Q stringlengths 18 13.7k | A stringlengths 1 16.1k | meta dict |
|---|---|---|
Is it possible to "see" atoms? As per my knowledge, atoms are small beyond our imaginations. But there is an image on Wikipedia that shows silicon atoms observed at the surface of silicon carbide crystals.
The image:
How can we see these distinct atoms if they are so small?
|
This is an image of a Sc2O3 nanocrystal obtained from an abberation corrected scanning transmission electron microscope.
The left image is recorded by measuring only electrons that have been bent/deflected by passing through the material (in this case we dont see the oxygen atoms very well)
The image on the right meas... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/168713",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "65",
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What are the quantum numbers of Majorana neutrinos? I have a question about majorana neutrinos.
Majorana particles are particles that are their own antiparticle.
From this I would argue that they need to have all quantum numbers equal to zero. My question is: what about the weak isospin? This cannot be zero, as neutrin... | You say about Majorana fermions:
"From this I would argue that they need to have all quantum numbers equal to zero."
which is not true. Charge conjugation is defined on Dirac spinors as $\psi^c := \mathrm{i}\gamma^0\gamma^2\bar\psi^T$. Being Majorana means $\psi^c = \psi$. While this would imply the spinor has zero e... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/168810",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "3",
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Resonant vs. Non-resonant Raman What does it mean to say that the conventional Raman effect is non-resonant? And, how/why does resonant Raman give a stronger signal than the non-resonant type?
| The normal nonresonant Raman scattering happens when a photon interacts with a molecule; the molecule absorbs the photon momentarily and re-emits it with slightly less energy.
In an energy diagram, that looks like this.
The frequency of the incoming photon is $\omega_i$, and the frequency of the scattered photon is $\... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/169044",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "1",
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Is there an infinite amount of wavelengths of light? Is the EM spectrum continuous? The electromagnetic spectrum is a continuum of wavelengths of light, and we have labels for some ranges of these and numerical measurements for many.
Question: Is the EM spectrum continuous such that between two given wavelengths (e.g. ... | Formally there are an infinite number of different wavelenghts. However, any given physical system can only be found in a finite number of distinct physical states. To create a light source with a wavelength $\lambda$ that is well defined up to some resolution $\delta\lambda$, requires observing it within a system of ... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/169209",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "40",
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Approximations of the kind $x \ll y$ I have an expression for a force due to charged particle given as
$$F=\frac{kQq}{2L}\left(\frac{1}{\sqrt{R^2+(H+L)^2}}-\frac{1}{\sqrt{R^2+(H-L)^2}}\right) \tag{1}$$ where $R$, $L$ and $H$ are distance quantities.
Now I want to check what happens when:
*
*$H\gg R,L$
*$R,H\ll L$
... | For $H\gg R,L$ And for $L\gg R,H$ you get pretty much the same thing.
First off, $(H+L)^2\sim H^2$ and the same goes for $(H-L)^2$. That means that $(H+L)^2+R^2\approx (H+L)^2$. However, $(H+L)\not\approx H$, which means that $\sqrt{R^2+(H+L)^2}\approx H+L$. This makes the first approximation have $\frac{1}{H+L}-\frac{... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/169371",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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100°C = 100 K =? I'm in first year. Our class is in lesson " Heat and Thermodynamics". While solving a numerical problem of a reversible engine he told us that 100 degree Celsius is equal to 100 kelvin. I inquired but could not get satisfactory answer. Pleas help me understand it.
Here is the numerical, please consider... | The important part is that it works "between two temperatures whose difference is 100°C". Celsius and Kelvin are not the same, but their degrees measure the same.
You can see that by direct substitution $T(ºC)=T(K)+273.15$
therefore
$T_2(ºC)-T_1(ºC)=T_2(K)+273.15 -(T_1(K)+273.15)=T_2(K)-T_1(K)$
| {
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What do spacelike, timelike and lightlike spacetime interval really mean? Suppose we have two events $(x_1,y_1,z_1,t_1)$ and $(x_2,y_2,z_2,t_2)$. Then we can define
$$\Delta s^2 = -(c\Delta t)^2 + \Delta x^2 + \Delta y^2 + \Delta z^2,$$
which is called the spacetime interval. The first event occurs at the point with co... | Spacelike separation means that there exists a reference frame where the two events occur simultaneously, but in different places. Timelike separation means that there exists a reference frame where the two events occur at the same place, but at different times. Lightlike means that, well, light could travel between th... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/169631",
"timestamp": "2023-03-29T00:00:00",
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How can you have odd nuclear spin angular momentum but positive parity or vice versa? How does it happen that you can get states like $J^\pi=3^+$ or $J^\pi=2^-$? I think this could be because $\pi=(-1)^l$ so you could have an even state in $l$ but the $J=l+s$ sum could be an odd number?
| Your guess is essentially correct.
If you want to think about the nucleus in a shell-model sort of way, you can say that
the nuclear spin $J$ is the vector sum of the spins $S_i$ and orbital angular momenta $L_i$ of all the nucleons in the nucleus.
In the deuteron, for instance, the nucleus must be antisymmetric unde... | {
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What is the mass of a sphere? A solid sphere of mass M is rotating along an axis.
We can consider it as a collection of large number of point masses, every point mass is moving with respect to center of mass with velocity which depends on its radius from rotating axis.
Then, according to relativity, the mass of every ... | The mass of a moving body increases only for the observer in a rest frame, not for the moving body, as it feels itself as being in rest.
The rotating sphere is a different story, there are other forces and the point on moving sphere feels them, you cannot play a simple paradox game here. The situation is more difficult... | {
"language": "en",
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Why are stars white? That is may be an easy question, but I am not a professional. The Sun is a star, and when I look at the Sun it is usually yellow. Why are stars in the sky at night white?
I suppose it could be due to their distance. What is the explanation?
| Our sun is actually white. Sun seen from space. It's just that when the sun rays enter the earth, our atmosphere scatters the white light resulting in different colors.
The reason why the Sun appears to be white sometimes is usually because it's directly overhead. Then the rays coming from the sun have to travel the le... | {
"language": "en",
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What does it mean for a state to have a negative partial decay width? I don't understand what it means when a particular decay mode has a negative partial decay width. I'm guessing the total decay width for a particular system must always be positive (now that wouldn't make much sense to me), but I'm not quite sure ho... | The negative sign for the partial decay widths denote the sign of the corresponding reduced width amplitude in the R-Matrix formalism, which is what the author of this paper (and everybody else analyzing cross sections of low-energy nuclear reactions) is using to do his analyses. He's using the R-Matrix code SAMMY, whi... | {
"language": "en",
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If I bend a rod, will its moment of inertia change? In the first picture, there is a homogeneous metal rod of length $2L$ and mass $M$. If it rotates around a normal axis passing by $O$ (which is the center of gravity), then its moment of inertia is:
$$I_{1}=\frac{M(2L)^2}{12} = \frac{ML^2}{3}.$$
After bending the bar ... | The answer depends on the direction of the axis of rotation.
If the axis is normal to the plane, then you have the same amount of material the same distance from the axis of rotation as before - and thus the moment of inertia about that axis would be unchanged.
However, if the axis of rotation you consider is in the pl... | {
"language": "en",
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What does it mean to "uplift" a supergravity solution to higher dimensions? What does it mean to "uplift" a supergravity solution to higher dimensions? This is a common term used in the literature but I cannot understand it. A very common example is "uplifting d-dimensional solution to 11-dimensional supergravity or M-... | An uplift is the opposite of a dimensional reduction. Take for example the relation between (the low-energy limit of) M-theory and type IIA supergravity: the former is eleven-dimensional, while the latter lives in ten dimensions. If you find a solution of M-theory, you can get its equivalent in type IIA by Kaluza-Klein... | {
"language": "en",
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Is there a difference in the energy output of a nuclear fission reaction as opposed to fusion? For example, if I split a Helium atom will I get the same amount of energy as when I fuse Hydrogen into Helium? If there is a difference, what will be the difference (in general not according to Helium/Hydrogen), and why?
| Splitting a helium atom requires energy, whereas fusing two deuterium atoms into helium liberates energy.
As it can be seen from this graph:
the energies you were talking about will be the same (since they involve the same number of nucleons), but the sign will be different. Note that for small nuclei, energy is relea... | {
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Do photons with a frequency of less than 1 Hz exist? A photon with a frequency of less than 1 Hz would have an energy below
$$
E = h\nu < 6.626×10^{−34} \;\rm J
$$
which would be less than the value of Planck's constant. Do photons with such a low energy exist and how could they be detected? Or does Planck's constant ... | The frequency $\nu$ is in seconds$^{-1}$, which is purely human-based unit having a relation to rotation of the Earth. Thus no reason why 1 Hz was a limit. Planck $h$ value is also not massless unit and it's value has relation to SI system.
Existence: while I don't see a principal reason for non-existence of such a pho... | {
"language": "en",
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How to heat water to 80°C? I'm trying to figure out an easy water to get 80°c to consistently make the perfect cup of coffee. Let's assume room temperature water is 22°c.
What is the ratio of boiling water to room temp water to achieve 80°? What is the formula with room temp being variable?
| Your post seems an awful lot like a homework question, so you should probably tag it as a homework-like question.
If by "cup" you mean 250 mL on the dot, then we can say that the ratio of boiling water (100 Celsius) to room temperature water (22 Celsius) to achieve 80 degrees is
$$ \frac {(T_1)(V_1) + (T_2)(V_2)}{V_1 ... | {
"language": "en",
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Dissipated Energy from Falling Object using Lagrangian
A plate of mass $M$ moves horizontally with initial speed $v$ on a frictionless
table. An object of mass $m$ is dropped vertically onto it from the height
$h$ and smashes. How much energy is dissipated in this process?
I have been taught E-L formulas, but don... | You are overthinking, it looks like a simple inelastic collision.
Before:
Vertical (potential energy):
$E_{plate} = 0$, $E_{object} = mgh$
Horizontal (kinetic energy):
$E_{plate} = \frac{1}{2}Mv^2$, $E_{ball} = 0$
After:
Vertical:
The object smashes, not bounces, so its entire potential energy dissipates
Horizontal:
Th... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/170989",
"timestamp": "2023-03-29T00:00:00",
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Chern-Simons action in 4 dimensions I can not understand why we do not have a Chern-Simons action for four or even forms?
And why is it not a good theory for (3+1) dim?
| *
*By definition, the Lagrangian form $\mathbb{L}$ of Chern-Simons (CS) theory (wrt. a Lie algebra valued one-form gauge field $A$) is a CS form, i.e. the CS action reads $$S[A]~=~\int_M\mathbb{L}.$$ The exterior derivative $\mathrm{d}\mathbb{L}$ of a CS form is (also by definition) the Lie algebra trace of a polynom... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/171087",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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Test whether a glass prevents you from getting your Vitamin D portion? I work in an office with glass, which I believe filters the UV radiation of the sunlight.
Is it possible to test if exposure to the light coming through the glass will supply Vitamin D for me as a mammal?
| The wavelengths that stimulate vitamin D production are between 280nm and 320nm, which is called UVB. You would need to use a detector capable of measuring light in this wavelength.
However there is no need, because normal windows are made from soda-lime glass and this transmits no wavelengths shorter than about 350nm.... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/171170",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "7",
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Hamiltonian from a Lagrangian with constraints? Let's say I have the Lagrangian:
$$L=T-V.$$
Along with the constraint that $$f\equiv f(\vec q,t)=0.$$ We can then write:
$$L'=T-V+\lambda f. $$
What is my Hamiltonian now? Is it
$$H'=\dot q_i p_i -L'~?$$
Or something different? I have found at least one example where usin... | The Hamiltonian is defined by
$$ H = \sum_{i=1}^n \left( \frac{\partial L}{\partial \dot q_i} \dot q_i \right) - L $$
So in your case: $ H' = H - \lambda f $
| {
"language": "en",
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"source": "stackexchange",
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Can someone clarify what should and should not be an operator in my verification of the 1D solution to the SE for a free particle? I just worked out the 1D free particle solution to the Schrödinger equation.
My wave function was
\begin{equation}
\psi(x,t) = Ae^{i(px-Et)/\hbar}
\end{equation}
So I plugged this into ... | Your solution is right. What you get verifying it is that $\psi$ is also an eigenfunction of the momentum operator, which means
$$\hat p\psi=p\psi,$$
where $\hat p=-i\hbar\nabla$ is momentum operator, and $p$ is its eigenvalue.
Now, applying $\hat p$ twice and dividing by $2m$, you can get
$$\frac1{2m}\hat p^2\psi=\fra... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/171341",
"timestamp": "2023-03-29T00:00:00",
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Why most of physics is somehow related to light? It seems that for the past 200 years, every physicist is concerned about light. For example : Newton's particle model, Young experiment, Photo-Electrict effect and Einstein's formula, Special Relativity (constant speed of light), Bohr's atom model (using Photons to emit ... | Instead of the word light it would be better to use the word electromagnetism. Newton and Young were fascinated about the decomposition of white light into it colors and about fringes behind edges. Since Maxwell it was obvious that light was only a small part of the electromagnetic spectrum. Later were discovered the w... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/171437",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "4",
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Microscopic definition of dynamic pressure of fluids So we have a moving fluid and we know from Bernouli's equation that there is a term called dynamic pressure(not to be confused with the hydrostatic pressure of the fluid).
So,what exactly is it and how can it be explained microscopically?
Note:do not involve relativi... | Dynamic pressure of fluids is the kinetic energy per unit volume of the fluid. Its unit are the same as pressure, and Bernoulli's equation,
$0.5\rho v^2 + \rho gy + p = constant$
can be written as
$P_{dynamic} + \psi_{gravity} + P = constant$, where $P_{dynamic} = 0.5\rho v^2$ and $\psi_{gravity}$ is the force po... | {
"language": "en",
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relationship of number of standing waves with Temperature? If we have let us say fixed air column of length 'L', in a open-closed column problem, lamba is equal to 4*L/(2n-1).
n = number of nodes / anti nodes in air column
How does 'n' changes with respect to the temperature? Is the "number of nodes / anti nodes" at r... | The wavelength is fixed by the dimensional length of the tube, but since wavelength is equal to the speed of sound divided by the wave frequency, temperature will affect the frequency because temperature determines the speed of sound.
| {
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"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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Can I blow soap bubbles (of air) inside a vacuum chamber? When I blow soap bubbles from a liquid dish soap mixed with distilled water at atmospheric pressure at ground level both internal and external air pressure nullify and the tension of the bubbles holds, can soap bubbles be formed inside a vacuum chamber with all ... | Unfortunately, you can not make a bubble with water and soap in a high vacuum.
as you can see in this phase diagram of pure water, if the pressure is lower than 611.657 Pa, liquid water will not exist no matter what the temperature is.
Maybe you should try some other material, but not H2O.
| {
"language": "en",
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"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "1",
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What's my $\mathrm dM$? Gravitational Potential inside a circle of mass
I'm trying to find the gravitational potential for an arbitrary point within a ring of uniform mass density. The point is constrained to be in the same plane as the ring.
So we start with:
$$\Phi=\int G\frac{\mathrm dM}{r}$$
Let's assume that the... | I think the following diagram should help:
It is perfectly legal (and makes the math simpler) to use the center of the circle as the "center of integration", as long as you use the right value of $d$ for the distance to the mass element $dM$.
So your equation for the potential should use $d=\sqrt{a^2+r^2-2ar\cos\phi}$... | {
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Magnetic field in a wire with constant current
I assume I have a wire parellel to the $z$ axis and with radius $R$. A constant current $I$ flows through it in the $z$ direction. I want to know the magnetic field inside the wire at distance $r<R$.
In the figure, the pink dots represent the flow of electrons in the z di... | Ampere's Law. That magnetic field that you calculated depends on $r$ and the enclosed current is $j*ds$ where $j$ is the current density and $ds$ is surface differential. So if you want to know the magnetic field outside of a wire you should take a $r>R$.
| {
"language": "en",
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"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "4",
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Could I break the sound barrier using circular motion? (And potentially create a sonic boom?) Ok, Lets say I get out my household vaccum cleaner, the typical RPM for a dyson vaccum cleaner reachers 104K RPM, Or 1.733K RPS. In theory, this disc would be travelling with a time period of 0.00057692307 seconds, If we take ... | It's very possible to spin something fast enough to create a sonic boom, but engineers usually try very hard to avoid it.
Several aircraft have been built, on purpose, with supersonic propellers. One production aircraft is the Tupolev TU-95 Bear long-range bomber. Eight counter-rotating 4-blade props turn fast enough s... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/172451",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "26",
"answer_count": 5,
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Binomial expansion of non-commutative operators I would like to determine the general expansion of
$$(\hat{A}+\hat{B})^n,$$
where $[\hat{A},\hat{B}]\neq 0$, i.e. $\hat{A}$ and $\hat{B}$ are two generally non-commutative operators. How could I express this in terms of summations of the products of $\hat{A}$ and $\hat{B... | There is a nice formula that provides the result in terms of the binomial expansion plus terms related to the noncommutative algebra
https://arxiv.org/abs/1707.03861
| {
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"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "15",
"answer_count": 4,
"answer_id": 3
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Feynman Diagram in QED non-relativistic limit I am following Peskin & Schroeder to read a Feynman diagram. But in this given image, they used the non-relativistic limit to write the incoming fermion gamma mu product. How did he derive the bottom formula? Any explanations in detail?
|
How did he get it?
How did he get what? Which part of the calculation it is that's confusing you. You have listed multiple equalities, which one is at issue?
Eq 3.55 of the pdf online version of Peskin and Schroder shows that:
$$
u^\dagger u=2E_p\xi^\dagger \xi
$$
and since
$$
\gamma_0^2=1
$$
we know that
$$
\bar u\... | {
"language": "en",
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"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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movement of particles in electric field I am confused about a homework problem. Let's assume we have two electrically charged particles of which we know the charge and mass respectively. Let's say that at first they are fixed at some distance $r_1$ and then released simultaneously. I want to find their velocities at di... | If one particle is fixed, some force is keeping it fixed, and in the presence of an external force, conservation of momentum doesn't apply. Your second equation is then $v_1 = 0$ (assuming particle #1 is the one that is fixed), not $m_1 v_1 + m_2 v_2 = 0$.
| {
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"source": "stackexchange",
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Does the electric force on a charged particle in a uniform electric field increase? If I have a proton in a uniform field between two parallel oppositely charged plates and the proton accelerates, the electric force acting on it stays constant seeing it is a uniform field and as a result the acceleration of the particl... | Your brain/mind might be processing the information in the wrong way. As field is uniform, force remains constant and acceleration remains constant. You see, the acceleration remains constant, but velocity doesn't remain constant, as the time to which your proton is accelerated increases, your proton's velocity also in... | {
"language": "en",
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"timestamp": "2023-03-29T00:00:00",
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If the Earth is a good conductor of electricity, why don't people get electrocuted every time they touch the Earth? Since the Earth is a good conductor of electricity, is it safe to assume that any charge that flows down to the Earth must be redistributed into the Earth in and along all directions?
Does this also mean ... | Firstly we are not the best conductors, so current might be having a relatively hard time getting through us.
But I believe the real reason is that you also need a high potential difference in order to get current flowing through you.
Like lightning which needs a huge potential difference between the clouds and earth (... | {
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Experimental evidence for Z boson coupling to right handed fermions I do have a question about electro-weak interactions.
I know the Z boson is an admixture of two fields, one that couples only to the left-handed part of the fermions (the neutral field introduced to make SU(2) a local symmetry) and one that couples to ... | In addition to TwoBs' comments, in the 90s, there had been many collisions at SLAC (USA) with polarized electron/positron beams of the SLC collider running at the $Z$ pole. Therefore, the right handed component of the electroweak interaction has been extensively tested.
See the wikipage:
http://en.wikipedia.org/wiki/SL... | {
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Error calculation in parallel resistances This is the question:
There are two resistors with resistance values $R_1=100\pm3$ ohm and $R_2=200\pm4$ ohm. Find the equivalent resistance of parallel combination.
According to what I've learnt, in any expression of multiplication or division, the percentage errors of each ... | My calculation dR/R = dR1/R1 + dR2/R2 -dR1/(R1+R2) -dR2/(R1+R2)
(Come from the derivative of R = (R1R2)/(R1+R2))
Do manipulation dR/R = [dR1/R1 -dR1/(R1+R2)] + [dR2/R2 -dR2/(R1+R2)]
dR/R = (dR1/R1)[R2/(R1+R2)] + (dR2/R2)[R1/(R1+R2)]
dR/R = (3/100)[200/300]+(4/200)[100/300] = 0.0267
dR=0.0267R= 0.0267(66.7) = 1.78
| {
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$\nabla^{\mu}\nabla_{\mu}$ in general relativity I am trying to work out $\square=\nabla^{\mu}\nabla_{\mu}$ in the metric
$
ds^{2}=-A(r)dt^{2}+B(r)^{-1}dr^{2}+r^{2}d\Omega^{2}
$$
My work:
when applying $\square$ to a scalar $\phi$, then
$
\square\phi=\nabla^{\mu}\nabla_{\nu}\phi=\nabla^{\mu}\partial_{\mu}\phi=g^{\mu\n... | I'll prove a formula that is probably easier to use for this.
\begin{equation}
\begin{split}
\frac{1}{\sqrt{-g}} \partial_\mu \left( \sqrt{-g} g^{\mu\nu} \partial_\nu \phi \right) &= \frac{1}{\sqrt{-g}} \partial_\mu \left( \sqrt{-g} \right) g^{\mu\nu} \partial_\nu \phi + \partial_\mu \left( g^{\mu\nu} \partial_\nu ... | {
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Waves on a guitar string Can there be traveling waves on a string that is attached at both ends (like a guitar string), or does such a configuration allow only standing waves ?
| Of course there can be (and are) traveling waves on a string - when you pluck anywhere except at the center, you are generating an asymmetrical impulse that will travel up and down the string. The fact is that your "pluck" consists of many different frequencies, and as these travel back and forth two things happen:
*... | {
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Magnetic force between two point charges I tried to derive the magnetic force between two point-charges for iterative computation. Starting out with Lorentz force and Biot–Savart law for a point charge. $$ \vec F = q_2( - \Delta \vec{v} \times \vec{B})$$ $$\vec B = (\vec \Delta v \times \vec \Delta x) ( \frac {q_1}{ ||... | It appears that you have used the Biot-Savart law which assumes no static electric field. Instead, you should use the Lorentz force law, $$ F =q(E +Δv × B),$$
which accounts for both magnetic and electrostatic interactions.
| {
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Special relativity mirror clock experiment inconsistency Say I set up a relativistic mirror clock experiment in which a spaceship contains a set of mirrors with a photon bouncing between them. Say the photon's motion is parallel to the direction of motion of the space ship, and the spaceship is moving at near to the sp... | That's a very long ship.
Your logic didn't go wrong. The concept of simultaneity is broken with special relativity. Although the clock doesn't appear symmetric to the stationary observer, the ticks (a complete trip) remain consistent with the speed of light when you account for length contraction. And yes, to the stat... | {
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What exactly is the mass of a body? What determines it? The term "mass" is very common. But what does it depend on? How is it known?
| In classical physics mass has two definitions:
*
*It measures the amount of inertia that you have. In order to accelerate something you have to apply a force to it. The heavier your thing is, the less it will accelerate,
$$ a = \frac{F}{m} \, .$$
If you know the force and can measure the acceleration, you have acces... | {
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Compact Disc Optics - Why use a linear polariser and a quarter wave plate? I just came across this website about the application of a quarter wave plate. Link: Compact Disc Optics.
My question is why does the beam need to be linearly and then circularly polarised before sending to the compact disc? And the returned be... | What you may not realize from that website is that the same optical element is shown on the left and on the right. Laser emission and detection happen simultaneously, but for clarity they are drawn separately.
See how circular polarization changed after the reflection from the CD. Now, when it comes through the quater-... | {
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Mass dimensions and weak interaction The Fermi constant has a mass dimension of $-2$ and a value of $10^{-5}GeV^{-2}$.
How can I infer from this information that the mass scale of the weak interaction is about $10^2 GeV$?
|
The Fermi constant has a mass dimension of -2
The Fermi constant, $G_F$ itself has (by defintion) the dimension "energy times volume".
You are apparently asking about the "reduced" quantity $\frac{G_F}{(\hbar~c)^3}$,
(which is considered to be more practical in some applications) and
which has the dimension of "inve... | {
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Do magnetic fields cause ionisation of gases? I am doing my final year engineering project on Magnetic Field Assisted Combustion and was curious to see what people thought about it.
Companies sell rare earth magnetic arrangements to be attached to fuel lines of gas burners and they are said to improve combustion effic... | I don't know about ionizing gas but I do know about magnetophoresis. Oxygen is paramagnetic so oxygen concentrations should be higher around magnets than in ordinary air. This could make it easier for fuels to combust.
| {
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Torque on puck moving on plane without friction
We have two pucks moving on a plane without friction. On one of them a force is applied on it's center of mass. On the second a force of equal magnitude is acting tangential to the puck and at a distance equal to it's radius. Which one will be faster?
Now if I try to so... |
We have two pucks moving on a plane without friction. On one of them a force is applied on it's center of mass. On the second a force of equal magnitude is acting tangential to the puck and at a distance equal to it's radius. Which one will be faster?...
So the pucks will not have the same acceleration of their center... | {
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Consideration of centrifugal force during descent If we imagine an object falling from a height h above the surface of the earth. We can go into a rotating frame and therefore introduce Coriolis and centrifugal forces.
Using the Coriolis force the deflection in the East-West Plane can be calculated. However, I am wonde... | You're presumably talking about objects dropped away from the equator. At the equator it causes a lower effective gravity. Away from the equator it causes a deflection towards the equator.
| {
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Why does it seem as if big vehicles "attract" mine when I drive close to them? When I drive a car at high speed and when I am near to another big car (like a van, or transport vehicle) I feel an attraction to or something push me toward the other big car. What's the physics in this case?
| No, not at all. It doesn't have anything to do with gravity. The masses of the cars are so very small that you can't even think of the gravity between them. There is gravity, but it is negligible.
And one person answered with pressure. It's not that, either. Yeah, if you put two pieces of paper against each other and b... | {
"language": "en",
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How does "contamination" through (radioactive) radiation work? Physically, what does it mean when people or objects are contaminated with radiation? Is it because they actually carrying heavy metal particles?
| There are two distinct ways for previously non-radioactive material to become radioactive.
*
*Contamination refers to any behavior where existing radioactive material sticks to or is incorporated in an previously non-radioactive object or body (this can include a tract of land). This requires you to go to where ther... | {
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Limits of Integration Trig, Mag Field Infinite Length Wire I don't understand how the limits of integration should be defined when doing basic integrals of trig functions. It seems like it's an arbitrary decision, I don't understand it.
Here's the set up: For the field near a long straight wire carrying a current $I$, ... | Over the length of the wire from -infinity to +infinity the angle theta varies from
-pi/2 to +pi/2 and cos(theta) ranges from 0 through 1 and back to 0. It's never negative and the distance from any point on the wire to P is always positive. I think you create an unnecessary problem by treating the line from wire segm... | {
"language": "en",
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How many atoms are in a piece of paper? How many atoms are there in a common sheet of paper?
The paper is A4, i.e. $210 \, \mathrm{mm} {\times} 297 \, \mathrm{mm}$ $\left(8.27 \, \mathrm{in} {\times} 11.7 \, \mathrm{in}\right).$
| You can estimate number of atoms by finding out average molar mass of paper and mass of one sheet of paper.
If we assume that paper is mainly composed of cellulose, we can neglect other components as insignificant. Then we find out that cellulose's molar mass is approximately $162.14 \, \mathrm{g}/\mathrm{mol}$. Mass o... | {
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Drying clothes with the sun's heat, without any air Will my wet clothes dry if I hang them under the sun, and if there is no air around the clothes? In other words, do I need both air and heat to dry wet clothes, or is heat alone (in the imagined absence of any air) enough to dry wet clothes? Related question : will w... | No air means no vapor too. So without air your clothes will dry more easily, because the wetness will vaporize more easily.
| {
"language": "en",
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"source": "stackexchange",
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Why are neutron stars mostly composed of neutrons? I understand that it is due to electron capture $(p + e \rightarrow n + v_e)$. My precise question is:
What are the conditions needed for a star core to start undergoing this process at a large scale?
| The minimum mass for one to form is 1.44 solar masses.
Energy barrier:
Neutron mass - 1
Proton mass - 0.99862349
Electron mass - 0.00054386734
$p+e→n+v_e$
Assuming that the neutrino mass is negligible, we get the difference between the neutron mass and the electron-proton mass to be 780 keV, meaning this is the energy ... | {
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Electric flux of a point charge in 2D I am working in two dimensions and have a point charge in the $x$-$y$ plane at the origin. The charge is surrounded by a square walls, $-0.5<x<0.5$; $-0.5<y<0.5$, which are grounded. If I have to calculate the electric flux through the boundaries of the square, should I just calcu... | Flux in two dimensions into a curve $\mathcal{C}$ should be
$$
\Phi=\int_{\mathcal{C}} \vec{E}\cdot\hat{n}\, d\ell
$$
Where $\hat{n}$ is the unit normal vector to the curve.
This for instance is consistent with gauss's law $\Phi=\oint_{\mathcal{C}} \vec{E}\cdot\hat{n}\, d\ell=q_{in}/\epsilon$, when you notice that pois... | {
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Are there any scales other than temperature that have different zero points? For most physical measurements, zero is the same regardless of the units used for the measure:
$0 \mathrm{mi} = 0 \mathrm{km}$
$0 \mathrm{s} = 0 \mathrm{hr}$
but for absolute temperatures, different systems have different zeros:
$0 ^\circ\math... | Motion.
Velocity is obviously relative, and no "absolute rest" frame is known to exist.
Even acceleration, which is in a sense absolute, is sometimes specified relative to a local inertial frame (ie. freefall), sometimes relative to the distant stars (so you can talk about the acceleration of astronomical bodies due to... | {
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How can static friction do work?
By definition, the work done by a force is $W = F\cdot d$, so how can static friction do work?
Can this force move the body a distance of $75~\text{m}$?
|
By definition, the work done by a force is $W = F\cdot d$, so how can static
friction do work ?
Can this force move the body a distance of $75~\text{m}$ ?
Friction does negative work on the truck, slowing it down and does not move it forward.
What does positive work on the truck, accelerates it and makes it transla... | {
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How to calculate the focal length of spherical shell (zero meniscus lens) I can get my head around the optics of a spherical shell (a meniscus lens that neither diverge nor converge, being neither positive nor negative etc).
I don’t see how I can describe in a formula how rays would diverge or converge towards some fo... | I know that this post is quite old. However, the answer is maybe interesting for you. Directly applying lensmaker's equation doesn't work due to the air inside the lens.
I would rather suggest the following:
Since the middle of such a shell consists of air we can conceptually cut it in two halves.
These two halves are... | {
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In special relativity, is it correct to say the speed of a body B relative to A is the same as measured by every observer? Here, two objects A and B are moving relative to each other. I use the Einstein velocity addition formula $v = {v_1 + v_2\over 1 + {v_1 v_2\over c^2}}$ to calculate the relative speed between A an... | Let's say you have 3 systems. $B$ moving relative to $C$ with velocity $u$ and $A$ moving relative to $C$ with velocity $v$, all along one axis.
$A$ will "measure" for the velocity of $B$:
$$ u' = \frac{u-v}{1-\frac{uv}{c^2}} $$
While $B$ will "measure" for the velocity of $A$:
$$ v' = \frac{v-u}{1-\frac{uv}{c^2}} = -u... | {
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Is there any such thing as a change in acceleration (ex: 3 m/s/s/s)? If there exists something like that, then in $distance/time/time/time$, how is it expressed?
| An actual example in which there is a non-zero change in acceleration, that is, jerk, occurs is a spring. A spring's motion is described by a sinusoidal function. The derivative of a sinusoidal function is just another sinusoidal function. As a result, you can differentiate such a function infinitely many times, and wi... | {
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Why do the $u$ and $d$ quark not have an associated quantum number? All the other quarks ($c$,$s$,$b$ and $t$) have quantum numbers of charmness, strangeness, bottomness and topness that are conserved in strong interactions.
This allows, among other things, flavour changing neutral currents in $K^0$, $B^0$ and $D^0$ m... | You certainly can say that up quarks have +1 upness and down quarks have -1 downness. See Griffiths' particle book, 2nd ed., p. 49. It's just not very useful. The only quark with $S = C = B = T = 0$ and electric charge of $+\frac{2}{3}$ is the up quark. The down quark has $-\frac{1}{3}$ charge.
You could also say the ... | {
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Do the copper connectors we used in measuring the resistance of a wire contribute to the said measurement? We measured the resistance of a wire by setting the multimeter to ohmmeter mode and connected the ends of the ohmmeter to the ends of the wire; and we also calculated the theoretical value using a table of resisti... | As noted by Floris, the best way to measure small-value resistance is to use a four-point Kelvin connection; unless the current drawn by the voltage meter is significant (in which case there are other problems) then provided that current-source probes are either the inner two or the outer two (as opposed to being inter... | {
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Why do we use capacitors when batteries can very well store charges? Can batteries be used instead of capacitors? I am trying to figure out a basic, superficial and any obvious difference between the two.
|
Why do we use capacitors when batteries can very well store charges?
There's an important point that, so far, I don't see in other answers.
Neither of these devices store charge!
A "discharged" battery or capacitor contain the same net quantity of electrical charge as a "fully charged" battery or capacitor.
What they... | {
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Are circles stronger than triangles? I've often heard in engineering that, "there is no shape stronger than a triangle." I also recall that arches are also very strong shapes, which can be crudely described as a perpendicularly-symmetrical half-an-ellipse; Which can be simplified to half a circle.
If there were no conv... | I'm glad that my head is spheroid instead of pyramidal: then the circle is favored.
The eggs have an extremely strong shape: then the circle is favored.
The insects are extremely strong and they favor the round shape.
The engineering/construction by humans are easier with rectilinear elements and the triangular s... | {
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Does it take more energy to open a door when applying force close to the hinge?
Assuming an ordinary hinged door (without any springs), would it take more energy to open it when applying force in the middle of the door (point b), rather than at the end of the door (point a), where the door knob is?
"Opening the door" ... | Torque=(R) x (F)
Energy req. to rotate=(T).(Theta),
Ta=Tb,
ONLY Fa is less than Fb. & T at Hinge=0,
it'll not rotate there. The force required will increase from A to hinge point. Energy needed hence is const from A to hinge(except hinge point).
[Ta means torque applied at A]
| {
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Photon: speed and mass Is it correct to think that the speed of light does not depend on the speed of light source because photons have no mass, so they have no the kind of inertia that is associated with mass, so they can not "feel" (acquire) the speed of the light source?
| Is it correct to think that the speed of light does not depend on the speed of light source because photons have no mass, so they have no the kind of inertia that is associated with mass, so they can not "feel" (acquire) the speed of the light source?
No. Photons have an energy E=hf or E=hc/λ where f is frequency and λ... | {
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How does force transmit through a solid block? If you take a solid block, say, a cube of side length $l$ with density $\rho$, you place it upon a solid floor, and you apply an external pressure of $p(x,y)$ on the upper face ($x$ and $y$ define a rectilinear coordinate system for a horizontal plane), what pressure, $q(x... | Your force will transmit through the cube to the bottom and it will spread like a projection from your pressure point. having sand underneath it will give away a pression mark the size of your cube showing how your force transmitted. the height will no matter, being a solid cube and your force will not deformed it and ... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/176452",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "2",
"answer_count": 2,
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Constants of motion in quantum mechanics What is the meaning of a constant of motion in quantum mechanics (an observable-operator that commutes with the Hamiltonian) in contrary with classical mechanics?
| According to the Wikipedia article "Constant of Motion"
A quantity $A$ is conserved if it is not explicitly time-dependent and
if its Poisson bracket with the Hamiltonian is zero
That is to say, if both
$$\frac{\partial A}{\partial t} = 0 $$
$$\{A, H\} = 0 $$
then
$$\frac{dA}{dt} = \frac{\partial A}{\partial t} + \... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/176511",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "1",
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Why is charge of the electron negative? How did scientists figure out that the charge of the electron was indeed negative? I know how the cathode ray tube experiment works, but how did Thompson know that the plate that the cathode ray beam was attracted to was positive, meaning the cathode ray was negative? What is the... | As Zeldredge said the name is arbitrary and does not matter electron could have been positive and protron negative just the name.
| {
"language": "en",
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"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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At what energy consumption would we get a 1 degree rise in the Earth's temperature? If energy consumption continues to rise at (say) 4% per year, how long before the heat dissipation seriously impacts climate?
| *
*Global energy consumption is $5\times10^{20}\ J/yr$
*Assume it is all used to power incandescent lightbulbs, so 95% goes to heating the atmosphere
*The mass of the atmosphere is $5\times10^{18}\ kg$
*The heat capacity of air is $1\times10^{3}\frac{J}{kg\cdot °C}$
Assuming all the heat goes to the atmosphere an... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/176683",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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In aircraft design why are light materials preferred to heavy ones? Especially given the relative cost between (say) steel and carbon composites. After all, I assume most fuel is consumed overcoming drag not accelerating mass. Once an aircraft reaches cruising speed it should not matter how heavy/dense the aircraft is ... | Building on Carl's comment:
The way any heavier than air aircraft works is that the wings exert a downward force on the air - increasing the downward momentum of the air results in a net lift force in the wing.
Now if you are heavier, you need to either move more air down per unit time, or move it down faster, in order... | {
"language": "en",
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"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "1",
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What really is the self-adjoint extension? Going through the Quantum mechanics book by Capri, am time and again held with some stupid doubts on this topic of self-adjointness. We have for the momentum operator in finite domain,
$$
p = -i\hbar \frac{\partial }{\partial x} \\
D_p = \big\{f(x),f'(x)\in \mathrm{L_2}(0,L) ... | A closed extension $A_c$ of an operator $A$ is an operator whose action is the same as $A$, the domains satisfy $D(A_c)\supset D(A)$ and $A_c$ is closed.
Given that, the smallest closed extension of a symmetric (densely defined) operator is its double adjoint $A^{**}$. We call it the closure of $A$, and denote it by $\... | {
"language": "en",
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"source": "stackexchange",
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The general equation for a wave packet derivation? On Wikipedia it gives the general equation for a wave packet (and therefore for a wave?) to be:
$$u(x,t)=\frac{1}{\sqrt{2\pi}}\int^{\infty}_{-\infty}A(k)e^{i(kx-\omega t)} dk$$
I have been trying to derive this but have had no luck. The closest I get is:
$$f(x,t)=\sum_... | A solution to the Schrödinger equation for a free particle is a plane wave, and because any combination of solutions is also a solution we can construct solutions by summing up plane waves.
The equation you quote is constructing a solution by Fourier synthesis. Since the plane wave function $e^{i(kx-\omega t)}$ is a so... | {
"language": "en",
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"timestamp": "2023-03-29T00:00:00",
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Why do $S_x$ and $S_y$ flip up/down spin states but $S_z$ does not? By using the notation $S\lvert s,m_s\rangle$, such that $\bigl\lvert\frac{1}{2},\frac{1}{2}\bigr\rangle=\lvert+\rangle$ and $\bigl\lvert\frac{1}{2},-\frac{1}{2}\bigr\rangle=\lvert-\rangle$ we can obtain following the eigenvalue equation for the compone... | You chose the $\lvert \pm \rangle$ to be an eigenvector of $S_z$ with eigenvalue $\pm\frac{1}{2}$ - that's what the $m_s$ is: The eigenvalue of the state w.r.t. the $z$-spin.
Since $S_x$ and $S_y$ do not commute with $S_z$, $\lvert \pm \rangle$ is not an eigenvector of them, hence the state cannot stay the same after t... | {
"language": "en",
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"source": "stackexchange",
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Is it possible to derive the angular frequency of a simple harmonic oscillator using total energy?
I want to show that
$$\omega=\sqrt{\frac{k}{m}}$$
using the fact that
$$E=K+U=\frac{1}{2}mv_x^2+\frac{1}{2}kx^2=\frac{1}{2}kA^2.$$
The issue is that I have derived a formula that isn't correct:
I first took the t... | Whenever you want to prove something, you need to get your hypotheses straight. I understand that you want to prove that a mass $m$ on a spring with constant $k$ moves harmonically with frequency $\sqrt{k/m}$, but you seem to be assuming that result in your "proof":
First off, writing $E = \frac12 k A^2$ already implie... | {
"language": "en",
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What compounds or elements only have one phase or two phases? Wood appears to be one. I think gases like helium and hydrogen cannot exist in the solid state under normal pressures, correct? And why do those "phase cheaters"-- those elements/compounds which sublimate directly, skipping a phase, or "procrastinators"-- el... | Iodine - solid to vapor when heated under normal condition. In this context the word you need to search for is "sublimation"
| {
"language": "en",
"url": "https://physics.stackexchange.com/questions/177755",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "3",
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Escape velocity for Schwarzschild metric I can't fill in the gaps in my solution to this and assistance or a reference would be appreciated.
The question begins with the straightforward derivation of the EoM for a massive particle orbiting in the equatorial plane, as
$$ \left( \frac{du}{d\phi}\right)^2 = \frac{c^2 k^2}... | Let $f(u)$ be the third degree polynomial, so that
$$\left(\frac{du}{d\phi}\right)^2 = f(u)\tag{*}$$
The experimenter starts at $u=1/a$ and must reach infinity, $u=0$. The crucial point is that if $f(u)$ is negative somewhere in the region $0<u<1/a$, then the equation of motion $(*)$ prevents crossing the negative regi... | {
"language": "en",
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"source": "stackexchange",
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How does mechanical energy conservation work? I am a little confused about how mechanical energy conservation operates when it comes to things like predicting velocity. I know that if conservative forces are the only forces acting on a body, then we can say that mechanical energy is conserved. This is simple to see whe... | When someone moves in a field then the work generated by field forces is independent of motion and related to the starting and ending positions. The quantity $U$
$$\int_{r_1}^{r_2} \mathbf F( \mathbf r) \cdot d \mathbf r = [U ( \mathbf r)]^{r_2}_{r_1}$$ is called potential energy and is associated with a potential $... | {
"language": "en",
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"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "1",
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Can we find the exponential radioactive decay formula from first principles? Can we find the exponential radioactive decay formula from first principles? It's always presented as an empirical result, rather than one you can get from first principles. I've looked around on the internet, but can't really find any informa... | Any population whether human, animal or atomic nuclei, will with no other complications
change proportional to the amount already there. Yielding a very simple differential equation.
$$
\frac{dP(t)}{dt} = k\,P(t)
$$
where $k$ is a constant with a negative sign for exponential decay and plus sign for exponential incre... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/178233",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "18",
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Does it mean the molecules of all matter above absolute zero temperature are moving? According to my knowledge, heat is the energy that is stored in form of kinetic energy of molecules in Brownian motion. However, in a macroscopic view, a rigid body seem to be "stable" but still store heat. I am wandering does it mean ... | Let us understand Brownian motion in liquids before we look at the motion in solids. If you observe a glass of water at rest on a table, it "appears" to be motionless. However, all we need is a magnifying glass to observe the random, incessant motion of water on the surface. This random motion is a manifestation of hea... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/178305",
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"source": "stackexchange",
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Can a brane have infinite volume? I'm asking this within the framework of brane theory. My intuition is that branes are objects with finite volume, but then how can they accomodate an Universe that is infinite in extent?
| Branes typically have infinite volume. As an intuitive example of a brane, imagine an infinite plane in 3D, which is a 2-brane. The brane is specified by (for example), $z=0$ if $(x,y,z)$ are the usual Cartesian coordinates. An infinite line is a 1-brane and is specified by (again, for example) $y=z=0$. If the branes a... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/178384",
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"source": "stackexchange",
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Why does the Magnetic Flux Density B, saturates in a ferromagnetic material with increasing H? I understand that the magnetization must saturate as more and more domains are aligned. But $B$ is still directly proportional to $H$, and hence it must increase linearly with $H$.
But every book that teaches $B-H$ curve, sa... | No, your understanding is wrong: $B$ isn't proportional to $H$, the relationship is $\vec{B}=\mu_0 (\vec{H} + \vec{M}(\vec{H}))$ where $\vec{M}$ is the magnetization (see Wiki page of this name). And $\vec{M}$ saturates for precisely the reason you state: its maximum value is reached when all the magnetic dipoles in a... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/178492",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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What is precisely the energy scale of a process? Coupling constants run with the energy scale $\mu$. But what is exactly this energy scale. My question is, if I have a physical process, how do I compute $\mu$?
| You go to the center of mass frame to find that $\sum_i \vec{p}=\vec{0}$, and the total momentum four vector is thus $$P_{\text{tot}}^{\mu}=\left(\frac{1}{c}\sum_{i}E_i^{\text{COM}}, \vec{0}\right)$$
then we define the energy scale covariantly as $\mu=\sqrt{-s}$ where $s$ is the mandelstam variable $s\equiv P_{\text{to... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/178754",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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Can electricity flow through vacuum? People say yes, and give a wonderful example of vacuum tubes, CRTs. But can we really say that vacuum (..as in space) is a good conductor of electricity in a very basic sense?
| The conductivity of the vacuum is not a very trivial issue. In fact, depending on how you look at it, it behaves in two different ways.
Firstly, there is no retarding force on any charged particle with constant velocity in vacuum. To this extent, no extra work is required in maintaining a constant current through any s... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/178831",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "17",
"answer_count": 8,
"answer_id": 3
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Why does light "expand"? The "opening" for light to travel out of a flashlight is circular. Why does the light shine on the objects the flashlight is pointed at over a much larger surface area than the surface area of the aperture? Why doesn't it just illuminate the whole room or wherever the flashlight is?
| Light is a wave , an electromagnetic wave classically. When leaving a point source a wave expands isotropically in angle, spherically, and its intensity falls like 1/r^2 where r is the distance from the source
If a point source lamp is set in a room, it will illuminate spherically all of it, as happens with the lamps ... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/178963",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "3",
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What does magnetic field vector mean? I am trying to understand what a magnetic field vector tells us about the magnetic field.
I understood that a vector is just a representation of a point and how much it is moved in x,y and z direction from its origin.
But how can this explanation apply to the magnetic field?
source... | Generally, a magnetic field is produced either by a moving charge or a magnet. This magnetic field's strength and direction at a point are described by magnetic field vector.
The closer we move the point to magnet, the denser is the field at the body. Thus, the length of magnetic field vector increases.
magnetic field ... | {
"language": "en",
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"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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Why can't I harness normal force? Lets say I have my palm flat with a book resting on top of it, and I have my feet on the ground. I extend my arm so that now it's kind of difficult to keep the book up. Why doesn't my hand just produce normal force on the book, cancelling out the force of gravity, and costing me no eff... | Name has a really great answer, but I'm gonna try to clarify it a little. If you hold the book, its very unlikely that our arm is perfectly at 90 degrees, perpendicular to the ground. That means you will have to counteract the book's torque. But even if you held your arm perfectly at 90 degrees you would still get tire... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/179143",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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The amount of potential energy at the height of h When we lift an object upwards with a constant velocity for a distance of $ h $ the work that we've done is $mgh$ and the work done by the force of gravity is $-mgh$. So the net work on the object is zero and it doesn't gain any energy. how its potential energy will be ... | Gravitational weight is a conservative force so work done against it is entirely equal to the change in potential between the start and end points (in the absence of dissipative forces like friction). The internal energy of the mass does not change as it is moved upwards and your assessment of the energy considerations... | {
"language": "en",
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"timestamp": "2023-03-29T00:00:00",
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What is the uncertainty principle? I looked on Wikpedia for information on the uncertainty principle, but after reading it I still had no idea. I know it has something to do with how many things you can hold at some spot for some amount of time (maybe?). This is inspired by this question.
| Let's forget physics for a moment and just talk about the mathematics of waves.
The uncertainty principle is a property of waves. Think of a single, narrow pulse traveling along one direction. The pulse is narrow, and so the position of the pulse at any given time is easy to quantify. But this is a single, non-perio... | {
"language": "en",
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"source": "stackexchange",
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Where do forces point in an equilibrium system
I have the system above, with three identical balls of weight $W$ and radius $r$. The angle joining the centres is $\theta$, and the coefficient of friction between the balls and the plane is $\mu$ and between the balls $A/C$ and $B/C$ is $\mu '$. The system is in equilib... | Okay, the system is in equilibrium so all the forces must be balanced.
First consider the weights
We have $W$ downwards from the centre of each of the 3 balls (assuming their centres of mass are at their geometric centres).
We also have $N_A = N_B = \frac{3}{2}W$ upwards from the points of contact between the plane and... | {
"language": "en",
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What is the state of water at exactly 0°C? Theoretically speaking, what is the state of water at bang on 0°C - not any lower or higher?
Any lower would make it a solid whereas any higher would make it a liquid. But what about bang on 0°C?
Thanks in advance
Edit: I understand that other factors are involved, such as pre... | Temperature defines the amount of energy and vice versa. However, supplying or taking small amounts of energy away from water strictly at zero degrees Celsius, is not going to change the temperature! First, this energy will be used to make transition between liquid and solid form, until you get just one kind of form, e... | {
"language": "en",
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"source": "stackexchange",
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Relative motion at almost the speed of light My title might not be precise but I didn't know how to decribe it better.
I've been reading about the special and general theories of relativity for a short while and I started wondering. First, every movement is only relative to some other object/observer, there is no absol... | The key point here is the "weird" change in the values you measure depends on what frame you observe them in relative to the object. There is no experiment you can conduct to determine an absolute value for your speed. Speed only makes sense relative to an object. So if a near light speed object relative to us was head... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/181085",
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Magnetic monopoles and special relativity I was thinking about magnetism as a product of special relativity and the result of this approach to the magnetic monopoles.
So if magnetism is a product of electricity(like electricity from another point of view),then why do we need monopoles to exist?I know that many theories... | Magnetic field appears in Relativity not in one step, but in several.
At first, one looks at two electrons in rest. They are subjects for Coulomb repulsion. The repulsion force is, say $F$ and it would cause acceleration of $a = F/m_e$
Now, one looks at the same two electrons from the moving frame.
According to relati... | {
"language": "en",
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"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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Electric field in a conductor Is it always true that the electric field in a conductor is zero?
What would happen if I put a very big charge inside an ungrounded hollow conducting sphere like this image?
The charges inside the conductor are supposed to rearrange so as to cancel the field created by the big charge.
So ... | Then there would be electric field inside that shell. Well if it is still intact. Because you need an immense positive charge to do that to a typical shell, more than 100000 Coulombs (assuming you have 1 mole of conductor with about 50 electrons per atom). To bring that much charge together requires immense force and e... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/182504",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "3",
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Do quarks violate quantization of charge? Does existence of various kinds of quarks like up, down, strange, charm, top, bottom violate the quantisation of charge or just redefine it as up quark have charge +2/3 and have -1/3. Or do things get even complex for unified theories like the proposed string theory?
| Quarks do not violate quantization of charge, it's simply that $\frac{1}{3}e$ instead of the electron charge $e$ is the smallest unit of electric charge.
| {
"language": "en",
"url": "https://physics.stackexchange.com/questions/182604",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "6",
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Particle Horizon and CMB If particle horizon is the maximum distance we can see presently in the universe, how come we are able to see CMB? CMB is radiation from surface of last scattering happened at t~380k years.
Suppose universe is expanding at a constant rate ( i.e. no acceleration), will we be able to see CMB aga... | The particle horizon is the distance from which light emitted at the moment of the Big Bang will just now be reaching us.
The CMB was emitted 380,000 years after the Big Bang. So the CMB radiation we see has been travelling for less time than the light emitted at the Big Bang, and therefore the CMB radiation has travel... | {
"language": "en",
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"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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Finding $p(z), \rho(z)$ of an ideal classical gas in a box We have a classical ideal gas of particles of mass $m$ at fixed chemical potential $\mu$ and fixed temperature $T$. We have a potential energy $U(z)=mgz$ and the gas is in a rectangular box of height $h$ and base area $A$. How do we calculate quantities like th... | The density is directly given by
\begin{equation*}
\begin{split}
\rho(z)&=\frac{\int dpAe^{-\beta(p^2/2m+mgz)}}{\int dp\int_0^hdzAe^{-\beta(p^2/2m+mgz)}}\\
&=\frac{e^{-\beta mgz}}{\int_0^hdze^{-\beta mgz}}=\frac{\beta mg}{1-e^{-\beta mgh}}e^{-\beta mgz}
\end{split}
\end{equation*}
since the momentum is homogeneou... | {
"language": "en",
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"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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How can I tell if the spectrum of an operator in QM is degenerate? I know that the collection of all the eigenvalues of an operator $\hat{Q}$ is called its point spectrum, and sometimes two or more linearly independent eigenfunctions share the same eigenvalue, and in this case the spectrum is said to be degenerate.
My ... | As Phoenix87 said, you need to solve the asociated eigenvalue problem. $\lambda$ is an eigenvalue if and only if $\hat{Q}|\Psi>=\lambda|\Psi>$. If you have a matrix expression for the operator $\hat{Q}$, then the usual way to solve the problem is writing the above equation as Phoenix87 did, writing everything in the le... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/182978",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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Rayleigh's Criterion I was just wondering, when two different objects have have light coming from them to our eyes, do the intensities of each diffraction interfere? For example, in the picture below:
Do the intensities interfere with each other?
| Rayleigh's criterion gives a quantitative measure of the angle ($\theta$), being a function of wavelength ($\lambda$) and diameter of the lens ($d$), necessary to distinguish between two light sources. In particular we have,
$$
\theta = 1,220\cdot \frac{\lambda}{d}
$$
The two light sources are non coherent which means ... | {
"language": "en",
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Is there a definite boundary between a powder and a fluid? Given a powder of solid substance what will happen if we make the granules smaller and smaller mechanically? Will this eventually make a liquid or gas from the powder?
Can there be gaseous substanse made not from single molecules but from microscopic granules o... | Why is solid not big gas particles. Where is the boundary between metals and non metals. Their properties? Their form? When does one change into the other. When does something stop and start being an antenna?
| {
"language": "en",
"url": "https://physics.stackexchange.com/questions/183186",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "10",
"answer_count": 5,
"answer_id": 4
} |
Why isn't ice a good electrical conductor? Water can conduct electricity, and some solids can conduct. Why can't ice? Are ice molecules too packed together to let valence shell electrons bounce across each other to create electrical charge? Does ice stop conducting completely at absolute zero?
| Conduction in water is mostly ionic - for pure water you have a very small fraction of ionized molecules (about 2 parts in 10$^{-7}$), so conductivity for pure water is poor. Add a little electrolyte (for example NaCl) and conduction improves. But in an ice crystal, the molecules / ions cannot move, so the main conduct... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/183265",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "6",
"answer_count": 1,
"answer_id": 0
} |
Expansion of a ket-physical interpretation of coefficients Consider I have a state represented by the Ket:
$$|\psi\rangle=\sum_i a_i |\phi_i\rangle$$
What are the physical interpretations of the coefficients $a_i$? My guess is that $|a_k|^2$ represents the probability that the 'paritcle' is in the state $ |\phi_k\rang... | It's convention to normalize the wave function, but this is purely something done to make calculations easier. States multiplied by a c number(complex number) are completely equivalent.
This is why we choose to normalize states (magnitude 1). It makes the calculations for things like the transitions probability between... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/183320",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "1",
"answer_count": 2,
"answer_id": 1
} |
Does lithium-6 "decay" when hit by a neutron? I am talking about the nuclear reaction
$$
^6\text{Li} + n \rightarrow\ ^4\text{He} +\ ^3\text{H} + 4.78\text{MeV}
$$
A neutron hits a lithium-6 nucleus and together they form an alpha and triton particle. Is it valid to say that the lithium nucleus "decays" when hit by a n... | Decays happen to individual nuclei ( particles). When more than one nucleus(particle) are involved it is called an "interaction". In this case neutron Li scattering
Neutron capture by a nucleus is a possibility, in this case there is an intermediate nucleus formed , which can then decay.
| {
"language": "en",
"url": "https://physics.stackexchange.com/questions/183391",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "3",
"answer_count": 4,
"answer_id": 1
} |
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