Q stringlengths 18 13.7k | A stringlengths 1 16.1k | meta dict |
|---|---|---|
Each elementary particle has its own field. What about antiparticles? I understand how particles correspond to their respective fields. What about antiparticles though? Do they have separate fields as well?
| Particle and anti-particle are described by the same field.
Let's look at the Dirac field:
\begin{equation}
\psi\left(x\right)=\int\frac{d^{3}p}{\left(2\pi\right)^{3}}\frac{1}{\sqrt{2E_{p}}}\sum_{s}\left(a_{\vec{p}}^{s}u^{s}\left(p\right)e^{-ip\cdot x}+b_{\vec{p}}^{s\dagger}v^{s}\left(p\right)e^{ip\cdot x}\right)
\end{... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/206958",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "5",
"answer_count": 2,
"answer_id": 1
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Wave equation - Cases where separation of variables doesn't work Separation of variables combined with the Fourier's theorem is the most common technique of solving D'Alembert's wave equation:
$$
\Delta\Phi-\frac{1}{c_0^2}\frac{\partial^2 \Phi}{\partial t^2}=0
$$
$$
\Phi\left(x,y,z,t \right)=X(x)Y(y)Z(z)T(t) \equiv R(... | This issue is thoroughly discussed in Chapter 5, volume 1 of Morse and Feshbach. Depending on the coordinate system, the PDE might be fully separable, partially separable or non-separable. M&F show the details for the Helmholtz equation (the temporal FT of D'Alembert) in over a dozen coordinate systems. As was point... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/207170",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "2",
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Calculating the number of particles in phase space I'm looking at the first part of question 7 here (I'm a mathematician trying to self teach some physics, this isn't a homework assignment so I'm just in need of hints)! I'm struggling to make sense of the set-up, but will explain what I've done.
The number of particle... | The energy $E$ of an oscillator is given by
$$E=\frac{p^2}{2m}+\frac12m\omega_1^2x^2 $$
This defines an ellipse in phase space! So now, when $E=E_1$ everything within the ellipse defined by $E_1$ will have energy less than $E_1$. To proceed with finding the limits of of integration, we consider the cases when the pa... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/207382",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "4",
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Why can scalars have a sign? I wondered to myself why some scalars have a sign, if they do not have a direction. After all, the plus and minus indicate the direction of the scalar on a one-dimensional axis.
So, for example, why can temperature have a sign? Why can't mass?
| It has to do with what point you define as a reference, what do you call (define) as zero?
When talking about temperature it depends which unit you measure in.
In example, when using Celsius, zero is defined as the freezing / melting point of water (under normal pressure etc). Do we know anything colder than that? Yes ... | {
"language": "en",
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"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "10",
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Why didn't accelerator mass spectrometry greatly improve the accuracy of carbon dating? My understanding of the limitation of radiometric dating is that background radiation swamps the radiation from C14 once the remaining atoms get few enough in number. Accelerator mass spectrometry seems to actually count every atom ... | In the end, the ability to accurately count small amounts of sample only gets you logarithmic gains in how far back you can date materials, due to the exponential nature of radioactive decay.
Suppose you have a material with mass $m$, a mass fraction $\chi_\mathrm{C/tot}$ of which is carbon. Then a fraction $\chi_\math... | {
"language": "en",
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Can I use fluorescent light bulbs to calculate Planck's constant? We did an experiment today to calculate Planck's constant, $h$. We measured the knee voltages $V$ of different LEDs (red, green, orange, blue, violet) and plotted them against the frequencies $f$ of these lights. The equation of the line is given by $V =... | According to http://www.scienceinschool.org/2014/issue28/planck, All you need to calculate Planck's constant is
Four LEDs emitting coloured light – one each of red, orange, green and blue. Choose LEDs w
*
*Four LEDs emitting coloured light – one each of red, orange, green and blue. Choose LEDs with a clear, col... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/207809",
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"question_score": "3",
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Method of image charge for cylindrical conductor I am simply puzzled that only for spherical and planar conducting surfaces the method of images is applied. Is it (really) impossible to find image charge or charge distribution which can simulate the behaviour of potential in the volume of interest. Is there any method ... | Image charge for cylinder interface may exist, but it is way more complicated. First, since the geometry is less symmetric compare with sphere or plane, the image will be distributed on a plane, i.e., it will be an "image surface charge density". Secondly, analytically obtaining the image formula seems extremely diffic... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/207918",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "6",
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How to make electrical connection to silicon wafer for testing? I am trying to make an electrical connection to a silicon wafer using a wire (approx 32AWG).
I find that conventional lead/tin (60/40, no flux) solder cannot adhere well to the silicon wafer, since the solder will simply fall off the wafer after cooling (s... | I used indium solder to do this. However, there is a trick to it. Silicon wafers typically have a layer of insulating oxide on them. You have to get the indium through the oxide layer into silicon. Put small blobs of indium on the silicon sample where you want to make the connections, and put the sample on a hot plate.... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/207985",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "3",
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Justification of $P_{\text{photon}}=E/c$ in derivation of $E=mc^2$ I recently was reading up on the derivation of $E=mc^2$. Now, I came across this derivation at this link. I noticed that several lines into the derivation they throw in the equation
$$P_{\text{photon}}=E/c.$$
How did they come to this equation so easily... | Well, if you accept energy-momentum conservation, then the equation you referred to can be easily obtained from the energy-momentum relation of E^2=(p c)^2+(mc^2)^2, where E is the energy of the particle, p is its momentum, m is its rest mass, and c is the speed of light (see Energy–momentum relation). For photons, the... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/208200",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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Quicker way to cool liquid I need to prepare a bottle of baby milk from formula quickly. To prepare it I must use some boiling water to sterilise the powder however it must be served at just above room temperature for the baby to accept it so I top up the bottle with cold water and leave it until it reaches the desire... | I'm going to give an answer that is more practical, rather than physics related. In my opinion, it would make sense to make up several bottles of milk with water as hot as you think you need. Then, let them cool off a bit and put them in the refrigerator. When you need them, put them in the microwave oven for 10-20 ... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/208300",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "2",
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How can the unstable particles of the standard model be considered particles in their own right if they immediately decay into stable particles? How can the unstable particles of the standard model be considered particles in their own right if they immediately decay into stable particles?
It would appear to a layman su... | I think the most direct answer to this would be the fact that a heavier particle can decay into many different lighter particles for different reactions. The abundance of occurence of these relations are const. Again the same heavy particle can be created in multiple types of collisions of various different lighter par... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/208410",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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Can tin foil hats block anything? This is joked about all the time, but...
Can tin foil hats actually block anything? If they can, what frequencies? Is there any research into tin or aluminum foil and radio blocking or amplifying abilities when shaped into a hat?
If they really don't do anything, what would be better? ... | Whereas a straight unfolded, uncrumbled piece of tin foil can block out some of the lower wave lengths permeating throughout the atmosphere, a folded or crumpled tin foil hat will not block out anything.
The reason is that tin (aluminium) foil is actually made up of two thin layers. There is a clear sheet in between t... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/208516",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "90",
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Calculated heat capacity different (lower) from experimental value? When treating gases as ideal, classical systems, the heat capacity can be found by multiplying the number of independent degrees of freedom by 1/2k, where k is Boltzmann's Constant. However, these values are usually lower than the real values of heat ... | You don't say whether your analysis includes rotational modes. I assume it does otherwise the disagreement between experiment and the ideal gas specific heat would be profound. A linear molecule will have two rotational modes, each adding $\tfrac{1}{2}R$, so the specific heat (excluding vibration) will be $C_p = \tfrac... | {
"language": "en",
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"source": "stackexchange",
"question_score": "2",
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Why do wider double wells have a lower $\Delta E$ than thinner ones?
In this diagram, in which an $n=1 (E_{1})$ and $n=2 (E_{2})$ wave have been superimposed, the probability density of the new, combined wave changes with time. The period of its shifting density is given by $\frac{1}{f}$ where $f = \frac{E_{2}-E_{1}}{... | Electrons are Fermions so they are forbidden from being in exactly the same state. Two identical quantum wells placed an infinite distance apart will be identical because the wave functions do not overlap. However at the quantum wells are moved closer together the wave functions begin to overlap and the exclusion princ... | {
"language": "en",
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What experiments have been done that confirm $E=mc^2$? What experiments have been done that confirm $E=mc^2$?
Are there experimental results that contradict $E=mc^2$?
Or are experimental results consistently showing this famous formula to be true?
| There is a huge mass of experimental evidence that confirms the mass-energy equivalence. The clearest example that it happens is, of course, nuclear power, both in its explosive and civilian forms. If you want a detailed breakdown of all the experiments that corroborate it, I would recommend the entire archive of Physi... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/209919",
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"source": "stackexchange",
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Why do voltmeters and ammeters have high and low resistance respectively? I understand why voltmeters are connected in parallel and ammeters are connected in series, but why is it that to measure voltage, you must have high resistance, and to measure current, you must have low resistance? Perhaps this is not within the... |
The current doesnt pass through the voltmeter so the the resistance of load R is not affected.
| {
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Black body in thermal equilibrium In the answer of an exam said that a black body in thermal equilibrium with it's surroundings won't emit any energy, but I don't really understand why.
My logic is that every object emits electromagnetic radiation because of it's temperature, which is a form of transmission of energy, ... | Thermal equilibrium with the surroundings mean no net energy. This means, the blackbody absorbs as much as it radiates energy at that temperature. Clearly, every body in your room radiates and absorbs energy. And it's temperature isn't changing.
| {
"language": "en",
"url": "https://physics.stackexchange.com/questions/210402",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "3",
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Inaccuracy at measuring gravity constant with Cavendish experiment For a scientific work for school I decided to measure the gravity constant with the Cavendish experiment.
I set up a structure like the one suggested on this website: http://www.school-for-champions.com/science/gravitation_cavendish_experiment.htm
I act... | Well, there are strong sources of error from the surrounding masses: furniture, walls, peoples around. To reduce them, you should ensure that everything has rectangular symmetry with respct to the two axis of the experiment up to a distance of few metres from the pendulum, and remove/symetrise large masses beyond that ... | {
"language": "en",
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"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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What are the functions of these coefficients $c_1,c_2,c_3,c_4$ in $ \psi_{sp^3}= c_1\psi_{2s}+ c_2\psi_{2p_{x}} + c_3\psi_{2p_y}+ c_4\psi_{2p_{z}}$? Hybridised orbitals are linear combinations of atomic orbitals of same or nearly-same energies. Atomic orbitals interfere constructively or destructively to give rise to a... | Yes, hybridization is superposition.
Assuming the basis functions are orthonormal, which we usually take to be the case, $\langle\phi_i\,|\,\phi_j\rangle = \delta_{i,j}$ the condition for normalization of $\psi$ is that the sum of the squares of the coefficients equal unity. More precisely, $$c_1^*c_1+c_2^*c_2+\cdots ... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/210777",
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What is used to measure the spin of a particle? I was wondering what is the specific system or method that is used to measure spin of a particle? e.g. In a lab what would they use to tell what a particles spin is?
P.S. I am new to stack exchange so please tell me if I formatted this wrong or need to change anything abo... | First, it is worth mentioning that while the word measurement is used, the experimental process involved actually changes the state rather than revealing some preexisting property.
This can be known by considering an interaction for the z component followed by the z component again followed by the x component as compar... | {
"language": "en",
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"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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Primitive unit cell of fcc When I consider the primitive unit cell of a fcc lattice (red in the image below) the lattice points are only partially part of the primitive unit cell. All in all the primitive unit cell contains only one single lattice point.
My question is how much each point at the corners of the red prim... | Well, The FCC's (along with BCC's) are conventional unit cells, not primitive unit cells. As for the contribution of points, it is different for the corners and face centers. Each corner of a unit cell in a lattice is joined to 7 other unit cells. so the corner point is shared equally between 8 unit cells. Hence the co... | {
"language": "en",
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"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "4",
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Terminal velocity and distance traveled with constant but limited power I'm trying to model how far to move an object over time according to a power applied resisted by friction.
So maybe... an object accelerates at a certain rate until the power provided can no longer overcome friction (in relation to mass of the obj... | Here are some simple cases applied from How to get distance when acceleration is not constant?
*
*Constant Power $P$, Constant Friction $F$
$$ \begin{align}
a(v) & = \frac{P}{m v} - \frac{F}{m} = \frac{P}{m} \left( \frac{1}{v} - \frac{1}{v_{final}}\right) \\
v_{final} &= \frac{P}{F} \\ t = \int \limits_{v_1}^... | {
"language": "en",
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"timestamp": "2023-03-29T00:00:00",
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Does a changing magnetic field impart a force on a stationary charged particle? Does a collapsing and re-establishing magnetic field impart a force on a stationary charged particle? Does the charge particle get repelled and or attracted? Does it move or spin?
| In the absence of any charge motion and current density then a changing magnetic field is accompanied by a changing electric field. From Ampere's law we can say that
$$ \vec{E} = \frac{1}{\epsilon \mu} \int \nabla \times \vec{B}(t)\ dt$$
This electric field will exert a force $q\vec{E}$ on the particle.
The above equat... | {
"language": "en",
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"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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Nature Of Bulb Glowing In Parallel LR circuit with bulbs
In the given circuit the switch is initially closed and then opened after some considerable time.Then which bulb will stop glowing first? Which bulb will glow more brightly?Why ?
.After opening which bulb will glow more brightly? Which one will stop glowing ... | When the ideal switch is opened the circuit comes series circuit. When in series, the instantaneous current $i(t)$ will be same through all the components. Now the voltage over the bulbs are exactly same in ideal world if the bulbs resistances are same i.e. $R_{B1}(t) = R_{B2}(t)$. In this series circuit the instantane... | {
"language": "en",
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How does the expansion of the Universe affect Black Holes? As know our Universe is expanding, which I have always visualised as some stretching of the metric of space-time, which "flattens" it. In the same time. our theoretical perception of Black Holes usually includes some kind of singularity (or at least some extrem... | There isn't an analytic solution for a universe expanding exactly like ours, but a black hole in a universe with just a cosmological constant (no matter) is described by the de Sitter - Schwarzschild metric. As our universe expands and the matter density decreases this will become an increasingly good approximation.
Th... | {
"language": "en",
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"source": "stackexchange",
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Zero gravity means zero friction? The frictional force acting on a body placed on a horizontal plane is
$F=\mu{R}$
where $R$ is the normal reaction and is equal to weight of a body in this case. And $\mu$ is the coefficient of friction. But, if gravity is zero, then is the frictional force zero (ignoring all other fri... | Yes there is friction in space. Friction and gravity are two different concepts. On earth mostly we experience friction because we are always in contact with earth surface due to gravity and whenever anything is in contact with other surface frictional force will come into picture(static of dynamic friction).
I have d... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/211706",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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Demonstration for the existence of longitudinal electrostatic oscillations How could I demonstrate that in a linear, homogeneous and isotropic medium without losses but electrically charged, Maxwell's equation admit as solutions longitudinal electromagnetic waves, beyond transversal waves?
| Kirk McDonald (Princeton) gives a nice proof and discussion of this possibility in "An Electrostatic Wave" (arXiv). The idea is that a plasma may support an electrostatic field of the form
$$
{\bf E} = E_x {\bf x} e^{i(kx - \omega t)}
$$
provided the electric displacement ${\bf D}$ is zero. Field ${\bf E}$ above satisf... | {
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Why is torque the cross product of the radius and force vectors? I understand the torque vector to be the cross product of the radius (moment arm) and force vectors, but that means the torque would be perpendicular to the radius and force vectors, which makes no sense to me, e.g. a force applied tangent to the surface ... | We need a quantity that conveys information about the direction of the radius vector and the direction of the force vector.
Two vectors determine a plane. So we need a quantity that specifies a plane. One way to do that is to specify the vector normal to the plane. That's what the cross product does for us. There... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/212042",
"timestamp": "2023-03-29T00:00:00",
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Sphere of uniform charge density with a cavity problem Suppose we have a sphere of radius $R$ with a uniform charge density $\rho$ that has a cavity of radius $R/2$, the surface of which touches the outer surface of the sphere. The question was to calculate the field inside the cavity.
Naively, I used Gauss' law to det... | $\rho$ is zero for any coordinate inside the cavity.
| {
"language": "en",
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"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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Pendulum's motion is simple harmonic motion For a pendulum's motion to be simple harmonic motion (S.H.M.) is it necessary for a pendulum to have small amplitude or S.H.M. can be produced at large amplitudes as well?
If it is really necessary for an S.H.M. to have small amplitudes then why is it? because even at large ... | As you stated, in order to have simple harmonic motion, you need to have an acceleration that is proportional to the displacement. For a pendulum, if you work out the details, you will find that
$\frac{d^2\theta}{dt^2} \propto -\sin(\theta)$
where $\theta$ is the angle the pendulum makes with the vertical. For small... | {
"language": "en",
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Limitations of particle in cell method for high desnity plasma Are there any limitations of particle in cell (PIC) method for high density plasma? To be more specific, is modelling of a narrow channel of high density plasma possible or are there any limitations connected with PIC approximation?
| The main limitation on PiC is not density per se, but rather that the plasma should be collisionless. The frequency of collisions is (as a rough approximation)
$\nu \propto \omega_p \cdot \frac{\ln(\Lambda)}{\Lambda} $
where $\Lambda$ is the number of particles in a Debye sphere $\propto T^{3/2} / n^{1/2}$
So what you ... | {
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How strong would the Earth's "magnet" be if it was the size of a fridge magnet? If you shrunk the "magnetic part" from inside the Earth down to a fridge magnet size, how strong would it be in Gauss?
This is not a home work question. I just watched this video which included the statement: "A fridge magnet is 100x stron... | Magnetic intensity doesn't increase due to size. A neodymium magnet the size of the Earth with have the same pull on a given object as if it was a dime.
| {
"language": "en",
"url": "https://physics.stackexchange.com/questions/212787",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "3",
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Do observers at rest at different positions in a gravitational field see the Universe expand at different rates If we consider observers at rest outside a Schwarzschild black hole, the amount of proper time elapsed in terms of coordinate time is given by $\Delta\tau=\sqrt\frac{r-1}{r}\Delta t$ (where r is measured in u... | The answer is yes.
The time between events within a gravitational field in the Schwarzschild metric is
$$ \Delta \tau = \Delta t \left( 1 - \frac{r_s}{r}\right)^{1/2},$$
where $\Delta t$ is the time between events seen by an observer at infinity and $r_s$ is the Schwarzschild radius.
If $\Delta t$ was (for example) the... | {
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Does the ray transfer matrix for a gap change, based on the index of refraction of the medium? The ray transfer matrix for a gap is typically:
$$\begin{bmatrix}
1 & d \\
0 & 1\\
\end{bmatrix}$$
If I know that my glass is a thickness $L$ does the ray of light that goes into it travel a distance $n' \, L$ where $n'$ is t... | Close.
From https://en.wikipedia.org/wiki/Ray_transfer_matrix_analysis
The transfer matrix upon entering the glass is:
$$\begin{bmatrix}
1 & 0 \\
0 & \frac1{n'}\\
\end{bmatrix}$$
The matrix inside the glass is:
$$\begin{bmatrix}
1 & d \\
0 & 1\\
\end{bmatrix}$$
And upon exiting the glass it's:
$$\begin{bmatrix}
1 & 0 \... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/213384",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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Does the magnetic force depend on the reference frame? Force due to a moving charge = qvB
Immagine a charge moving with some velocity on earth and I calculate the force due to its magnetic field with Earth as reference frame for me.
An astronaut in space also calculates the force but space as reference frame.
For ease ... |
Immagine a charge moving with some velocity on earth and I calculate the force due to its magnetic field with Earth as reference frame for me.
A charge that exists in the universe generates both an electric and a magnetic field, in general. An observer in the reference frame $S$ (whether at rest or integral with the ... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/213464",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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How to compute Gravitational potential energy
Find the potential energy of a system of four particles placed at the vertices of a square of side $\ell$. Also obtain the potential at the centre of the square.
In the question above can somebody explain what values should be taken to compute the gravitational potentia... | How 6 pairs are made:
*
*${m_1, m_2...m_4}$ are 4 masses.
*Now ${(m_1,m_2)(m_1,m_3) (m_1,m_4), (m_2,m_3)}$ since ${(m_1,m_2)}$ will be same as ${(m_2,m_1)}$ being scalar, ${(m_2,m_4), (m_3,m_4)}$ will be the six pairs.
*Put ${m_1}$ on the origin, ${m_2}$ on the $x$-axis, and ${m_4}$ on the $y$-axis.
| {
"language": "en",
"url": "https://physics.stackexchange.com/questions/213523",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "2",
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Characteristics of a tight string There was a question which I came across in newtons law of motion chapter in the physics book by H.C.Verma which was based upon simple atwood machine (atwood machine consists of two unequal masses connected by string going over a clamped smooth , light pulley).
The question asks us to ... | Before the block was stopped, both the heavier and light blocks were moving with the same acceleration, a= (Net Force)/(Total Mass). When you stop the heavier block, the net force gets a different magnitude and direction.
In this condition the direction is opposite to the earlier one. Thus, the lighter block will accel... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/213637",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "3",
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How much energy would be required to make one tea cup full of Earl Gray tea at 100F? On the TV show "Star Trek: The Next Generation", Captain Picard is often pictured using a replicator to materialize a cup of "Earl Gray tea, hot". Besides wondering what they do with all the empty teacups, I've often wondered just how ... | Well, the first thing to do is to discard the tea itself, because it not only accounts for a truly miniscule overall volume within the beverage, but also it is composed of molecules enormously more complex than those of water and hence we would be here all day. The second thing to do is discard the cup - it is too much... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/213846",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "2",
"answer_count": 2,
"answer_id": 1
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Ideal Gas Law in a Rotating Galaxy Cluster There is evidence that some galaxy clusters may experience some bulk rotation. If this is true, how valid is it to use the Ideal Gas Law to estimate the mass (actually, it calculates the acceleration needed to create the pressure gradient - from which the mass is derived)? O... | Unlike in a keplerian disk (for example), the rotational support in a cluster is definitely very small compared to the thermal pressure. Thus it is negligible in estimating the mass. In general, however, the radial velocity dispersion is an important component (as would be expected from virialization). Note that the... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/213957",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "2",
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Killing vectors in General Relativity? I'm looking to derive the surface area of the event horizon of a Schwarzschild black hole. I was just wondering if it were possible for someone to explain to me this:
$$
\sqrt{g_{\theta\theta}g_{\phi\phi}}
$$
I don't know what it is, or how to compute it. I don't even know what it... | In general, the square root of the determinant of the metric will give the volume element. That is,
$dV = \sqrt{|\det g|} dx_1 \cdots dx_n$.
Here you have the metric restricted to surfaces of constant $t$ and $r$, so you will get the area element on these. Since the metric is diagonal, the determinant is just $g_{\th... | {
"language": "en",
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"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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Particle in a box: value for wave function $u(x)$ when potential $V(x)$ is infinity The time-independent Schrödinger equation (TISE) is:
$$ -\frac{\hbar^2}{2m}\frac{d^2 u(x)}{dx^2}+V(x)u(x)=Eu(x) \hspace{15pt}$$
where $E$ is a constant.
Imagine now a infinity potential well as we can see on the following picture:
Th... | Go back to your time-independent Schrödinger equation:
$$
-\frac{\hbar^2}{2m}\frac{d^2 u(x)}{dx^2}+V(x)u(x)=Eu(x)
$$
This is a differential equation that must be satisfied for all values of $x$. In particular, if we look at the equation for $x = x_0 > a$, we have
$$
-\frac{\hbar^2}{2m}u''(x_0) + (\infty) u(x_0) = E u(... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/214188",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "2",
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Show that translation and rotation operator are unitary I have a problem understanding how to show that operators are unitary if they are not in the "normal" matrix form.
The translation operator is defined as $$(T_v \psi)(x) = \psi(x-v)$$ and the rotation operator is defined as $$(R_{\alpha} \psi)(x) = \psi({R^{-1}}_{... | If $\Gamma : \mathbb R^n \to \mathbb R^n$ is an isometry, define
$$(U_\Gamma\psi)(x) := \psi(\Gamma^{-1}x)\quad \forall \psi \in L^2(\mathbb R^n, dx)\:.$$
With this definition you have, using the fact that the Lebesgue measure is $\Gamma$-invariant, $d\Gamma x = dx$ (which is the same as $dx = d\Gamma^{-1}x$)
$$\langl... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/214502",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "1",
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Does a humming bird eating flower juice in an accelerating train, need to fly forward or just fly to remain at the same place? Does it need to fly forward? Or just need to fly to keep at the same position as usual?
| The key part to this question is the fact that although the bird is supported by the air (which does move with the train), it is not floating in it. The bird must use its wings to overcome gravity (which is similar to an upward acceleration of the train).
If an additional acceleration forward is introduced, the birds ... | {
"language": "en",
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Why does a ray passing through optical centre remain undeviated? How can it be explained using the laws of refraction that a light through optical centre of a lens passes undeviated?
If we assume the portion of the lens in the middle to be made of even number of alternately place up and down prisms, then it's clear, b... | Look at the lens as a slab of finite thickness. In a small vicinity around its center we may consider its opposing surfaces as parallel to each other. A ray incident on this area, at any angle, will be refracted twice at parallel interfaces. Therefore it will emerge on the other side of the lens on a direction slightly... | {
"language": "en",
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"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "7",
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"answer_id": 1
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Why is kinetic friction less than static friction? Ex: A wooden block is lying on a table.
I am told that because the block is still, the microscopic surface irregularities form more complicated interlocking structures. Is it because the force of the block on the table deforms the molecular structure of the table and w... | Consider the logic if the reverse were true: kinetic friction was greater than static friction.
Then you could have the situation where static friction is too small to stop an object on a ramp from sliding, but kinetic friction is great enough to stop the same object when it was moving.
So what is an object to do?
| {
"language": "en",
"url": "https://physics.stackexchange.com/questions/214953",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "2",
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Perception of Depths and Stereovision I watched a video on Youtube and read a few articles which say that human beings see 3D because we have two eyes.
But does that mean when I close one of my eyes, I should see 2D? It doesn't happen so. Why am i still able to be understand depth? Would a person with one eye not be ab... | Stereo vision is just one (though powerful) source of depth information.
Eye focus and microsaccades still give one-eyed people some depth perception and combined with pure reasoning/inference from 'known' objects allows to approximate distance.
A species with a single eye could be expected to augment those features f... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/215047",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "7",
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Why does $\omega = \sqrt{V''(x_0) / m}$? I know that in an equation such that $$\ddot{x} + \omega^2x = 0,$$ the angular frequency $ = \omega$. But why is that ever $ \sqrt{V''(x_0) / m}$? (where $x_0$ is the equilibrium point). I just saw that used in the solutions to a problem set without explanation.
| Consider an arbitrary potential energy $V(x)$; take $x_0$ to be an equilibrium point, that is, $V'(x_0)=0$. Next, Taylor expand $V(x)$ for $x$ close to $x_0$:
$$
V(x)\approx V(x_0)+(x-x_0)V'(x_0)+\frac{1}{2}(x-x_0)^2 V''(x_0)
$$
The first term is just a constant (ie, irrelevant for energies), and the second one is, by ... | {
"language": "en",
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"timestamp": "2023-03-29T00:00:00",
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Exact closed form solution to the quantum harmonic oscillator I came across this question in Griffiths QM, which asked to show that this equation
$$\Psi(x,t)=\left(\frac{m\omega}{\pi \hbar}\right)^{1/4} \exp\left[-\frac{m\omega}{2\hbar} \left(x^2+\frac{a^2}{2}(1+e^{-2i\omega t})+\frac{i\hbar t}{m}-2axe^{-i\omega t}\ri... | This is the wavefunction of a coherent state; it is a well-known solution of the quantum harmonic oscillator and it has a large number of nice properties. There is a good number of independent ways to derive it so it is pretty pointless to try and guess which one Griffiths was thinking of.
| {
"language": "en",
"url": "https://physics.stackexchange.com/questions/215255",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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Why is light energy 100% reflected in total internal reflection? during reflection of light energy transfer is not 100%.
when light from a rarer medium like air strikes a denser medium like glass slab, some part of light is reflected back and some of it is refracted.
But during total internal reflection (TIR) when a be... | I got my answer.
When light enters in glass from air, it likes to reflect back by wave front theory (although 1-2%). In case of from denser to rarer medium first below critical angle some part of it is reflected back and some is refracted, but above critical angle some is reflected and other part (which was earlier ref... | {
"language": "en",
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"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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Is Earth really a magnet? I am a student of class 9. When I was going through magnetism and read that an earth is a magnet I got some doubts. My question is: is earth really a magnet? Doesn anyone have any proof that earth is a magnet? Is there a magnetic core at the center of the earth? Has anyone reached the core of ... | Yes, Earth does have a magnetic field(check it out with a compass!).
In geology, they explain this in this way:
The Earth's core is divided between the inner and outer cores. The inner core is solid because of the very high pressure. The outer core, although it also has high pressure, it is not as high as the inner cor... | {
"language": "en",
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"source": "stackexchange",
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Is it (practically) possible for a large building to be a Faraday cage? In my sophomore year of high school, my P.E. teachers kept on complaining about how phones didn't have a network connection in our gym, regardless of model, service provider, etc. A couple of feet outside the gym, cellular reception was crystal cle... | In general the answer is "yes it is possible" - but in your case the answer is "that is not a Faraday cage".
Radio waves are (partially) reflected by any discontinuity in dielectric constant of the medium they propagate through. The ones that propagate (through walls etc) will also experience attenuation.
A faraday cag... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/215809",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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What is the smallest item for which gravity has been recorded or observed? What is the smallest item for which gravity has been recorded or observed? By this, I mean the smallest object whose gravitational effect upon another object has been detected. (Many thanks to Daniel Griscom for that excellent verbiage.)
In oth... | Gravitation effect on neutrons have been demonstrated.
Bouncing neutrons
To obtain neutrons with quantized gravitational energy states, the team used a technique first described in 2011, in which a nuclear reactor produces neutrons travelling at 2,200 metres per second. These are then slowed to less than 7 metres per ... | {
"language": "en",
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Why can't I push myself in a chair? If I am sitting in a chair with wheels and someone pushes on the back of my chair with sufficient force it will role along the ground. However, if I push on the back of the chair with the same force it will not move the chair. Why?
| If you have no contact with floor and walls outside the chair other than through the wheels of the chair, you will not be able to fulfill the requirement of Newton's Third Law with respect to the floor and walls other than through the wheels of the chair.
You can push on any part of the chair you like, but an equal and... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/216094",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "4",
"answer_count": 5,
"answer_id": 2
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Why do tall buildings have low resonant frequencies? I know that tall buildings have low natural frequencies, hence they're more vulnerable to earthquakes, but why do they have low natural frequencies?
| Generally speaking mechanical structures, if they 'ring' at all, will ring at frequencies determined by the properties of stiffness (elasticity) and mass. The frequency in most cases increases with increasing stiffness, but decreases with increase in mass.
Buildings have considerable stiffness, but not necessarily tha... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/216232",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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What is Pressure Energy? While deriving Bernoulli's Theorem, our teacher said that the sum of KE, PE and Pressure Energy per unit volume remains constant at any two points.
$$P + \rho g h + \frac{\rho v^2}{2} = \text{Constant}$$
In this, he stated that the first term is Pressure Energy per unit Volume. What exactly is ... | Your teacher refers to a common and simple but incorrect understanding of the Bernoulli theorem.
Unfortunately, it is quite common to understand the equation
$$P + \rho g h + \frac{\rho v^2}{2} = \text{Constant}$$
in the following way:
Total energy of a fluid element is $\text{Constant}$ times its volume and besides ki... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/216342",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "26",
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Have we observed sufficient extra-solar planetary systems to establish a planetary distribution pattern? From Kepler And Extra-Solar Planetary Observations
As of January 2015, Kepler and its follow-up observations had found 1,013 confirmed exoplanets in about 440 stellar systems, along with a further 3,199 unconfirmed... | the answer is no: for now there is a high correlation between the properties of planets (size, distance to their star) and their probability to be detected, which totally bias the observed distribution.
| {
"language": "en",
"url": "https://physics.stackexchange.com/questions/216420",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "3",
"answer_count": 1,
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What prevents me to accelerate an object to near light speed in space? As far my limited knowledge go, things in space aren't slow down unless something interferes with them, so what prevents me to build a spaceship powered by nuclear power that will keep accelerating until we get to the limits of physics?
Like the voy... |
Wouldn't that greatly reduces the time you need to get to a distant star, since you can increase your speed exponentially?
In addition to hft's answer, due to relativistic kinetic energy $KE$ , assuming you use high constant thrust your actual acceleration would start tailing off quickly at relativistic speeds, so yo... | {
"language": "en",
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Derivation of $E=pc$ for a massless particle? In classical mechanics, massless particles don't exist because for $m=0$, $p=0$.
The relativistic relation between energy, mass and spatial momentum is: $E^2= (pc)^2 + (mc^2)^2$ . So it is said that setting $m=0$ in the first equation you get $E=pc$.
How could setting $m=0$... | The relation (setting $c = 1$)
$$
E^2 = m^2 + p^2
$$
is more fundamental than $E = \gamma m c^2$ and $p = \gamma m v$.
The former arises naturally as a primary constraint from varying the action
$$
S = -m \int \sqrt{\dot{x}^\mu \eta_{\mu \nu} \dot{x}^\nu} \, d\lambda
$$
The latter expressions only arise when you choose... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/216907",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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Calculating effective capacitance of a circuit Please refer to the image below.
The question asks: 'The effective capacitance between terminals A and B in the network shown in the adjoining figure is?'
Here is my working:
(C5 and C6 connected in series.. in parallel to C2 and C4 connected in series).. connected in se... |
Using Kirchhoff's First Rule,finding charges in capacitors between D & C (Let it be $Q_m$).
$$
Q_1-Q_m-Q_2=0\\
Q_3+Q_m-Q_4=0\\
$$
Using Kirchhoff's Second Rule,finding voltages loops ADC & DBC.
$$
\frac{Q_1}{C_1}+\frac{Q_m}{C_m}-\frac{Q_3}{C_3}=0\\
\frac{Q_2}{C_2}-\frac{Q_4}{C_4}-\frac{Q_m}{C_m}=0
$$
When the Bridge ... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/217017",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "2",
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How do I properly apply the parallel axis theorem to a rod-sphere system rotating about its center of mass? In the image below you see a rod with a sphere attached to its right side. The rod-sphere system is rotating around the entire system's center of mass. How do I apply parallel axis theorem to find the moment of i... | You have two bodies $m_1$ and $m_2$ placed with distances $d_1$ and $d_2$ from some arbitrary point A to their center of masses, then combined mass moment of inertia at that point is
$$ I_A = (I_1 + m_1 d_1^2) + (I_2+m_2 d_2^2) $$
The combined system has mass $m_1+m_2$ and if the required mass moment of inertia about ... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/217205",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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Is the direction of gamma-ray emission by a nucleus totally random? Let's consider an excited nucleus emitting one gamma-ray (not cascade etc). Is the direction of gamma-ray emission completely random? In other words, is the probability to detect this gamma equal for any angle?
Will the answer change in case of presenc... | There are examples of nuclei whose emission is not isotropic in the presence of a magnetic field. Feynman gave an example of this during a lecture on symmetry in physical laws (vol 1-52).
In particular in 52-7 he mentions an experiment in which the emission of an electron by a cobalt nucleus (Co-60) is asymmetrical wi... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/217315",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "10",
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What experimental evidence shows that sound velocity is the same for all wavelengths? I'm studying sound waves with Halliday's book, and after reading the whole chapter, one of the questions suggested was:
What is the experimental evidence that allows the assumption that the sound wave velocity in air is the same for ... | Good theoretical answer is that it results from linear acoustical wave equation and its presuppositions. It is therefore good approximation whenever linear acoustics still can describe the wave propagation (that would by e.g. 90% of room acoustics practical examples). Typical examples of problematic models are large-am... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/217424",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "2",
"answer_count": 3,
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Which is more fundamental: $H$ or $B$? According to Wikipedia, $B$ is called the
Magnetic flux density / Magnetic induction / Magnetic field,
while $H$ is called the
Magnetic field intensity / Magnetic field strength / Magnetic field / Magnetizing field.
Which of them is more fundamental? Is it meaningful to say one... | Look at the equation $\mathbf \nabla \times \mathbf H = \mathbf J_\textrm{free}$, and at the same time at $\mathbf \nabla \times\mathbf B = \mu_0 \mathbf J$. Now, $\mathbf J = \mathbf J_\textrm{bound} + \mathbf J_\textrm{free}$, and $\mathbf H = \frac1\mu_o \mathbf B - \mathbf M$, where $\mathbf M$ is called the Magnet... | {
"language": "en",
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Why are potential differences equal across two capacitors in parallel, but charge on each capacitor is not? Two or more capacitors are said to be connected in parallel if each one of them is connected across the same two points. In a parallel combination of capacitors potential difference across each capacitor is same ... |
Why are potential differences equal across two capacitors in series, but charge on each capacitor is not?
This is based on a false premise. There is no rule that says that "potential differences are equal across two capacitors in series".
In a parallel combination of capacitors potential difference across each capac... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/217628",
"timestamp": "2023-03-29T00:00:00",
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Are the 7 base quantities in SI system really independent? In a typical description of the 7 base quantities of the SI system we see the following two points:
*
*All other quantities can be derived from them.
*They are "independent".
My question is about the term "independent". It seems to mean that none of th... | Only the definitions of one second, one Kelvin and one kilogram are completely independent of each other (see this scheme). All other base units are derived from these three units.
In earlier days, the meter was just an etalon which was defined as 1 meter. Currently it is defined via the second with the help of the spe... | {
"language": "en",
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"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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Rotating disc problem This question comes into my mind this evening.
Suppose I have a rotating disc whose maximum rotation speed is $500$ rpm (say). On this rotating disc I have placed another small rotating disc with same property and in such a way that both can rotate in this configuration. Now if I started the disc... | If they rotate in the same direction at the same speed, there will be no effect. This is because the disks do not move relative to one another.
If they rotate at different speeds or in different directions and there is friction between the disks, their speeds will gradually come closer to one another's until their rota... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/218166",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "2",
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Visualising gas temperature and gas pressure Gas pressure is created when gas molecules collide with the wall of the container creating a force.
Gas temperature is a measure of how fast the molecules are moving / vibrating.
However, they both seem to be concerned by "kinetic energy" of the molecules, or in other words,... | Pressure is a measure of force per unit area exerted on the 'measuring device', while the temperature is a measure of kinetic energy of the individual molecules of the gas. Thus, high pressure can arise when there are either many slow moving molecules with low kinetic energy colliding with the container, or a few fast ... | {
"language": "en",
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"source": "stackexchange",
"question_score": "2",
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Operators for a Perturbed Hamiltonian: Heisenberg Picture ($\hat{x}$, $\hat{p}$) Problem
I am trying to calculate the Equations of Motion in the Heisenberg picture for $\hat{x}$ and $\hat{p}$ in a perturbed Hamiltonian,
$$
\tag{1}
\hat{H} = \hat{H}_0 + \hat{H}'
$$
Assume the Heisenberg Equations of Motion are g... | It seems like your answer sidestepped the whole question.
When you do the same for $\hat p$ you'll find that its derivative depends on $\hat x$, and on $\lambda$.
But these coupled equations can then be solved as a second order equation for the terms individually, which should be what you are looking for.
| {
"language": "en",
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"timestamp": "2023-03-29T00:00:00",
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Why can't I see the blue color scattered by the lower atmosphere of the earth? I understand that the blue colour of the sky is because of the scattering of blue light by molecules in earth's atmosphere. The scattering appears to be happening from molecules that are far above in the earth's atmosphere. What about the sc... | If I understand you right, you're referring to the phenomenon seen in this picture (from the first Google hit), that near the horison the color of the sky is more light-blue (not exactly white):
Rayleigh scattering
The scattering in the atmosphere is for a large part Rayleigh scattering off of nitrogen and oxygen mole... | {
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Question about north and south poles of a magnet I've always been taught: North poles attract south poles.
Yesterday after studying electromagnetism, I've a question to ask.
Here's a diagram:
In circuits like these, this is how the north and south poles of these electromagnets are defined. Now my question is, is the ... | The magnetic attraction/repulsion is a fundamental property of magnetism. N-poles attracts S-poles and so on, and this is based on our observations of how nature works.
Now, there is a strong relationship between electricity and magnetism, which explains why a flowing electrical current produces magnetic fields. Once... | {
"language": "en",
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"source": "stackexchange",
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magnetic force from v=0 and dB changing magnetic force is defined as:
$ \mathbf{F}=q \mathbf{v} \times \mathbf{B}$
so if v=0 there is no force. However Faraday's law states that if $d\mathbf{B}\neq0 $ then we have an induced emf even though speed of q in a circle is 0 and the magnetic force is not moving. Does this mea... | The Lorentz force for the magnetic field $\vec F$=q$\vec v\times\vec B$ states that if you have a charge q moving in a region in which there is a magnetic field, then a force proportional to the speed of the charge acts on it. Correctly if $ v=0$, then $F=0$.
I don't understand what you mean with "the magnetic force is... | {
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How do we know that the x-ray pattern is in the reciprocal space? I wonder if any one can tell that why do we consider the x-ray pattern (for example, a x-ray pattern on a film for a crystal) in the reciprocal space?
(I don't want any explanation about the Ewald bubble and so on... those are according the fact that we ... | After x-rays hit a substance they will be scattered in all directions; if the material is a crystal then you will obtain a diffraction pattern where each point is created by the constructive interference of the scattered rays.
The connection between the diffraction pattern and the reciprocal space is readily found:
tak... | {
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What depth should water be filled to in a cylinder flask to make it the most stable As said in title, a cylinder flask with a mass of 100g and radius of 3 has a center of balence 10cm above the base. Assuming negligible wall thickness, to what depth should water be added to this flask to make it the most stable.
The q... | Goutham is quite correct in some ways but overlooks something. Look at the diagram below:
We known the centre of gravity (COG) of the empty cylinder is $z_1=10\:\mathrm{cm}$ and the mass of the empty cylinder is $100\:\mathrm{g}$.
If we fill the cylinder up with water to height $2z_2$ then the COG of the water is $z_2... | {
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What causes loud sound when popping a balloon/bubble? As I chew my gum, I wonder: when I blow and pop bubbles, what creates the snapping sound?
Or similarly, what causes the loud POP when one pops a balloon? Is it the rush of air from inside the pocket rushing out and colliding with the air previously outside the pock... | It's for the same reason as fireworks making that short lived, sharp noise.
During explosion, huge amount of heat is created in a fraction of second that the pressure surrounding firework rapidly increases. This pulse of highly compressed wave results in a high dB sound.
As @Hilmar pointed out, the pressure inside a b... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/219664",
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"source": "stackexchange",
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The NERVA had to use liquid $H_2$... But why? The NERVA engine, developed at the late 60ies, was a nuclear thermal rocket developed for vacuum use in space craft. It was supposed to use Liquid Hydrogen, a cryogenic fuel with quite a few issues such as high cost and difficulty in containment that has greater efficiency ... | Here are some thoughts on using water instead of hydrogen as reaction mass: The complications of storing hydrogen compactly are certainly a factor to weigh against the extra thrust per unit weight achievable with hydrogen. Since water molecule weighs 9 times more than hydrogen molecule (18 vs 2) and the thrust at given... | {
"language": "en",
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Special Relativity in water If there are 2 observers in water moving relative to each other as well as to water, they measure different speeds of light. So does time dilation occur for them? (since Time dilation is based on constancy of speed of light)
| Relativity just requires "constant speed of light in vacuum". It makes no claims about the speed of light in a medium.
When you are moving relative to water, you will observe a different speed of light depending on your relative velocity. But you will still have all the other effects of relativity at work - such as tim... | {
"language": "en",
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"source": "stackexchange",
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The maximum distance for which Coulomb's law has been verified? We know that Coulomb's law, $F_{12} = \frac{kq_1q_2}{r^2}$, was experimentally verified for small distances by Coulomb himself at the and of the XVIII century.
The question is what is the maximum distance, experimentally confirmed, between two charges for ... | If you want to research the question more deeply, I would suggest you take a look at the Solar Wind. This is composed of charged particles (mostly protons) emitted by the Sun. The flow and behaviour of the Solar Wind has been studied quite deeply, not least because it affects greatly satellite operations, spaceflight, ... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/220250",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "12",
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Light and Gravity
The gravitational force does not affect the speed of light rather affects the frequency of light (hence light changes colors, red to blue and vice-versa).
I know this has been verified but I have 2 questions:
1.Why the speed of light is not accelerated due to gravity?
2.Why the frequency is affecte... | Anything with mass and/or energy warps space-time. When Light with different energy level passes through gravitational field of a massive object, higher energy will be attracted under the influence more than lower energy light. But, Higher energy of light particle will have more inertia than low energy particle. And si... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/220421",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "2",
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Time dilation in the movie Interstellar I know that the science in movies is questionable and sometimes ridiculous but I would think this question would have been more obvious to the script writers. When they visited Miller's planet they were almost killed by a re-occurring tidal wave. In a few short minutes they ended... | A few minutes on the planet (meaning, deeper in the gravitational well of the black hole) corresponds to a couple decades where the ship is orbiting. Thus in the couple decades the ship is waiting, it only sees the one passage of the wave.
This is akin to the popular science depiction of an astronaut falling into a bla... | {
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When does normal force equal to $mg$? Can someone once and for all explain when does normal force equal to mg?
I know for sure that when there is no friction, normal force will be equal to mg.
But, i encountered some questions when there is some mass on an incline with friction, and then the normal force was the y comp... | Briefly, the normal force is $F_N=mg$ when the surface that mass $m$ is resting on is horizontal (when the surface is inclined by an angle $\theta$ to the horizontal, then it's just $F_N=mg\cos\theta$). Friction has nothing to do with $F_N$, per se. But the frictional force experienced by $m$ sliding down an inclined p... | {
"language": "en",
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Find the height and the velocity of the object A bolt is detached from the lower part of an elevator cabin that is ascending with velocity 6meters/second and for 3 seconds comes to the point from where the elevator started to ascend. Find:
in which height is the end of the elevator in the moment when from it the bolt w... | This type of problem can be simplified if you use the frame of reference of the elevator. Now the bolt falls from rest, chasing the "starting point" which starts a distance $h$ below and moves down at a constant $6 $ m/s. The bolt catches up in $3$ seconds.
Same problem, but the equations are simpler...
| {
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How to keep a helium balloon between 1 to 5 meters above ground? (without it being tied) I understand that helium balloons rise because their density is less than air, so they can rise up to a point where the air surrounding it has the same weight as the balloon.
I was thinking to fill it with something like half air a... | if we confine our discussion to weather balloons, like this one
and assume the Ideal Gas Law, we can greatly simplify the problem. The balloon is limp; it is not under tension, and the pressure and temperature of the hydrogen or helium are the same as those of the surrounding air.
Assume that we put 2 grams of hydro... | {
"language": "en",
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General Solution to Linear Schrodinger equation I am trying to find a solution to
$$\displaystyle \left[-\frac{1}{2}\nabla^2 - \frac{2}{r} + C(r)\right]\phi(r) = E\phi(r)$$
where $C(r)$ is a known function of r. I am just looking for some help on the strategy to solve explicitly for $\phi(r)$. I have read through the s... | I feel like this question is a little too open ended and I'm sorry for that...but I did find a WONDERFUL HF walk through http://www.phys.sinica.edu.tw/TIGP-NANO/Course/2011_Spring/classnotes/CMS_20110511.pdf that clears everything up.
| {
"language": "en",
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"source": "stackexchange",
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Inconsistency with electrostatic energy formulas The energy of point charge configuration can be written as:
$$W = \frac{1}{2}\sum_{i=1}^{n}q_{i}V(r_{i}) \, ,$$
which can take both positive and negative values.
However, when we integrate the equation to get the energy of a continuous charge dustribution:
$$W = \frac{1}... | The difference is the zero point. When summing over charges, the reference is a state in which this charges are infinitely separated. Those are still distinct, localized charges, just separated from each other.
When integrating $E^2$ over all space, the reference state has all charge separated. Even the individual cha... | {
"language": "en",
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Can light have zero wavelength? As you increase the energy of a photon it's wavelength shortens. Is it theoretically posible for light to not have a wavelength? Like a still pond?
| How about doing it the other way? Quote "The earth is a magnet, and it is accelerating as it rotates the Sun, so it radiates EM waves with a period of 365 days and a wavelength of 1 light year." The frequency would be so low as to have no detectable wavelength. Like a still pond.
| {
"language": "en",
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About bosonic, fermionic state in identical particles The upper picture is my ideas which represent states by using the tensor product. but the lower picture, as you see, includes uppermost states. i don't know how to treat the uppermost states in lower picture. could you help me?
| I think what the exercise aims at is making the connection between the occupation-number representation to the tensor product representation.
The occupation-number representation only makes sense if the particles are indistinguishable, as it tells you "$n_g$ particles are in state g, $n_e$ particles are in state e, $n_... | {
"language": "en",
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How do point particles transfer angular momentum between each other? I know that quantum physics says that one can't change the magnitude of spin of a point particle but that still leaves the question of how one changes the direction of spin.
One possible way point particles can exchange angular momentum is by electrom... | It's not like there is a rigid body with angular momentum that you are applying a torque to. You can change the direction by applying magnetic fields. This is because there is an energy associated to the alignment of the spin and the magnetic field.
| {
"language": "en",
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"source": "stackexchange",
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How is an electron beam generated? I am trying to get a better handle on how the EBPVD machine works in the lab I am working in. I understand that it produces an electron beam with a tungsten filament and that beam is then directed toward a crucible holding silver or aluminum using a magnetic field. All of that I und... |
My best guess for the process here is that by heating the coil the electrons are excited enough to break loose from the tungsten atom and become free electrons where they are directed into a beam structure by the magnetic field.
Yeah, that's (almost) it. You detach the electrons from the cathode by thermal excitation... | {
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Mössbauer effect - Deriving the recoil energy formula I am working on a problem that deals with the Mössbauer effect and calculating the recoil energy on a iron-57 atom, initially at rest and excited to 14.4 keV, after it emits a photon. In the Wikipedia article, the author states that we can find the following:
$$ E_{... | The relativistic equation for the energy of a particle is:
$$ E^2 = p^2c^2 + m^2c^4 $$
This applies to a photon but we have to set the rest mass $m$ to zero and this gives us:
$$ p = \frac{E_\gamma}{c} $$
From conservation of momentum the momentum of the nucleus must also be $p$ (in the opposite direction). Since the e... | {
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Visualizing Physical Units in Phyiscs I do best in physics when I can make sense of the units that accompany values, and I do this by visualizing in my mind what is happening. Take for instance, $v=\frac{s}{t}$. When I think of velocity I can visually see an object moving a distance, $s$, over a certain time, $t$. What... | I find that newtons are easiest to intuitively understand if I think of it as corresponding to how much force I have to put on an object to keep it from falling. The heavier the object, the more force I need, but in a different gravitational environment, I would not have to use as much force, even though the mass of t... | {
"language": "en",
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Relativistic acceleration in sinusoidal electric field Consider a relativistic charge $q$ moving with an oscillating electric field $E_z$ with phase velocity $v_p=c$ in direction $\hat{z}$ (e.g. radially polarized laser coprogating with electron). What is the energy gain of this charge as a function of time?
I set thi... | So actually this is not as easy as you assume, since for charged particle velocities being a significant fraction of c, you cannot omit the magnetic field in the Lorentz force anymore. Then the equation of motion has an additional term, leading to the so called figure of eight motion, which an electron in an intense la... | {
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Magnetic vector potential of an infinite wire Using the integral $$A=\frac{\mu_0}{4 \pi} \int \frac{I \vec{dl}}{r}$$ for calculating magnetic vector potential of an infinite wire we get $$A = \left(\frac{\mu_0 I}{4 \pi}\right) \ln(\sec \theta + \tan \theta)$$ which diverges when the limits are from $-\pi$ to $\pi$. We ... | Below picture shows an infinite wire and an imaginary loop for calculating the vector potential super much easier.
$$
\begin{align}
B &= \nabla \times A \\
\iint B \cdot \mathrm{d}a &= \oint A \cdot \mathrm{d}l \\
\int_a^b \frac{\mu l}{2 \pi r} L \, \mathrm{d}r &= AL \\
A &= \frac{\mu l}{2 \pi} \ln{\frac{b}{a}} Z
\end... | {
"language": "en",
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"timestamp": "2023-03-29T00:00:00",
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Frequency shift for accelerating source due to equivalence principle? Do cosmologists consider it alongside the Doppler shift? It's a question that's been bugging me since I first read Einstein's paper on gravitational frequency shift. He derives it using the equivalence principle, and considers an accelerating source ... | In the case of a constant gravitational field and a non-relativistically moving observer, the redshift $z$, i.e. the relative change in frequency $z=\frac{\nu_e}{\nu_o}-1$, is (there's a nice short explanation here under 'Gravitational Redshift'):
$$z=\frac{gL}{c^2}$$
The analog in cosmology would be Hubble's law:
$$v ... | {
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Velocity of a leak in a closed water tank Bernoulli's equation states
$P_1+{1\over2}\rho v_1^2+\rho g h_1 = P_2+{1\over2}\rho v_2^2+\rho g h_2$
In a classic "water tank with an open top and a leak" scenario, "point 1" is the surface water in the tank, and "point 2" is the leak. The equation could be rewritten for $v_2$... | A closed-off tank can be considered to be 0 Pa. Assuming the outside air is 1 atm in pressure, $P_1$ and $P_2$ would no longer cancel out. The simplified equation would not apply here.
(I'm doing homework, and Googled for multiple hours. I never found an explanation. I made an assumption it turned out to yield a correc... | {
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What is the time imaginary method? I have to submit homework about the scheme which solves the time-independent Schrödinger equation and finds the ground state by the imaginary time method.
I know the substitution $-\mathrm{i}\tau\mapsto\tau$ and $\tau\to\infty$, but I don't know how to start it and finish it. I am goi... | You can propagate the Schrödinger equation to imaginary time. This means solving the following equation
$$ \frac{\partial}{\partial t} | \Psi > = -H |\Psi> $$.
The initial state can always be expressed as a linear combination of eigenstates of $H$
$$ |\Psi(0)> = \sum_n c_n |n>$$
Solution to to imaginary time Schrödinge... | {
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Are charges always uniformly distributed on conductors? As the title says. For example, if I take a fat metal wire with non-negligible thickness, and then wind it into a spiral, but such that none of the parts touch one another (there are no topological 'holes'), then if I add a charge to the wire, would it equally dis... | I think that the either ends of your wire no matter how you fold them have higher amount of surface density of charge than the middle, however, the amount of charge is different as follow.
Imagine your wire to be approximated by the figure below
The first three spheres have the same radius and the rest have different ... | {
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What does "the fabric of space and time" actually mean? I've heard the term "the fabric of space and time" in both physics and science fiction, and although I know it has something to do with general relativity, I don't understand what, specifically, they're referring to.
| I think it is a poetic or at least suggestive way to talk about the metric of space-time, about the fact that space-time can be curved, and its curvature changes from point to point, depending, as the other poster says, on the amount of mass-energy present at that point.
| {
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Can we speed up the evaporation of black holes manually by accelerating it? If we throw an object to pass near a black hole, to bypass it, it will change the speed of the black hole, just like gravitational assist for a space probe. Does an accelerating black hole evaporate faster because:
*
*When object accelerates... | No,usually we can not speed up the evaporation of black holes manually by accelerating it under normal circumstances,but we can of course write a letter to our dead ancestors to speed it up
| {
"language": "en",
"url": "https://physics.stackexchange.com/questions/223449",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "1",
"answer_count": 5,
"answer_id": 1
} |
Derivation of canonical position-momentum commutator relation We know that the position-momentum commutator is fundamental in quantum mechanics, but would it be possible to derive it starting from a different set of first principles, more specifically starting (in Dirac notation) from
1) Closure relations $ \int|x\ran... | The only ingredient that one needs to prove the commutation relations back is the action of either of the two operators on the other basis; namely one must assume that $\langle x|\hat{p}| \psi\rangle = i \partial_x \psi(x)$, i. e. the momentum operator acts as derivative on the position (or viceversa). From there the c... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/223633",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "7",
"answer_count": 2,
"answer_id": 1
} |
Does 'focal length' mean something different with lenses and pinhole cameras? Sometimes different but related things have the same name by some tradition or accident, causing a lot of headache to newcomers to a field.
I would like to come to clear terms with this: does the expression 'focal length' mean something disti... | While your sketch is correct, its scales may confuse you in this case. Do remember that, denoting the distances from the lens to the object and image plane by $z_o$ and $z_i$, respectively, we have $$\frac 1f = \frac{1}{z_o} + \frac{1}{z_i}.$$
Now in real world scenes, usually the camera dimensions are very small, so t... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/223738",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "13",
"answer_count": 3,
"answer_id": 1
} |
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