged)? E.g.
*
*If we had a jar of marbles or something else of different densities and shook it, the most dense ones would go to the bottom and the less dense ones to the top.
(Image Source)
*If I put a cube... | I like to answer by reinterpreting your question: if you expect the ice to be completely atop the water because ice is less dense than water (as indicated in your left image), then you would also expect the ice to be completely below air because ice is more dense than air (in order for this to be true, think pushing yo... | {
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Does the top plate of a capacitor hold half of the capacitor's charge or all of it? I am a little confused conceptually about the charge of a capacitor held by the top plate. Is it equal in magnitude to $q$, or is it half of $q$? It makes more sense to me for it to be half of $q$, with the other half existent on the ot... | The charge of a capacitor is the magnitude of $q$. The charge of one plate is $+|q|$ and the other plate has the charge $-|q|$.
| {
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Electromagnetic action in differential forms The electromagnetic action can be written in the language of differential forms as
$$S=-\frac{1}{4}\int F\wedge \star F.$$
$$=-\frac{1}{4}\int \left(\sum_i E_i\,{\rm d}t\wedge{\rm d}x^i - \star\sum_i B_i\,{\rm d}t\wedge{\rm d}x^i\right)\wedge \star \left(\sum_j E_j\,{\rm d}t... | Just continue your second line:
Expand the wedge product and notice that the non vanishing terms are only the $EE$ terms and $BB$ terms and more over, $dt\wedge dx^i\wedge \star(dt\wedge dx^j)=\delta^{ij}dV$. There is a mistake in your second line: $\star\star=(-1)^{s+p(n-p)}$, where $s$ is the number of minus sign in... | {
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Problem with physical application of Dirac Delta Consider the problem of projectile motion in 2 dimensions. Launch angle is constant. Range of projectile, $x$, then depends only on launch speed, $v$, and is given by
\begin{equation}
x=v^2, \quad v\in [0,1] \tag{1}
\end{equation}
Above equation has been non-dimensionali... | *
*Besides ACuriousMind's suggestion to check dimensions, you could also integrate the wrong distribution $$\delta(\sqrt{x}-v)=2v\delta(x-v^2)$$ over $x$ and see that you don't get the p.d.f. (2) that you started from, but instead a wrong distribution $f(v)=2v$.
*The moral is that the Dirac delta distribution $\delta... | {
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Coulomb's law accuracy for small distances My physic teacher told me that experimental deviations from the predictions of Coulomb's law occur at small separations because, being inverse square, Coulomb's law work best for larger values of r. Why is this the case?
| Almost every source of electric field in our day life is more than an point-like, having complex structure on the distribution of charges. The naive aplication of the Coulumb's law assume that the sourcer is point-like or spherically symmetric. This is a good approximation if the dimensions of the sourcer is neglegible... | {
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What is the difference between "Elastic limit" and "Yield point"? Elastic limit - the point till which the wire retains its original length after the force is withdrawn.
Yield point - the point where there is a large permanent change in length with no extra load force.
This is how these two terms are defined in my A Le... | Yield point is well defined and shown on graph for mild steel and it's beyond elastic limit. For other materials like copper or aluminum is defined as the point of intersection of stress-strain curve and a line drawn parallel to linear part fron 0.2 percent deformation (strain ε) and it is also beyond the elastic lim... | {
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How can a particle which is not moving have an acceleration? Suppose a rod is rotating around a fixed point located at an extreme point of it and there are two points on it. One, somewhere in the middle and the other at the other extreme.Call them $A$ and $B$ respectively.
The Question is relatively simple, but it is ... |
How can a particle which is not moving have an acceleration?
Using the Taylor series expansion for the trajectory of the particle $x(t)$ about $t = 0$, we have
$$x(t) = x(0) + \frac{dx}{dt}t + \frac{1}{2}\frac{d^2x}{dt^2}t^2 + \cdots = x(0) + v(0)t + \frac{1}{2}a(0)t^2 + \cdots$$
This is a perfectly general result. ... | {
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Simple harmonic motion : why is the period independent of amplitude even when angular velocity is related to the amplitude?
Period is independent of amplitude. (Vias.org)
But given that,
Simple harmonic motion can be defined by
$$x = A * \sin(\omega t) \tag{1}$$
where $A$ is the amplitude of oscillation, $\omega$... | It's because $x$ depends on $t$ in such a way that there is no dependence on $A$ left in the expression. $A$ and $\omega$ are constants that don't depend on time, and $x$ is a function of time; it's the position at time $t$, usually written $x(t)$.
When the force isn't Hooke's law, then you can get a relationship betwe... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/290929",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "1",
"answer_count": 2,
"answer_id": 1
} |
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