Q stringlengths 18 13.7k | A stringlengths 1 16.1k | meta dict |
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Regarding the Boltzmann entropy formula, is the Boltzmann constant really arbitrary? In the top answer to this question (Is the Boltzmann constant really that important?) I read that the Boltzmann constant is just a dummy factor which converts energy to temperature.
But that allows me to put another numerical value in ... | In thermodynamics, the temperature is actually defined in terms of the entropy:
$\frac{1}{T} = \left(\frac{\partial S}{\partial U} \right)_{V,N}$.
Therefore, if you would change the definition of the bolzmann constant to $k' = a k$, the temperature would scale accordingly with a factor $1/a$, and the combination $kT$, ... | {
"language": "en",
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"timestamp": "2023-03-29T00:00:00",
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How are atoms supported on each other in a material? Suppose we have a ball made up of iron. There are a "lot" of atoms in the ball.
My question is "how" are the atoms supported on top of each other?
And, is it due to the repulsion of electrons the atoms maintain distance between themselves?
| The atoms in any object never come into contact with one another for exactly the reason you stated - the outermost electrons repel. Furthermore, the boundaries of an atom are ill-defined in quantum theory, meaning that to discuss contact between them does not make much sense.
In the case of iron, a metal, the positive ... | {
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Physical intuition behind torque converter A torque converter (also here) is a device used in some cars. It uses several "fans" coupled through a liquid (transmission fluid) in order to perform the function of a clutch, but more importantly it acts as a liquid gear in the sense that it multiplies the torque going from ... | Check this video below that perfectly describes the operation of torque converters.
Fluid Coupling: Principles of Operation (1953)
Torque converters (TC) are defined by a torque ration, which is in turn defined by the turbine design withing the converter. There are two turbines, as described in the video. If you make a... | {
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Why does the potential difference across a type of parallel circuit not act like a potential divider?
Image credit (Q3)
In this attached circuit, when $R_1=0\Omega$, I am failing to understand how the two cells affect the potential difference across the central resistor R3. I understand that potential difference is co... |
so 12 volts should be distributed between R2 and R3 as a potential divider
If you're trying to solve this with superposition, you've forgotten a step or two.
When solving for the effect of the 12-V source, you need to zero out the other source. So you set $V_1$ to 0 V. Then R1 is in parallel with R3, and you need to ... | {
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What are “vibrations” in a field in Quantum Field Theory (QFT)? For example, in a 2013 article for NOVA Don Lincoln writes:
Everywhere in the universe there is a field called the electron field. A physical electron isn’t the field, but rather a localized vibration in the field. In fact, every electron in the universe ... | The word vibration has more of a historical sense, and we use excitation more often. In QFT, real particles are excitation of the underlying field.
Now the reason why we use vibration is because historically, these fields were modeled through waves, mathematically, and if you imagine a guitar string, and create a vibra... | {
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Information content in black holes Bekenstein-Hawking formula for entropy of a black hole tells us that information content in a black hole is proportional to its area which is in fact proportional to the mass^2 of the black hole. The information content before the formation of the black hole can be different which has... |
Is there any kind of information loss during the formation so that we get two black holes with an equal amount of information.
If I'm understanding correctly, this sentence is describing two different sets of initial conditions leading to two black holes with the same area, and therefore the same entropy.
You're usin... | {
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Does light take the path of least time because it travels in straight lines or vice versa? My question is which of these two feats is a consequence of the other?
Light travels in straight lines, mostly. Does it do that as a result of Fermat's principle of least time? and if so, is there a reason as to why it follows th... | The fact that light travels at straight lines has the same reason as any particle moving on straight line if there is no external agent to change its path - the fact that spacetime is homogeneous and isotropic in any inertial frame of reference (actually that is the definition of inerial frame of reference).
In general... | {
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OPE of three operators In the process of thinking about this question, I realized that I don't understand something very fundamental about operator product expansions.
Consider a product of 3 local operators in a 2d CFT:
$$ X(x) Y(y) Z(z) = \sum_{n=-N}^{\infty} A_n(x) Z(z) (x-y)^n, $$
where we have substituted $X(x) Y(... | Let me redo the calculation, while explicitly writing OPE coefficients. Let $(A_n(z))_n$ be a basis of operators at $z$. We use the two OPEs
$$
Y(y)Z(z) = \sum_n c_n(y,z) A_n(z)
$$
and
$$
X(x)A_n(z) = \sum_m d_{m,n}(x,z) A_m(z)
$$
We end up with the result
$$
X(x)Y(y)Z(z) = \sum_{m,n} c_n(y,z)d_{m,n}(x,z) A_m(z)
$$
wh... | {
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Is motion smooth? It's obvious that for every particle velocity is smooth i.e it cannot undergo sudden finite change in its position in infinitisiminal time.
Similarly any particle's velocity cannot undergo a change instantaneously (Infinite acceleration can't happen, intuitively).
Does this pattern apply to higher tim... | Typically these higher derivatives are assumed to be smooth.
The key question will be what causes a discontinuity in the n-th derivative. If you focus on classical mechanics, the forces on an object boil down to the positions of particles in the system, which are continuous. This means there would need to be a discon... | {
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2 windows - will I see the reflections?
I have a question regarding photons nature. Let's say I have a single source of light - regular bulb and the observer - in the same room.
The observer looks through a glass window (normal glass window-nothing special about it) and sees his reflection, but some of the light is p... | It will reflect some of the light back, depending on the thickness of the glass. The partial reflection of light from the two glass windows varies from 0%-16% (that is, on average 8% of the light is reflected back by both windows combined). Definitely read QED by Feynman for more detail.
| {
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Movement of bubbles in a cup of tea Why is it that when I try to scoop bubbles out from the surface of a cup of tea, they always slip off the spoon even if some of the tea does not?
| For contrast, consider what happens when you scoop dirt with a shovel. As you lift the shovel, a pile of dirt stays on the shovel, and an empty space opens up below the shovel as you lift it. You can lift the pile of dirt all the way up out of the hole, above the level of the surrounding ground, and the dirt still stay... | {
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Can a wire having a $610$-$670$ THz (frequency of blue light) AC frequency supply, generate blue light? We know that when we give alternating current across a wire then it will generate an electromagnetic wave which propagates outward.
But if we have a supply which can generate 610 to 670 terahertz of alternating curre... | Even at tens of gigaherts, one does not carry current "in" a conductor -- it is carried along the outside (Google "skin effect").
There are transmission lines for high-frequency RF that basically launch an RF wave along a single naked wire, and catch it at the other end -- think of a coax without the outer shield. If ... | {
"language": "en",
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Does rotation happen throughout the whole x axis of an object simultaneously? For example, if I draw a line on the side of a pencil top to bottom, then snap one end of it as in launching it due to the pressure of my fingers. Anyways, if I record the pencil launch in slow motion (perhaps it’s my phone that has to do wit... | In general for a rigid body you have the combined motion of translation of the center of mass and rotation about the center of mass at any instant.
The COM moves with $\boldsymbol{v}_C$ and the body rotates (simultaneously) with $\boldsymbol{\omega}$.
So the motion of any other point P, located at $\boldsymbol{r}$ rela... | {
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How much energy is needed to make fire? I'm so curious about fire. So I searched a lot in the internet. And now, I knew that fire is some kind of chain reaction and combustion energy make the other molecule hot and the other molecule makes other chemical reaction and so on...
Then does the first given energy make this ... | The amount of energy needed to start a fire depends on the combustibility of the substrate. The energy supplied needs to be enough to heat a small quantity of the material to its ignition temperature. If it is something highly inflammable like methane,hydrogen or aviation spirit,a tiny, almost invisible spark is enoug... | {
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Difference continous - discrete symmetry I am trying to understand the difference between the two types of symmetries.Wiki
Wikipedia says that
*
*Translation in time : $t \rightarrow t + a$
is a $\textbf{continuous}$ symmetry, for any real $t,a$
but
*Time reversal: $t \rightarrow -t$ is a $\textbf{discrete}$ symm... | When we say a symmetry is continuous, it is shorthand for saying that the group of symmetries is continuous.
For time translations, the group consists of all translations for any a, where $a$ is a continuous parameter. There are an infinite number of these group elements, and there are elements of the group which are i... | {
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Unorthodox way of solving Einstein field equations Usually when we solve field equations, we start with a stress energy tensor and then solve for the Einstein tensor and then eventually the metric. What if we specify a desired geometry first? That is, write down a metric and then solve for the resulting stress energy t... | You can certainly go from the metric to the energy-momentum tensor, but then you’re not “solving” anything. There are no differential equations to be solved if you’re doing that. It’s just a straightforward, although often tedious, computation (of the Einstein curvature tensor, which is proportional to the energy-momen... | {
"language": "en",
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Why does a helium balloon rise? This may be silly question, but why does a helium ballon rise? I know it rises because helium is less dense than air. But what about the material of the ballon. It is made up of rubber/latex which is quite denser than air. An empty ballon with no air in it falls, so why does a helium fil... | Lots of good answers here, but none address the main issue with your questions. The balloon doesn't rise due to any direct mechanism. Instead, the denser air around the balloon pushes itself down, with the net effect pushing the balloon up.
This is similar to the misstatement that 'heat rises'. Again, it doesn't. I... | {
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How can system of charges be static? I am a beginner in electrostatics.
I don't understand the below:
When we have a set of charges, those charges exert a force on the test charge but what I don't understand is how are these set of charges at rest?
Isn't this against the Coulomb's law?
Won't each charge affect each oth... | Remember that for charges to flow, we require a potential difference, and a low resistance path(not an insulator). So, charges can't flow in case of insulators, when no free charges are available, even if there is a difference of potential.
| {
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Temperature relation to Archimedes principle I have a probably very simple problem which I cant solve. I am weighing animals in seawater by placing them on a small PVC arm that is fixed on a balance and reaches into a beaker of seawater. On the arm, I place an organism and measure the specific weight of the animal. Now... | It is highly unlikely the differences you are seeing are due to temperature unless this is occuring outdoors.
As you can see on this page, the density of water changes less than 1% between -20 and +20 C. If you are indoors, it is highly unlikely it's changing outside +15 to +25, which would be much less than 1%.
Even o... | {
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Why does the Schrödinger equation work so well for the hydrogen atom despite the relativistic boundary at the nucleus? I have been taught that the boundary conditions are just as important as the differential equation itself when solving real, physical problems.
When the Schrödinger equation is applied to the idealized... | The boundary conditions that pick up the hydrogen wave functions are the "constraints" placed on the wave function solutions. Remember that the observable is the probability distribution from the $Ψ^*Ψ$, not a particular location. Please read the link. The solutions are within the quantum mechanic postulates after all.... | {
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If entropy decreases for cold systems, isn't the heat death of the universe a state of low entropy? Entropy is a consequence of heat. The heat death of the universe results in an approach to absolute zero temperature. Does this mean the end of the universe is low entropy?
| First of all, I agree with @anna v answer. I just want to expand (no pun intended) on the last paragraph.
Entropy is related to the dispersion of energy. In that sense, it is related to the universe gradually moving to its most probable state on order that all the energy is equally dispersed throughout the universe. A... | {
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Is plane altitude limited by engine power and if so does air density cause this? I notice that, for example, human-powered flight operates at low altitudes. This might of course be due to safety but I wonder if in fact the delta in air pressure is greater at lower altitudes and this prevents low-powered aircraft from r... | Human-powered flight is only barely possible because humans cannot generate large amounts of power. Human-powered planes therefore fly almost exclusively in what is called ground effect, where the plane is no more than about one wingspan off the ground. When flying this close to the ground, the plane is partly supporte... | {
"language": "en",
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Why choosing for prime numbers eliminates vibration? I have read that the spokes of a car wheel are usually five because, besides other substantial reasons, five being a prime number helps to reduce vibrations.
The same also happens with the numbers of turbine blades and the way a microwave grill is spaced. Prime numbe... | In trying to answer this question I came across a lot of interesting phenomena related to primes. This is not a very detailed answer but will hopefully I can share the intuition and feel of the concepts involved.
The phenomena we are dealing with is resonance.
In any machine, there are several parts. Each part has some... | {
"language": "en",
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Why don't we use Ampere's law to find the magnetic field due to a wire of finite length at its perpendicular bisector? I know that finite length doesn't have symmetry and thus it's hard to apply maths here but take the case of magnetic field of a wire of finite length at a distance $r$ from axis of the wire exactly at ... | we take circular amphere loop for infinite wire because field due to the part parallel to that wire is neglected .but when you talking about a finite wire(whose other part of given current carrying circuit) loop we have to consider the field due to other part of the circuit hence by applying the amphere circuital law y... | {
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If a RG fixed point (FP) is CFT, do all theories flowing into FP CFTs? Suppose that a RG (renormalization group) fixed point of some RG trajectory (or flow) is a CFT. Then do theories in this trajectory have to be CFTs as well?
| No. The points along the RG trajectory represent the theory’s behavior at some scale. The most baby example of this is a massive free field $\mathcal{L} = (\partial \phi)^2 + m^2 \phi^2$. This can be viewed as a perturbation of the Gaussian fixed point by the relevant operator $\phi^2$. In the deep UV the mass is negli... | {
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Neutral lithium ionization energy for removing an electron from the $1s$ orbital How much energy does it take to singly ionize a neutral lithium atom by removing an electron from the $1s$ orbital?
| You can obtain this directly from the energy-levels part of the NIST Atomic Spectra Database.
*
*In Spectrum, put Li I for the energy levels of neutral lithium, or Li II for the energy levels of the first cation.
*Choose whatever Level units you're most comfortable with.
Click Retrieve Data to get the results.
Th... | {
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If the pressure inside and outside a balloon balance, then why does air leave when it pops? Sorry for the primitive question but when we inflate a rubber balloon and tie the end, its volume increases until its inner pressure equals atmospheric pressure.
But after that equality is obtained why does the air goes out when... | But after that equality is obtained why does the air goes out when we penetrate the balloon? If there is pressure equality what causes the air flow?
You need to take into account that the elastic tension of the balloon skin pulls inwards. This makes the pressure in the balloon greater than its surroundings. Since there... | {
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Why charge induction is limited to some amount? Polarization occurs when a charge is placed next to a conducting object. When we ground the side of the object opposite the charge, that side becomes neutral.
But this neutralization disturbs the previous equilibrium. Thus, more polarization should be induced by the charg... | Let me help you clear your concept first. Consider $-q$ charge placed next to the conductor. Let the side facing the conductor be $A$ and the opposite side be $B$. The $-q$ charge induces a positive surface charge density ($\sigma_A=q/\text{area}$) on surface $A$. Therefore, a negative surface charge density ($\sigma_B... | {
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Could $\nu_e+p\rightarrow e^-+\pi^++p$ occur via the weak interaction? If so, how would be the Feynman diagram? I checked if the reaction conservate baryon number, charge and leptonic number and it seems like it does. But I tried to draw the Feynman diagram and I don't understand how the proton interact, so maybe the r... | No problem.
The neutrino emits a virtual $W^+$ and thereby turns into an electron.
The $W^+$ is absorbed by the $d$ quark in the proton, which turns it into a $u$ quark.
One of the many virtual gluons around in the proton splits to become a $d$ and a $\overline d$.
The 4 quarks and the antiquark arrange themselves into... | {
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Localization of $4f$ in rare earth and $3d$ electrons in transition metals Is there a justification for why are the $4f$ electrons strongly localized about the nucleus in rare-earth atoms but the $3d$ electrons in transition metals extend further out from the nucleus? I have hit upon this question while reading about m... | The crystal field splittings are much larger in transition-metal salts (mostly due to covalency, the ligand-field effect), of the order of electronvolts. In rare-earth salts, crystal field splittings are two orders of magnitude smaller.
| {
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Does the second-order correction to degenerate perturbation theory vanish? Consider a degenerate two-state system with states denoted by $|1\rangle$ and $|2\rangle$. If we apply a perturbation $H^\prime$, the first order correction to the energy is obtained by choosing two linear combinations of $|1\rangle$ and $|2\ran... | For degenerate levels the first order correction is obtained by the exact diagionalization of the Hamiltonian for the degenerate states. If all the states are degenerate, belonging to the same energy eigenvalue, then this is equivalent to the exact diagonalization of the Hamiltonian - no perturbation theory is needed (... | {
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Conservation of Angular momentum or Work = 0 , which is valid?
In the figure, the block on the smooth table is set into motion in a circular orbit of radius "r" around the Center hole. The hanging mass is identical to the mass on the table and remains in equilibrium. Neglect friction. The string connecting the two blo... |
Because the force(Tension) is always acting perpendicular to the motion of the block , so the work done on the block should be zero...
This is not true. As you pull the hanging block down the tension force does do work on the spinning block. The spinning block moves inward, hence it has some motion along the directio... | {
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How thick would the atmosphere have to be to block all the sunlight? this is a question I haven't been able to find an answer to anywhere.
How thick would our atmosphere have to be for the surface of the planet to be completely dark? Is that even possible?
Thank you!
| From a Wikipedia article on the Solar Constant:
At most about 75% of the solar energy actually reaches the earth's surface
You can roughly estimate that if the atmosphere were $n$ times as thick, the fraction would be $(0.75)^{n-1}$ compared with what we get. For example, if the atmosphere were 10 times as thick, sun... | {
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Rotation as an example of symmetry in classical mechanics I modified the question because it was confused.
On my book there is this mathematical definition of symmetry transformation:
"The equations of motion have a symmetry, if the solutions of the equations transformed by the symmetry are still solutions of the equa... | Suppose you keep track of the total energy in the system at hand and it remains unchanged with time. This is Conservation of energy. However you transform the time coordinate, the energy remains constant. Symmetry is in the system if some transformation leaves certain elements of the system unchanged. This includes tra... | {
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Time dilation and twin paradox - can this be explained in plain English? If one twin goes with an extremely fast rocket to Alpha Centauri and back, time is going slower for him, so when he comes back, the twin that stayed on the Earth is older.
But... if we look from the relative position of the rocket, the Earth rushe... |
So, does that mean that acceleration and deceleration make the twin in the rocket younger?
The twin on the rocket changes inertial frames. The twin on Earth does not. This is why the situation is not symmetric. If you want to not invoke acceleration, then do the following. At the time the twin would (instantaneously)... | {
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Which particle mediates the Aharonov-Bohm effect? BACKGROUND
The Aharonov-Bohm (AB) effect induces phase shifts between the two paths that an electron could take around an enclosed magnetic field. In radial coordinates, assume that the magnetic field is localized around the origin and that the two paths traced by the e... | Useful physics exercise here would be to study the problem of the solenoid with a current increasing with time. The field is growing inside the solenoid, and so is the field energy there. Where is the energy coming from? Answer is: work done by the current against an electric field. The electric field exists not only a... | {
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Why isn't my calculation that we should be able to see the sun well beyond the observable universe valid? I recently read an interesting article that states that a human being can perceive a flash of as few as 5 or so photons, and the human eye itself can perceive even a single photon. The brain will filter this out, h... | The problem with your derivation is that you distributed the photons over a 360° circle, so the photons only spread out in a two-dimensional circle. This means that the intensity of light drops off at a rate proportional to $1/r$ instead of $1/r^2$ (where $r$ is the distance from the center of the sun) like it does in ... | {
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Fourier optics - Transfer function of free space In all consulted literature, the transfer function of the free space is given as follows:
$$\exp(-i k_z d) = \exp(-i2 \pi d \sqrt{1/\lambda^2 -\nu_x^2-\nu_y^2})$$
When referring to this source, they derive the transfer function from the following equation:
$$H(\nu_x,\nu_... | The source is specifically referring to the input and output being a plane wave. The key point on that slide is that complex exponentials in the form $\exp(i 2\pi\nu_x x)$ are eigenfunctions of linear, shift-invariant optical systems. Thus, a complex exponential signal goes into the system, and another complex exponent... | {
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Temperature of vacuum chamber on Earth Does the temperature of a vacuum chamber drop if left for 24 hours or more, since some in space in quite cold somewhere and quite hot how does vacuum become cold near to absolute zero.
| @AlonsoPerezLona already explains it, I just want to clarify even further in terms of thermodynamics.
It's all about thermodynamic equilibrium. Everything exchanges heat through vacuum via thermal radiation, so if you have a vacuum chamber with walls at different temperatures, these walls will eventually equilibrate. A... | {
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Deriving Planck's Constant from Wien's Displacement Law So I'm reading an introductory book on Quantum Theory (David Park, 3rd ed.) and I am having trouble with the following question:
"According to Wien's displacement law, the wavelength $\lambda_m$ at which blackbody radiation at temperature T has its maximum intensi... | You do not need to convert the electromagnetic energy into the energy of a particle. You just posit that a photon with wavelength $\lambda_{m}$ has energy roughly $kT$; then you get that $h\approx ckT/\lambda_{m}\approx\times10^{-34}$ kg$\cdot$m$^{2}\cdot$s$^{-1}$, which is the correct order of magnitude. (Note that ... | {
"language": "en",
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Percentage of Neutron Stars that leave the Galaxy When a neutron star(NS) is born the supernova kick gives the newborn NS a certain boost in a supposed isotropic direction and, depending on how strong the boost is and on the position of the NS at birth time, its kinetic energy might exceed its gravitational potential o... | I couldn't tell you exactly what percentage of neutron stars leave the galaxy, neither could anybody else, but it must be a very tiny percentage indeed. After a supernova explosion, most neutron stars stay where they are. If you look at supernova remnants, there is usually a neutron star at the dead centre. To send th... | {
"language": "en",
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Why is the drag force proportional to $v^2$ and defined with a factor of $1/2$? $$Drag = \frac{1}{2}C_d \rho Av^2$$
I understand that the strength of the drag depends on the density of the fluid the body passes through, the reference area of the body, the drag coefficient, and the velocity of the object.
I don't, howev... | The drag force is doing negative work on the object that it is decelerating. By the work/kinetic-energy theorem, the work done is equal to the change in kinetic energy that the object experiences. Since kinetic energy is defined as $E_k = 1/2 mv^2$, you can expect the "1/2" and the $v^2$ terms to show up in the equat... | {
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In relativistic QFT, is it ever possible that the bare mass be finite and equal to the physical mass? In renormalization, one follows the philosophy that the bare mass is unobservable and could be infinite, and the physical mass comes from the pole of the two-point function. Is it possible that in any case the bare mas... | Yes, it is possible.
One possible example is the non-interacting theory, for example, a free scalar (bosonic) field with action
$$ S[\phi] = \int d^4 x \left( \frac{1}{2} \partial_{\mu} \phi \partial^{\mu} \phi - \frac{m^2}{2} \phi^2 \right). $$
If you're looking for examples of interacting theories, Yang-Mills theory ... | {
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Why can't we take space as universal frame of reference? Suppose we have a ball filled half with water in space with nothing else around (nothing else in the whole space except the ball) and suddenly it accelerates for time t. obviously, there would be movement in water which will tell us that the ball underwent motion... | I don't know if you came with this thought experiment by yourself but if you did you are crazy smart. This is actually very close to the argument made by Newton, usually called Newton's Bucket. He believed that absolute space was a real physical scenario where physical processes were to happen. And something similar to... | {
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How to know if a sine wave must be described as a sine function or as a complex exponential? In problems, sine waves (electromagnetic, acoustic, ...) are often described as $\psi(\mathbf{x},t) = \psi_0\sin(\mathbf{k}\cdot\mathbf{x} - \omega t)$.
However, they sometimes need to be described as $\psi(\mathbf{x},t) = \psi... | Answered by Lith in comments.
The exponential notation is introduced to make calculations easier by using the complex plane, but you are free to use whichever formulation you prefer, they are equivalent (as long as at the end of the problem you recover real function).
| {
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Peskin and Schroeder Section 7.1 Mass Shift I'm slowly reading my way through Peskin and Schroeder. Near the end of section 7.1 they compare the mass shift of the electron from QFT to the classical value, both of which are divergent but in different ways.
The calculation from QFT gives:
$$\delta m = \frac{3\alpha}{4\p... | Fundamentally, it has to do with 't Hooft's technical naturalness argument: since the electron mass term breaks the chiral symmetry, the quantum correction to the electron mass has to be proportional to the weakly broken mass scale $m_0$, thus linear in $m_0$ (with logarithmic divergent factor).
A counter example is t... | {
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Nuclear Physics Question How could I calculate the chance of a proton actually joining the nucleus and 2 protons and 3 and so on? Assuming a large number of protons are fired at a substance?
| What you're looking for is the absorption cross section $\sigma$ of the target. This quantity has units of area, and is typically measured in barns (1 barn = 1 b = 10-28 m2.) There are many such cross-sections one can define, for any particle interaction you might care to name. If you have a beam of protons with a f... | {
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Torque and angular acceleration in elliptical orbit I am stuck in a supposedly simple aspect. Consider the Sun-Earth system. The torque is zero and angular momentum is conserved. $L = I\omega$ is constant, but since $I$ changes, $\omega$ should change as well. That means there is a non-zero angular acceleration.
Now co... | The problem here is that your system is not a rigid body. We can think of it as a point particle (the Earth) rotating about another point particle (the Sun). The system is not rigid because the distance between these two point particles changes over time. Therefore, we need to be more careful with how we apply these ro... | {
"language": "en",
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Gaussian path integral is equivalent to saddle-point? If we have a path integral involving many fields,
$$Z = \int \mathcal D \phi_1 \cdots \mathcal D \phi_n \exp(-S[\phi_1,\ldots, \phi_n]),$$
and $\phi_n$ occurs only quadratically-- i.e. the $\mathcal D \phi_n$ integral is Gaussian-- I've been told that integrating o... | The gaussian integral
$$
\int dx\,e^{-\frac12 a x^2 + bx + c} = \sqrt{\frac{2\pi}{a}}\, e^{c+b^2/(2a)}\,,
$$
is similar to its path integral counterpart, which is
$$
\int \mathcal{D}\phi\,e^{-\frac12\phi \cdot A\cdot \phi + \phi\cdot b + C} \propto \exp\left(C + \frac{1}{2} \, b\cdot A^{-1}\cdot b\right)\,.
$$
By the d... | {
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Rotation of a rigid body within another orbiting body I would like to understand the physical behaviour of the following rotating sytstem.
There are 3 rigid bodies (1 is blue, 2 are red). We assume that there is no friction between the blu body and the red bodies, i.e. no friction along the dashed line.
The blue body... | Lab Frame
You have posited the system is began with a rotational rate $\omega$. In this state, only a radial force is required to satisfy the constraints of the blue object. With only a radial force and an initial tangential velocity, the motion of the CM of the red objects is uniform circular motion.
The red objects... | {
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Idealization of Eletric Field at a point According to Jackson "Classical Electrodynamics", in the first chapter about electrostatics:
[...] point charges or electric fields at a point must be viewed as
mathematical constructs that permit a description of the phenomena at
the macroscopic level, but that may fail to... |
why also the electric field at a point fails to have meaning microscopically?
You have no problem with a point particle being an idealization, right? Now, remember
$$
∇.E = ρ
$$
If you put garbage in the right hand side, do not expect anything better out of the left hand side.
what does it mean in practice that ... | {
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How does a heated lid in a thermal cycler prevent evaporation? A thermal cycler is a chemistry lab device that increases or decreases the temperature of the material inside it. The lid of the device is heated to prevent condensation and evaporation of the mixture inside.
I understand the condensation bit, as a hot lid ... | You were wise to be suspicious, because the answer is that thermal cyclers do not reduce evaporation relative to a similarly sealed chamber.
| {
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Why is it that when a chalk board gets cleaned, the area that used to have chalk is the cleanest? Why is it that when you erase a chalk board, the area where the chalk used to be becomes the cleanest? By that I mean that when you erase a chalk drawing, the board gets smeared with chalk dust, but the area where the draw... | My guess is that the chalk you have just applied binds to the existing chalk particles underneath. Then, when you swipe it, you are drag these particles along with the big lump of chalk that makes up your drawing. This is possible thanks to the internal cohesion of the material.
In the other areas of the board, you hav... | {
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Wouldn't gravitons themselves theoretically be affected by gravity? (I wrote this using the assumption that the graviton exists, which I know is not necessarily true; this is asked from a theoretical standpoint)
It is my understanding that General Relativity states all massive and/or energetic particles must be affecte... | Yes, gravitons must necessarily respond to each other via gravity. This means that in addition to communicating forces between objects that bend spacetime, the force carrier particles bend spacetime themselves.
But for very weak gravitational fields, the math gets easier to deal with because in this simplified case, ... | {
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How did Einstein know the speed of light was constant? I often hear the story of how Einstein came up to the conclusion that time would slow down the faster you move, because the speed of light has to remain the same.
My question is, how did Einstein know that measuring the speed of light wouldn't be affected by the s... | When using the term 'the speed of light' it is sometimes necessary to make the distinction between its one-way speed and its two-way speed.
The "one-way" speed of light, from a source to a detector, cannot be measured independently of a convention as to how to synchronize the clocks at the source and the detector. What... | {
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What are change of frame and change of coordinates? What's the difference between a change of frame and a change of coordinates?
I feel like both are transformations on the coordinates but change of frame changes also the vectors.
| It depends what you mean with 'change'. If 'change' is 'rate of change' i.e. the operator $\frac{d}{dt}$ acting on a vector $\vec v$, then the following is the case:
Any vector that is the element of a vector space can be split into its basis vectors $\vec e_i$ and its scalar components $v^i$, so that $\vec v = \sum_{i... | {
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Is there a way to see the sun's outer layers from earth outside a solar eclipse using polarization? ¿Is there a way to filter sky light using light polarization?
in https://en.wikipedia.org/wiki/Coronagraph#Invention it says:
High Altitude Observatory's Mark IV Coronagraph on top of Mauna Loa, use polarization to disti... | The SOHO satellite uses polarization analysis to study direction of coronal magnetic fields. I guess this could also be done from Earth.
| {
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How can I understand if an object stay (zero velocity) or moving with constant velocity (zero acceleration) I thought a scenario like; lets say I am looking an object and there is nothing except this object. Is there a way to understand that if this object is stay on its position or if object moving with a constant spe... | You cannot tell the difference. In fact many would say there is no difference. If you're really in a universe where there's nothing except the object like you say, there would be no difference between just sitting still and moving at a constant speed. There are no stars to see whizzing by, no atmosphere to make you fee... | {
"language": "en",
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In a circuit having one resistor why do the electrons lose all their potential energy across that resistor and not do so if there are many resistors In a simple circuit which consists of a battery and one resistor, why do electrons lose all their potential energy across this one resistor regardless of the magnitude of ... | The voltage drop across an ohmic resistor is given by Ohm's law:
$$V=IR$$
Therefore, for a set resistance the potential drop is determined by the current. So really, your question about adding a resistor becomes Why does adding a resistor to the circuit decrease the current flowing through the circuit?
For resistors in... | {
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Does throwing a penny at a train stop the train? If I stand in front of a train and throw a penny at it, the penny will bounce back at me.
For the penny to reverse its direction, at some point its velocity must go to zero. This is the point it hits the train. Two objects in contact have the same velocity, so the train ... |
Two objects in contact have the same velocity
No, not always. Take two balls and make one roll faster than the other and make them collide. They do collide with different velocities!
But, in your case, if the coin hits the train and exerts a force capable of accelerating it in the opposite direction of its movement u... | {
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Electromagnetic waves according to Maxwell If a variable Electric field creates a variable magnetic field and VICE VERSA (according to Maxwell's equations), then why don't we enter a loop where E vector and B vector keep creating one another until they reach infinite magnitudes?
| This can not happen if only by energy conservation. The Maxwell equations may seem to indicate otherwise but electric and magnetic fields do not generate one another. They are mutually dependent quantities and it is this fact that is expressed in two of the four equations.
| {
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Zero mass Kerr metric When mass in Kerr metric is put to zero we have $$ds^{2}=-dt^{2}+\frac{r^{2}+a^{2}\cos^{2}\theta}{r^{2}+a^{2}}dr^{2}+\left(r^{2}+a^{2}\cos^{2}\theta\right)d\theta^{2}+\left(r^{2}+a^{2}\right)\sin^{2}\theta d\phi^{2},$$
where $a$ is a constant. This is a flat metric. What exactly is the coordinate ... | As mentioned in @Umaxo's comment,
according to Boyer-Lindquist coordinates - Line element:
The coordinate transformation from Boyer–Lindquist coordinates
$r,\theta,\phi$ to Cartesian coordinates $x,y,z$ is given
(for $m\to 0$} by:
$$\begin{align}
x &= \sqrt{r^2+a^2}\sin\theta\cos\phi \\
y &= \sqrt{r^2+a^2}\sin\the... | {
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Definition of "specific gravity" I've learnt that a specific quantity is an extensive quantity divided by the mass. How does the definition of specific gravity fit into this scheme?
| That's one definition of the term "specific quantity"; but the qualifier "specific" is used in other ways for other terms.
For example, Wikipedia's page actually gives plenty of examples of other terms using specific that don't rely on mass.
Basically, the definition of "specific quantity" that you use would not includ... | {
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Is $X\otimes X$ not the simultaneous position operator? I had thought that $X\otimes X$ would be the operator on $H_1\otimes H_2$ to simultaneously measure the x-positions of two particles.
But there seems to be something wrong with this -- for a given eigenvalue $z$, there is an entire subspace $\mathrm{Span}\left(|x... | It's easier to think about one particle first. In a one-dimensional case, $\hat{x}$ is the position operator. When we move to three dimensions, the position operator must have vector eigenvalues, because position is vector-valued. This is achieved by using a vector operator,
$$\hat{\mathbf{x}} \equiv \begin{pmatrix} \h... | {
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Do objects besides strings, ropes, and rods have tension? Why do we define tension only in strings and ropes and rods and such? Shouldn't every object experience tension force? Like when you pull a paper from opposite sides, it gets taut, and experiences what seems like a state of tension. If every object does experien... | Tension is not defined only for strings.
However, the unique thing about ideal strings is that they can ONLY experience tension, whereas rigid bodies can experience tensions and compression. Ideal strings would collapse.
Hope this helps
| {
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If I stood next to a piece of metal heated to a million degrees, but in a perfect vacuum, would I feel hot? A friend of mine told me that if you were to stand beside plate of metal that is millions of degrees hot, inside a 100% vacuum, you would not feel its heat. Is this true? I understand the reasoning that there is ... | The black body answers are fine, but I would like to point out that no one has accounted for the amount of material present. If you had a metal gas with 100 atoms obeying a Maxwell-Boltzman distribution at the stated temperature, you would feel nothing.
| {
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What is a mass moment? I am currently reading through a document Finding Moments of Inertia from MIT, page 4, and I am a little confused as to one of the concepts that they use.
In this document, there is mention of a mass moment. Could someone possibly define this for me please? I can't find anything too clear on the ... | Mass moment is slightly different from moment of inertia. It is moment of inertia x total Mass
| {
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Trouble with Math in Physics I am a current high school student and I am very interested in physics, especially particle physics (that stuff is super cool!). Unfortunately, my school only teaches classical physics, so I have to continue my study at home. I've read several books and watched videos and online lectures on... | Now is not the time to worry about quantum mechanics. There's a reason it's not taught at high school: it's not a simple topic, and you need prerequisite mathematics (especially calculus & linear algebra) that takes time to learn.
If you must attempt it anyway then in my experience the most common QM undergraduate text... | {
"language": "en",
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Intuition of Maxwell's Equations Is there an intuitive explanation for Maxwell's equations?
I know they are axioms but is there a logical understanding of why instead of mathematical. Both forms don't explicate the scientific reasoning behind them to me.
I would appreciate a non- or minimally mathematical approach to t... | They’re not axioms: They’re experimental results.
Coulomb, Faraday, etc did a lot of experimental work to observe and systematize the underlying phenomena. Maxwell then reformulated them (though not in the modern form) and added the displacement current term which itself was later confirmed experimentally.
So the “wh... | {
"language": "en",
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"timestamp": "2023-03-29T00:00:00",
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Do air conditioner power ratings violate the 2nd law of thermodynamics? I just got a new AC rated at 6000 BTU and wanted to determine its power consumption. Some research on AC conventions quickly reveals that 6000 BTU really means 6000 BTU/h, where BTU is a measure of energy (British thermal unit). This is supposedly ... | The industry rates air conditioner power consumption based on an average which takes into account the fact that once the air conditioner has got your room to the desired temperature, the compressor (which draws most of the power required to run the unit) is cycling on and off every few minutes, so the overall duty cycl... | {
"language": "en",
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"timestamp": "2023-03-29T00:00:00",
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Why do jet engines sound louder on the ground than inside the aircraft? Everyone is familiar with the whirring sound of jet engines when seeing an aircraft taking off from a nearby airport. It is distinctly very loud on the ground and one can hear it even when the airplane is miles away.
Although one can hear a 'white... | There is a howling 500 - 600 mph gale blowing outside the aircraft, the like of which you have never experienced on the ground, and this carries away most of the sound before it can enter the fuselage. Some sound is also reflected by the fuselage. A few passenger aircraft like the Caravelle, VC10 and Tristar have engin... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/492353",
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"source": "stackexchange",
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Understanding Shankar's standard deviation: Is $\langle\psi|\Omega|\psi\rangle$ shorthand for $\langle\psi|\Omega|\psi\rangle I$? On page 128 of Shankar's book, he defines the standard deviation as follows:
$$\Delta\Omega=[\langle\psi|(\Omega-\langle\psi|\Omega|\psi\rangle)^2|\psi\rangle]^{\frac{1}{2}} $$
Now, this equ... | So if you want to explicitly combine $(\Omega-\langle\psi|\Omega|\psi\rangle)^2$ into a single operator without actually using it on a state, then you would need to put the identity operator in for the math to make sense.
However, as pointed out in the comments, multiplying a state by a scalar is a perfectly valid ope... | {
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How can we see the microstructure of steel samples at room temperature? When we intend to see the microstructure of a steel sample at a temperature say 950 $^\circ$C they say we quench it in order to freeze the microstructure. However, if we quench it are we not going to have Martensite formation? Again if we anneal it... | By choosing the correct quench rate for the alloy at hand, you will indeed freeze into the metal the microstructure it had at the temperature at which you began the quench. Different quench rates will yield different microstructures, with the slowest quench rate producing room temperature microstructure.
In all cases,... | {
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Momentum operator in QM - scalar or vector? The momentum operator for one spatial dimension is $-i \hbar\frac{\mathrm d}{\mathrm dx}$ (which isn't a vector operator) but for 3 spatial dimensions is $-i\hbar\nabla$ which is a vector operator. So is it a vector or a scalar operator?
| $-i\hbar \frac{d}{dx}$, a scalar, is the position space representation of $\hat{p}_x$, the $x$ component of the momentum operator, a scalar. The momentum operator itself, $\hat{\textbf{p}}$, is a vector operator. The position space representation of $\hat{\textbf{p}}$ would be $-i\hbar \nabla$, a vector.
Again, the mo... | {
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Delayed eraser experiment (Kim experiment) Will I receive an interference pattern on D0 detector https://en.wikipedia.org/wiki/Delayed-choice_quantum_eraser#The_experiment_of_Kim_et_al._(1999) if D1, D2, D3, D4 exist in the set up of the experiment, but they are thousands of light years far? Simply, to set up the expe... | The interference patterns in the delayed-choice quantum eraser experiment are only ever observed via post-selection: using the notation from Wikipedia, the $D_0$ detector will detect a formless blob, which will only resolve into complementary interference patterns once you post-select on detections by $D_1$ and $D_2$ (... | {
"language": "en",
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Is there 100% pure white? Is it possible to have an object 100% pure white without sky blue or sun color tinting the pure whiteness of the photons reflecting/deflecting off an object? Are there any lights that can produce pure white photons (RGB)? And can we see that the color is white or is our eyes going to trick us ... | I would think that a light source which has an emission spectre $f(\omega)$ that looks something like
$$
f(\omega)=\begin{cases}
\infty & \text{if infrared} < \omega < \text{ultraviolet}\\ 0 & \text{else}
\end{cases}
$$
could be considered pure white, but then, as others have pointed out, "pure white" has to be defined... | {
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Is the only absolute difference between types of light frequency? Probably a bad question but for some reason, it seems too simple in my head that anyone at home could theoretically create anything from radio waves to gamma waves by generating electrical signals at different frequencies.
Say I had a electronic frequen... | Your question is a little confused at the end, but I think the answer to what you're trying to ask is "yes". Names like infrared and gamma apply here to ranges that have been divided up for historical and practical reasons, but they do not denote something other then an electromagnetic wave within certain frequency ra... | {
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In QFT, are forces made out of multiple fields? I’ve been reading about 1,5 books about quantum physics and I’ve also watched a few YouTube videos. In one book, I learnt that there are fields, such as the electromagnetic field, which carries forces between particles (vibrations in the field) via virtual particles. But ... | There is no clear notion of what exactly a "force" is in quantum field theory (obligatory xkcd).
Every field has particles associated with it, and we tend to associate those particles/fields with "forces" whose interactions with the rest are such that they have a major influence on their behaviour even when they are n... | {
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What is the difference between position, displacement, and distance traveled? Suppose the question is somewhat like this:
If $v=8-4t$ and the position at time $t= 0\ \rm s$ is $2\ \rm m$, find the distance traveled, displacement, and final position at $t=3\ \rm s$
Since $\text dx/\text dt=v=8-4t$, ... |
So the 8m is displacement or distance?
The 8m is the position of the particle. The displacement is 6 m.
When you integrated the velocity function to get position you included a constant of integration (2 m) to account for the initial position of the particle, that is, its position at time t=0, which is given as 2 me... | {
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Circuit - solve Kirchhoff's laws with determinant? Here is an exercise from my textbook.
]1
At first I solve it by using Kirchhoff's laws directly and using complex impendance:
$$U_{in}=\frac{1}{Cs}(i_1-i_2)+i_1R_1$$
$$0=R_2i_2+\frac{1}{Cs}i_2+\frac{1}{Cs}(i_2-i_1)$$
By solving above equations, both $I_1$ and $I_2$ bec... | As has been pointed out, $\Delta$ is the determinant of the nodal admittance matrix $\mathbb{Y}$. It's also clear that $\mathbf{V}$ is the vector of node voltages. What wasn't clear to me is that $\mathbf{I}$ is the vector of injected currents rather than the currents the OP has drawn in red.
That is, $I_1$ is the (ph... | {
"language": "en",
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What are estimated magnetic properties of liquid metallic hydrogen? I understand that liquid metallic hydrogen isn't easy to produce, or keep it stable on Earth, but can be liquid metallic hydrogen magnetised? Does it have magnetic properties at all?
| There is no reason to expect metallic hydrogen to be any more magnetic than say metallic sodium, that is, patamagnetic. One caveat is that at sufficiently high pressure and low temperature it may become superconducting.
Apparently, rotating liquid sodium will generate a magnetic field as this experiment aims to prove :... | {
"language": "en",
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Does stacking two magnets together increase the magnetic strength? Just wondering if adding two (or more) identical magnets together increases their magnetic strength (in Tesla) as I am doing a physics write-up on the Lorentz force (Fleming's left-hand rule) as I tried stacking magnets together but found that the force... | Assuming that the field from one magnet does not effect the magnetization of the other, then the resultant field at each point will be the vector sum of the two separate fields. That in tern depends on the position and orientation of the two (as described by Andrew Steane).
| {
"language": "en",
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Motion between two particles in a relative manner Suppose a particle A is travelling in east direction with velocity of x m/s and another particle B is travelling with velocity y m/s in the west direction. Why does the the particle B appears to move towards A with a velocity of x+y and not just y m/s?
| The top diagram shows the velocities in the lab frame. Particle $A$ is moving east at speed $x$ and particle $B$ is moving west at speed $y$. I'm taking the east direction to be positive, so the velocity of $A$ is positive and the velocity of $B$ is negative.
To find the velocity of $B$ relative to $A$ we have to tran... | {
"language": "en",
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A best definition of proper acceleration In this link of Wikipedia https://en.wikipedia.org/wiki/Hyperbolic_motion_(relativity) there is a definition of proper acceleration:
The proper acceleration to a particle is defined as the acceleration that a particle "feels" while accelerating from one inertial reference syste... | As far as I know, the definition of the proper acceleration was the derivative of the proper velocity with respect to proper time, $$\vec{\alpha}=\frac{\mathrm{d} \vec{w}}{\mathrm{d} \tau}=\frac{\mathrm{d}^2 \vec{r}}{\mathrm{d} \tau^2}.$$ It is the spatial part of the four acceleration, and in Wikipedia in English it s... | {
"language": "en",
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Why is "a very silent room" louder than "leaf noise" / "breathing noise"? I recently was at night in my bed room and used the Schallmessung Android App (on a Samsung S7). It showed 20 dB while laying on some furniture. I could not hear anything; to me, the room was completely silent.
Now I looked at some examples of no... | They are most likely talking about just the "leaf noise" by itself. If you were in your silent room with additional "leaf noise" then your app would obviously record a higher decibel reading (assuming it is sensitive enough).
| {
"language": "en",
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Boundary condition for partial reflection I want to solve a wave equation for the wave $\psi(x,t)$.
One boundary is moving, therefore I impose the velocity
$$v(x=0)=v_a\cos(\omega t)$$
the other boundary is fixed, but reflecting. If the reflection is total the proper boundary condition is
$$ \frac{\partial \psi}{\parti... | Consider a boundary condition of the form
$$
\alpha \psi + \beta \frac{\partial \psi}{\partial x} + \gamma \frac{\partial \psi}{\partial t} =0
$$
on the boundary, where $\alpha$, $\beta$, and $\gamma$ are real coefficients. Standard Dirichlet boundary conditions correspond to $\beta = \gamma = 0, \alpha \neq 0$, while... | {
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Can the flow be irrotational if the viscous forces act on fluid? I tried to answer the question only using the definitions and the Navier-Stokes equation:
$$\rho \frac{Dv}{Dt} = -\nabla P +\rho g -\mu[\nabla \times(\nabla \times v)] $$
In my opinion if the vorticity is zero, then the fluid is irrotational, regardless ... | First, unlike the other answers, I believe your equations are correct thanks to the identity
$$\nabla \times \nabla \times \mathbf v = \nabla (\nabla \cdot \mathbf v)-\nabla^2 \mathbf v$$
Irrotational flow means $\nabla \times \mathbf v=0$ so in fact as you note correctly Navier-Stokes predicts viscosity plays no role ... | {
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Can a macrostate of a system be defined upon distributional quantities of the energies? Is it valid to define for a system, a macrostate based upon statistical quantities of the particle energy distributions? Eg. that a macrostate is based upon the variance of the kinetic energies of the particles? Would another potent... | Mathematically, the answer is yes. Whether this makes physical sense is a different story.
Let's do the math first. We have a collection of particles $i=1,2,\cdots$ with energies $E_i$ and all we know is their variance. By the maximum entropy principle we seek the probability distribution $p_i$ that maximizes the entr... | {
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Huygens-principle Huygens principle states that every point on the wave front acts as a source. If it is true, then why can't a single source (let's say a bulb) illuminate a whole big room? Why is it dark after some distance from the bulb? According to him it should continue to infinite.
Where am I wrong?
|
Why is it dark after some distance from the bulb? According to him it
should continue to infinite.
That's a great observation! I must have seen Huygen 100 times and never thought of this.
The basic answer is that Huygen's principle is mostly concerning the phase of the waves, in a way. He's talking about how the wa... | {
"language": "en",
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Normalization constant of a planar wave As we know for the plane waves ( $ae^{i k x}+b e^{-i k x}$), the normalization constant can be easily obtained from the integral $\int^{x_{2}}_{x_{1}}\psi^{*}\psi dx=1$ by the relation $|a|^{2}+|b|^{2}=1$. But what happens if the parameter $k$ is imaginary, i.e. $k=i \kappa$ wher... | Using your parameterization, the wave is $ae^{-\kappa x}+be^{\kappa x}$. Note that this particular wavefunction blows up at $x=+\infty,-\infty$; so that it cannot be normalized unless we impose $a=0$ for $x<0$ and $b=0$ for $x>0$. If you do this, you can simply carry out an integration to find out the relation between... | {
"language": "en",
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Are the electrons' orbitals the same for all atoms? Are the electronic orbitals of an atom always quantified in the same way (i.e. the same energy required to reach the next level), or does each atom have its own values for each level?
If the quantification is universal, then the creation of photons (due to the deexci... | The diagram you posted shows the electron energy levels for the hydrogen atom only. Other atoms will have different energy levels. Also note that the hydrogen atom itself has an infinite amount of energy levels which the diagram does not really show.
This information is very useful. The energy levels for each atom are ... | {
"language": "en",
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Why are you doing no work when carrying a body through a horizontal distance? Work done on an object is equal to $$FD\cos(\mathrm{angle}).$$
So, naturally, if you lift a book from the floor on top of the table you do work on it since you are applying a force through a distance.
However, I often see the example of carr... | Work-energy theorem would be quite helpful to you.
$$dW_{net}=dK_{system}$$
As speed is constant,$$dK_{system}=0$$
$$dW_{hand}+dW_{resistance}=0$$
It doesn't imply that work done by your hand is zero but the net work done by your hand as well as resistive forces is zero.
| {
"language": "en",
"url": "https://physics.stackexchange.com/questions/496644",
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Entropy vs energy graphs How to interpret temperature from entropy vs energy graphs?..
And what do the different behaviour of the graph signify and how should I interpret them?(provided volume of the system and number of particles are kept constant)
| As pointed out in the comments (or in any good text book), the temperature is given by
$$\frac1T=\left(\frac{\partial S}{\partial U}\right)_{V,N}$$
where $T$ is the temperature, $S$ is the entropy, $U$ is the internal energy, $V$ is the volume, and $N$ is the number of particles.
You stated the graphs already assume co... | {
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Is kinetic energy always conserved in an elastic collision/impact? While working out through some problems I encountered this problem :
A ball moving with a velocity $v$ hits a massive wall moving towards the ball with a velocity $u$. An elastic impact lasts for a time $\Delta t$
Now I have to answer whether the Kin... | While @Rumplestillskin has basically answered your question, here is an intuitive explanation. The total kinetic energy of the wall and the ball together is preserved after the ball bounces off. Now, since the wall was moving towards the ball, however small the ball is, it had slowed the wall a bit. So part of wall's ... | {
"language": "en",
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Complex Scalar Fields and Killing Vectors In a stationary and axisymmetric spacetime, there are two Killing vectors, say $\zeta^\mu$ and $\xi^\mu$, one timelike and one space like.
I understand that for a real scalar field, $\phi$, that obeys the symmetry of this spacetime one can say
$$\zeta^\mu \nabla_\mu \phi = \xi... | You're right to conclude $\nabla_\mu\phi_j\nabla^\mu\phi_j\ge0$ for $j\in\{1,\,2\}$, so $\nabla_\mu\Phi^\ast\nabla^\mu\Phi=\sum_{j=1}^2\nabla_\mu\phi_j\nabla^\mu\phi_j\ge0$.
| {
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Total force on upper block in two block system If a block $m$ is placed on another block $M$ and a force $F$ is applied on bolck $M$. Then how many forces are acting on block $m$.(Friction is non zero)
The image is taken from this site.
Is pseudo force acting on block $m$ or not?
| No pseudo-force ever acts on anything. A pseudo-force is - as the name indicates - imaginary and non-existing. It is just a "feeling" or "illusion" of a force. So don't worry about pseudo-forces; just stick to inertial reference frames (references that aren't accelerating), and you never have to worry about them.
In yo... | {
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How does the introduction of the charm quark suppress FCNC? I did some reading on the GIM mechanism today, and simply fail to understand how it works. I understand how the CKM-matrix can be used to do the basic calculation of the probability of, say, observing an up quark after a strange quark's decay over the weak int... | Well, the two interfering amplitude diagrams do not quite cancel each other out: they almost cancel each other out. That is to say in the notional limit that the mass of the u and the mass of the c were identical, the two diagrams would be identical except for the minus sign of the Cabbibo (CKM for 3 generations) matri... | {
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Symmetry reason why magnetic dipole transitions are suppressed In the theory of light-matter interaction, electric dipole transitions between two atomic states of same parity are forbidden. This is because the Hamiltonian conserves parity. Is there a symmetry reason why magnetic dipole transitions happen but their ampl... | This comes from the heirarchy of length scales in the atomic problem. Very briefly, the EM-atom transition matrix element has a term like
$$\int e^{i\vec{k} \cdot \vec{x} }\psi'(\vec{x})\left[\vec{A_0} \cdot (-i\hbar \vec{\nabla} )\right]\psi(\vec{x}) d^3x $$
A standard approximation to this is the dipole approximation... | {
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Why do all fields in a QFT transform like *irreducible* representations of some group? Emphasis is on the irreducible. I get what's special about them. But is there some principle that I'm missing, that says it can only be irreducible representations? Or is it just 'more beautiful' and usually the first thing people tr... | This is only semantics. A reducible representation $\mathbf R$ of the symmetry group can be decomposed into a direct sum $\mathbf R_1 \oplus \cdots \oplus \mathbf R_N$ of irreducible representations. A field that transforms as $\mathbf R$ is the same thing as $N$ fields, which transform as $\mathbf R_1, \dots, \mathbf ... | {
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"answer_id": 2
} |
Basic band structure reading In band diagrams (e.g. GaAs below), symmetry points are sometimes indicated with a numerical index. I first thought it was the band index in the Bloch function (so two electrons with the same wave vector but different band index would have different energies), but the same point appears at ... | Those are the labels of irreducible representations corresponding to the wave-function on that symmetry point, derived via group theory. They classify how wave-function at that symmetry point evolves under crystal symmetry operations, similar as the classification of odd and even function $f(x)$ by whether it changes s... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/498298",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "1",
"answer_count": 1,
"answer_id": 0
} |
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