Q stringlengths 18 13.7k | A stringlengths 1 16.1k | meta dict |
|---|---|---|
Minimum time required to reach a point A police inspecter P is at point $ (\acute{x},\acute{y})$ and a thief X is at point $(x, y)$. X has a constant velocity $V_x\hat{i} + V_y\hat{j} $, where $\hat{i}$ and $\hat{j}$ are unit vectors in $X$ and $Y$ direction respectively. Maximum speed of P is S.
What is the minimum t... | Let me make a few variable substitutions to make life easier:
Initial coordinates of the thief: $(x_0, y_0)$, initial coordinates of the officer: $(0,0)$. Assume the thief to have velocity $(t_x,t_y)$. The officer has speed $(p_x,p_y)$ with maximum speed $p_m^2 \geq p_x^2 + p_y^2$.
Since the thief has a constant veloci... | {
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Does matter with negative mass exist? Or does it exist mathematically?
Is it really inconsistent with a common-sense, mathematics or known physical laws?
As far as I understand, if it exists, it must be far away from the "positive" matter because of repelling force, so it explains why there is no observations of such... | No. Matter must have nonnegative mass for reasons of causality. This follows from relativistic quantum field theory, as it is impossible to define free causal quantum fields (modeling the asymptotic = observable bound states) with negative masses.
Speculations that there might be particles of mass_square smaller than z... | {
"language": "en",
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"timestamp": "2023-03-29T00:00:00",
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Velocity vs Time Bounce Could someone please explain the trajectory of the ball that is bouncing in this picture...
The vertical component of the velocity of a bouncing ball is shown in the graph below. The positive Y direction is vertically up. The ball deforms slightly when it is in contact with the ground.
I'm not ... | This is a graph of velocity versus time, so the slope of the graph at any point gives the change in velocity over time, or dv/dt which is acceleration. Acceleration occurs due to the application of force to a mass (f=ma, or a=f/m).
Any change in the slope of the graph must occur due to a change in (dv/dt), which is a c... | {
"language": "en",
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Hamiltonian in position basis Let $ H = \frac{-h^2}{2m}\frac{\partial^2 }{\partial x^2}$. I want to find the matrix elements of $H$ in position basis. It is written like this:
$\langle x \mid H \mid x' \rangle = \frac{-h^2}{2m}\frac{\partial^2}{\partial x^2} \delta(x -x')$.
How do we get this? are we allowed to do $\l... | If the matrix elements of your Hamiltonian are given by $ \langle x|H|x`\rangle $.
This can be written as $\langle x|Hx`\rangle$, so if you take a complex conjugate, you end up with $\langle x`H|x\rangle$, since $H$ is hermitian. Therefore, the expression you have obtained is valid in both cases.
| {
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"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "3",
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"answer_id": 2
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Velocity of real gas molecules? It is known that the velocity of ideal gas molecules can be computed using Maxwell-Boltzmann law of distribution of molecular velocities, with average velocity given as:
$\overline{v}=\sqrt{\frac{8RT}{\pi M}}$
What would be the corresponding average velocity for a real gas (which are not... | There is an important thing to note about your question, which is the understanding the relationship between math and physics. Physics uses mathematical equations to describe reality. Physics equations are approximations and may assume certain conditions (pressure, temperature, etc.) to offer an equation that is strict... | {
"language": "en",
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Higgs boson in LHC Recently, the Higgs boson was discovered in the LHC. My question is:
How did they come to know that the particle created was actually the Higgs boson?
On the basis of which properties did they confirm it as the Higgs boson?
| They know the particle is a Higgs boson because they trace the decay products. If there is a slight increase in one type of particle. Lets say it the bottom-antibottom pair then this might be clue that the Higgs boson was discovered. Especially if they see this bump over and over again. There has to be a Higgs otherwis... | {
"language": "en",
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Mechanics Problem I'm trying to follow Feynman's lecture. Unfortunately I'm a bit stuck on a small piece, so if you could show me what I'm doing wrong then I'd greatly appreciate your help. I want to exactly know how Feynman came up with $W_{ac} = \int^c_a \bf{F} \cdot d \bf{s} = F s \cos \theta$ when this implies $\bf... | Your first question deals with a comparison of the paths $a$ to $b$ to $c$ with the direct path from $a$ to $c$. The law of conservation of energy deals with this and you can apply it to prove that only the starting and end points matter, the path doesn't.
As for working out the the forces involved, is that part of th... | {
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Diffraction through the slit In book "Quantum Mechanics and Path Integral", 3-2 Diffraction through the slit:
Under the fig. 3-3, why did Feynman say that we cannot approach the problem by a single application of the free-particle law motion, since the particle is actually constrained by the slit?
And why Feynman use G... | I don't have a copy of the book, so can't comment on the Gaussian slit, but you can't use the free particle propagation equation in the presence of a slit, because the slit (a conventional slit) can be modelled by a rectangular shaped potential function. Straightforward free particle propagation only applies when the ... | {
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If acceleration causes relative time dilation does the eventual deceleration reverse it? If acceleration causes relative time dilation does the eventual deceleration reverse it?
For example: traveling to Alpha Centauri
Based on me reading this site: http://www.convertalot.com/relativistic_star_ship_calculator.html
-
| As was pointed out it is relative velocity, not acceleration, which results in time dilation. Acceleration does, however, play a role in the perceived amount of time elapsed between events. So, special relativity can give insight into your question about "reversing" the effects of acceleration. Have a look at the Twin ... | {
"language": "en",
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SUSY, ways to boost Chargino/Neutralino production? Does anybody know a good reference that works out the equations for the Chargino/Neutralino production cross section in SUSY? I'm trying to understand if there are any tricks for boosting the production cross section.
So far, I have just been testing using Prospino an... | $pp$ collisions can produce neutralinos and charginos directly via electroweak production. This can occur via $s$-channel $\gamma$, $Z$ or $W$, e.g.,
$$
q\bar{q} \to Z \to \chi^0_i \chi^0_j,
$$
which is a Yukawa Z-Zino-Higgsino interaction (and is significant if $i\ne j$), or via $t$-channel squarks, which is a $q$-$\t... | {
"language": "en",
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Will I recieve a shock if I charged a capacitor, then I touch the 2 poles in same time? What happens if I charged a capacitor, then I touch the 2 poles in same time?
| If the charge in the capacitor is large enough, you'll get a nice little shock:-), as the capacitor will discharge through you. I remember grabbing a rectifying valve disconnected from the mains a long time ago - that was not pretty (apparently, it contained a capacitor). I was "clever" enough to grab it again:-)
| {
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Building a LED lamp, which is the brightest? 3 LEDs of 2500 mcd or 1 LED of 6000 mcd? I want to build the brightest lamp, for it to be seen at daylight, should I use 3 2500 mcd LEDs or 1 6000 mcd?
And also Why?
| In terms of overall light output then you just sum the mCd - it's just power.
However if you want that light to do something useful then it's how much of the light can you focus on the target?
A single LED at the focus of some reflector will put more of the light into the beam than a cluster of three - simply because ... | {
"language": "en",
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Why don't we use the concept of force in quantum mechanics? I'm a quarter of the way towards finishing a basic quantum mechanics course, and I see no mention of force, after having done the 1-D Schrodinger equation for a free particle, particle in an infinitely deep potential well, and the linear harmonic oscillator.
... | We use the concept of force in quantum mechanics. For instance the Heisenberg equations, which are the quantum analogue of Hamiltonian equations of classical mechanics, use quantum forces --the hat denote matrices--
$$\frac{\mathrm{d}\hat{\mathbf{p}}}{\mathrm{d}t}=\hat{\mathbf{F}}$$
What happens is that the Heisenberg ... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/45869",
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"source": "stackexchange",
"question_score": "12",
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How did we find out the shape of our own galaxy without going out of it? As far as I know, scientists have been able to see a lot of differently shaped galaxies in our visible universe through modern age telescopes. But I was wondering how it was possible to know how our own galaxy looks like without going out of it to... | We obviously do not know the shape exactly, but by measuring the positions of visible stars in our neighborhood We can tell that it is a spiral arm galaxy. In fact to the naked eye, the fact that we see a band of diffuse light called the Milky Way shows that we are in a flat type of galaxy and not in a globular cluster... | {
"language": "en",
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Gaussian integration and dimension argument I made a mistake recently regarding the Gaussian density, by putting the determinant of the variance to the power $\frac{d}{2}$. Would the following argumentation be valid to highlight it should be to the power $\frac{1}{2}$? :
The argument of the exponential must be dimensio... | I) Well, Gaussian integrals
$$\tag{1} \int_{\mathbb{R}^n} \! d^n x ~e^{-\frac{1}{2} x^t A x}
~=~ \sqrt{\frac{(2\pi)^n}{\det A}}$$
are easy to calculate exactly, where the matrix ${\rm Re}(A)$ is positive definite, cf. e.g. this math.SE post.
II) But if OP just wants to confirm that the power $p$ of the determinant $... | {
"language": "en",
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Tachyon vertex operator (Polchinski's book)
*
*I would like to know how does Polchinski in his book "derive" what is the "tachyon vertex operator" (..as say stated in equation 3.6.25, 6.2.11..) I can't locate a "derivation" of the fact that $:e^{ikX}:$ is the tachyon vertex operator.
(..I understand that it follows ... | Polchinski explains the state-operator correspondence in section 2.8, in particular equations 2.8.3, 2.8.4, and 2.8.9.
What you call "higher vertex operators" create multiple particles (if there are multiple exponential vertex operators) with higher spin (if there are extra derivatives multiplying the exponentials).
| {
"language": "en",
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Showing symmetry of the stress tensor by applying divergence theorem to $\int\int_{\delta V(t)} \vec{x}\times \vec{t} dS$ I'm currently working through the symmetry of the stress tensor, in relation to viscous flow. I am looking at this by examining the conservation of angular momentum equation for a material volume $V... | The $i$th component of the integral is $\oint_S \epsilon_{ijk} x_j \sigma_{kl} n_l\, dS$ We see that $\epsilon_{ijk} x_j \sigma_{kl}$ has its $l$ index contract with $\hat{n}$. Thus the divergence theorem allows us to convert this integral to $\int_V \partial_l \epsilon_{ijk} x_j \sigma_{kl} \, dV = \int_V \epsilon_{ij... | {
"language": "en",
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Why can't one see tidal effects in a glass of water? Why can't one see the tidal effect in a glass of water like in an ocean?
| The gravitational pull of the moon on the oceans or on a glass of water is the same assuming a specific location. Because of this the force exerted on the glass is the same, but due to the small volume of water in a glass as opposed to an ocean it would be very hard to measure any change. Because of this a very sensiti... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/46157",
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"source": "stackexchange",
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Is there a small enough planet or asteroid you can orbit by jumping? I just had this idea of orbiting a planet just by jumping and then flying upon it on its orbit kind of like superman. So,
Would it be theoretically possible or is there a chance of that small body to be & remain its unity?
| Since the calculations are already in others' answers, I'll just refer to this great, classic xkcd. Deimos and Phobos, the two small moons of Mars, match (or almost match) the criteria SF and Claudius derive.
As Munroe points out,
(The diagram is a representation of the gravity wells of both moons, represented by thei... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/46318",
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What is the motivation for the definition of concurrence in quantum information? What is the motivation for the definition of concurrence in quantum information? On the surface, the definition looks pretty ad hoc.
The definition is often given for the case of 2 qubits only. What is the generalization to higher dimensio... | The basic motivation behind defining "Concurrence" is its faithful quantification of quantum entanglement and hence also is useful as a strong separability criterion. "Faithful" means that Concurrence = 0 <=> Unentangled/Separable state, and if Concurrence is non-zero then it would "quantify" how much far these states ... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/46443",
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Why can't there be a trap door under nuclear reactors in case of meltdown? This may be a naive question, but after the Fukushima Daiichi partial meltdown and studying the aftermath of Chernobyl it seems they could be helped by this idea.
In Chernobyl, the liquidators that cleaned up the disaster tunneled concrete under... | If the core ever touches air during its meltdown, it will get so hot that it will maintain a steady independent reaction that will continue until the fuel is spent. It is so hot that it melts through concrete, steel and other man-made obstacles. If it were to hit water, the steam that would result would be disastrous. ... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/46520",
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Why doesn't the dark matter halo co-rotate with the luminous disk? What keeps it from falling into the center if not angular momentum?
*
*Why doesn't the dark matter halo co-rotate with the luminous disk?
*What keeps it from falling into the center if not angular momentum?
| Because it does not interact much the individual dark matter components (whatever they may be) have no efficient way to shed their energy and end in lower orbits.
They do fall into the center and then fall right back out again, never losing significant amounts of energy.
| {
"language": "en",
"url": "https://physics.stackexchange.com/questions/46634",
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The Role of Gravity among the Fundamental Forces of Nature If we look at the standard model, we have 4 fundamental forces which include
*
*Gravity,
*Electromagnetism,
*Nuclear weak force,
*Nuclear strong force.
I would like to look at Gravity for a minute. Scientists are still searching for what causes gravity. B... | On a large (i.e. non-quantum) scale describing gravity as a property of spacetime works well, and in fact it's exactly what General Relativity does. The problem is that the equation that describes the curvature of space-time is:
$$ G_{ab} = 8\pi T_{ab} $$
where the quantity on the left, $G_{ab}$, describes the curvatur... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/46879",
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If we charge a capacitor can we discharge it into a battery? I have read that we can charge a capacitor using a battery, but can the vice versa happen? My project needs to show a battery being charged through a fully charged capacitor.
| All you need to charge a battery from a capacitor is to have more voltage charged on the capacitor than the voltage of the battery. The size will only affect how much time the capacitor will charge the battery. If you could charge the capacitor over and over and discharge it into the battery every time it was full it w... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/47077",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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Why does the nature always prefer low energy and maximum entropy? Why does the nature always prefer low energy and maximum entropy?
I've just learned electrostatics and I still have no idea why like charges repel each other.
http://in.answers.yahoo.com/question/index?qid=20061106060503AAkbIfa
I don't quite understand w... | Nature has no preferences, and therefore entropy tends to increase.
Sounds paradoxical?
The point is that each microscopic state (describing the exact position and velocity of each atom in the system) is equally likely. However, what we typically observe is not a micro state, but a course-grained description correspo... | {
"language": "en",
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experimental technique for measuring temperature of an ant I am taking a course on thermodynamics. I have a question from my text(halliday & resnick,physics-1). They asked me to measure temperature of an ant or an insect or a small body,like a small robot. If I build a thin thermometer then it is probable that surface ... | Put ant in small volume of cold water, maybe 5ml. Measure the final temperature of water using some thermometer and solve for temperature of ant using the thermal equilibrium equations.
$$m_\text{ant}c_\text{ant}T_\text{ant} + m_\text{water}c_\text{water}T_\text{water} = m_\text{(ant+water)}T_\text{final}(c_\text{water... | {
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Is the superposition principle universal? In David J. Griffiths' Introduction to Electrodynamics, he claims that the superposition principle is not obvious but has always been found to be consistent with the experiments. So I was wondering have we found some physics quantities which do not follow superposition principl... | The answer is that there are "physics quantities" that do not obey a superposition principle. The energy density of the electric field is proportional to $E^2$ so if $\bf{E}=\bf{E}_1+\bf{E}_2$, the energy density is not the sum of the energy densities due to $E_1$ and $E_2$ separately.
Superposition is far from bein... | {
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When you apply the spin operator, what exactly is does it tell you? The example I'm trying to understand is:
$ \hat{S}_{x} \begin{pmatrix}
\frac{1}{\sqrt{2}}\\
\frac{1}{\sqrt{2}}
\end{pmatrix} = 1/2 \begin{pmatrix}
\frac{1}{\sqrt{2}}\\
\frac{1}{\sqrt{2}}
\end{pmatrix} $
My interpretation of this is that the vector show... | Your equation says that your "vector" is an an eigenvector of your operator, i.e., that the x-projection of the spin is certain an equal to 1/2. As well it says that probabilities to find certain z-projections are equal to 1/2.
This "vector" is not an eigenvector $\begin{pmatrix}
0\\
1
\end{pmatrix}$ or $\begin{pmatrix... | {
"language": "en",
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How are constraint forces represented in Lagrangian mechanics? Suppose we try to obtain the movement equation for a particle sliding on a sphere (no friction, ideal bodies...). The only forces acting on the particle are its weight and - here's my problem - a force that keeps the particle attached to the sphere*. How I ... | Constraints are handled in Lagranian mechanics through either of two approaches:
1) The constraint equation is used to reduce the degrees of freedom of the system. For example, if a particle is constrained to the surface of a sphere, then the Lagrangian can be written entirely in terms of two generalized coordinates a... | {
"language": "en",
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Why is the colour of sunlight yellow? I was going through the preliminary papers of other schools and found a question that I did not know. It was "Why sunlight appears yellow?". Can anyone answer it?
| It's not. It's white.
At least, most of the time it's white. When the Sun is near the horizon, and its light is passing through ~2000km of atmosphere rather than through only ~20km, then the blueish end of the spectrum is scattered out, and the Sun looks reddish/yellow.
But when higher in the sky the Sun looks white. W... | {
"language": "en",
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Could the Bernoulli effect be causing my ceiling to come down? Very 'applied' question, but I have nowhere else to turn, so I'm asking the physics experts here: I have a carport whose ceiling is made of very lightweight paneling. I've had several times now that those panels have fallen down, without an evident reason. ... | If a downward force was applied to the panels to 'pull' them down it would be the result of a pressure difference on either side of the panel. Consider a flat plate in a wind tunnel. On each side of the plate the freestream velocity is equal, thus the static pressures are equal (assuming the flow is homogeneous and the... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/47925",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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Adiabatic process of an ideal gas derivation I am working through the derivation of an adiabatic process of an ideal gas $pV^{\gamma}$ and I can't see how to go from one step to the next. Here is my derivation so far which I understand:
$$dE=dQ+dW$$
$$dW=-pdV$$
$$dQ=0$$
$$dE=C_VdT$$
therefore
$$C_VdT=-pdV$$
differenti... | I think the last line does not follow from the previous steps. It is used to show how $\gamma$ comes in place, so I extrapolated a bit and show the next few steps:
Since
$$
\frac{C_V}{Nk_B} = \frac{C_V}{C_p-C_V} = \frac{\frac{C_V}{C_V}}{\frac{C_p}{C_V}-\frac{C_V}{C_V}}=\frac{1}{\gamma-1}
$$
Therefore,
$$
\frac{C_V}{Nk_... | {
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How does Bell's theorem rule out the possibility of local hidden variables? It seems to be common consensus that the world is non-deterministic and this is proved by Bell's theorem.
But even though Bell's experiments proved that the theory of quantum mechanics work, How does it prove the non-existent of local hidden va... | The term "local hidden variables" is a poor expression, and I haven't found the term used by John Bell anywhere. Bell showed that any theory with pre-existing spin cannot produce the right correlations predicted by quantum mechanics. Almost nobody I talk to seems to get this. Tim Maudlin is one. I highly suggest readin... | {
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Pictures of nuclear explosions some milli/nano seconds after detonation Where I can find photos of nuclear explosions just after detonation (before 5-10 ms, the shorter the better)?
| Never underestimate the power of googling.
I googled "high speed nuclear explosion photos" and got a large number of them. Here is one:
This image captures two common elements: the spikes (called "rope tricks") and an uneven surface shape
The duration of the exposure is typically 10 nanoseconds
At this stage of the d... | {
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Banach Space representations of physical systems I think most physicists mostly model physical systems as some kind of Hilbert space.
Hilbert spaces are a strict subset of Banach spaces.
Questions:
*
*Can physical systems really have non-compact topologies, as a Banach
space has?
*Does anyone have an example of ph... | Sobelev spaces (in which the norm of a function is a weighted sum of $L^p$ norms of the function and its derivatives) are Banach spaces, and they do come up in the analysis of PDE. Some physicists might regard the use of such spaces as intrinsically mathematics rather than physics.
| {
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Circular polarization of variable-frequency light by 3D cinema glasses A dominant method to obtain 3D images in the cinemas seems to be circular polarization. Separate pictures are projected with (alternating) circular polarization filters and passive glasses of the viewers block the wrong images for each eye (left-han... | It doesn't need to be perfectly half-wave.
The linear polarizer does the important part of separating the left-right eyes. It's important that there is a high level of discrimination or the image will be blurred.
But it's only necessary to partially circularize it in order to allow some head rotation. If you make the q... | {
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Where and how is the entropy of a black hole stored? Where and how is the entropy of a black hole stored?
Is it around the horizon? Most of the entanglement entropy across the event horizon lies within Planck distances of it and are short lived.
Is it stored near the singularity? How can you pack so much information i... | You can find most of entropy of black hole on the surface of Event Horizon associated with strings. The rest is associated with Hawking Radiation etc. As region inside event horizon is fully disconnected from our universe, this must be true to prevent "entropy decrease" of system (our universe).
The same duplicate entr... | {
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How come vibrations? We all know that sound sensation is produced only when sound waves reach upto us. We all know that sound waves are disturbances propagating in air, Vibration is necessary for the generation of sound, but it always forces me to ponder that how was it known or deduced that vibration is necessary for... | Sound doesn't require vibration, sound is vibration.
If you take something and make it vibrate, say by plucking a guitar string, you see it vibrate and you hear it vibrate.
The vibrating string makes the air vibrate, and that air vibration travels outward like ripples in a pond. The part that hits your ear is what you ... | {
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Quantum superposition of states: experimental verification How can somebody demonstrate the quantum superposition of states directly by other means than the double slit experiment?
And why can't macroscopic objects like a pen be in superpostion of states? Will it ever be possible to have an object like a pen to be in s... | Observation of a kilogram-scale oscillator near its
quantum ground state
Abbott, B. et al.
http://eprints.gla.ac.uk/32707/1/ID32707.pdf
Quantum Upsizing Aspelmeyer, Schwab, Zeilinger.
http://fqxi.org/data/articles/Schwab_Asp_Zeil.pdf
| {
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Relaxation time for deviations from spherical shape of a black hole's event horizon (and waves) A different question about truly spherical objects in nature (Do spheres exist in nature?) made me think of a lecture I had been at where, as I recall, it was mentioned that the most perfectly spherical object in nature is i... | How would you detect the rotation of a black hole , nothing escapes .
If the ergosphere or a black holes force is oblate is then centrifugal /centripetal force stronger than a black holes gravity !
| {
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Can the overall sign of the Minkowski metric be changed? If we take the Minkowski metric, $\eta_{\mu\nu}=(1,-1,-1,-1)$, instead of the usual $(-1,1,1,1)$, does this change the form of the Lorentz Transform? I think the standard Lorentz Transform looks like:
$$
\left(
\begin{matrix}
\gamma & -\gamma\beta & 0 & 0\\
-... | An interesting question indeed :-) Yes, you can flip the overall sign of the Minkowski metric, and in fact a lot of physicists do this! The sign choice $\operatorname{diag}(-1, 1, 1, 1)$ is conventional in fundamental quantum field theory and in quantum gravity, if I remember correctly, whereas $\operatorname{diag}(1, ... | {
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Gravity in other than 3 spatial dimensions and stable orbits I have heard from here that stable orbits (ones that require a large amount of force to push it significantly out of it's elliptical path) can only exist in a three spatial dimensions because gravity would operate differently in a two or four dimensional spac... | One brief point to add to the answers posted above, even though I can't pretend to understand all the math:
As far as I know, orbits in 2D are stable in the sense the orbiting body does not escape or collapse to the primary. See e.g.
https://www.reddit.com/r/askscience/comments/q8fmo/what_would_orbits_look_like_in_a_2d... | {
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Is 't Hooft's Determinism based on the holographic principle? Does 't Hooft's determinism work need the holographic principle in order to work or is it just an extension of his work?
| Determinism was a theme in 't Hooft's original paper on holography, and holography is a recurring theme in his papers on hidden variables e.g. http://arxiv.org/abs/quant-ph/0212095 section 2, http://arxiv.org/abs/gr-qc/9903084 section 8. The idea seems to be that quantum mechanics would emerge alongside gravity and the... | {
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Is it possible for an object to stop sinking after a while? Suppose you drop an object into a body of fluid (on a planet with constant gravity). Suppose the fluid is pure (as in, there are no solid granulates or bubbles present in it), and finally suppose that there are no waves in the fluid, and that its density is co... | I see this is a follow-up post to Suppose a hollow metal sphere filled with helium is dropped in a body of water
Well, the situation you are describing is possible if the object in question can change its average density while in the water. It will stop sinking when $\rho_\text{average} = \rho_w$.
In fact, there's a ve... | {
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Crystal momentum and the vector potential I noticed that the Aharonov–Bohm effect describes a phase factor given by $e^{\frac{i}{\hbar}\int_{\partial\gamma}q A_\mu dx^\mu}$. I also recognize that electrons in a periodic potential gain a phase factor given by $e^{\frac{i}{\hbar}k_ix^i}=e^{\frac{i}{\hbar}\int k_idx^i}$. ... | Because crystal momentum and the vector potential appear together, introducing the vector potential changes the conserved quantity from just crystal momentum to crystal momentum + electromagnetic momentum.
| {
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What is the change in flux through a loop that has been rotated? We have a number of field lines perpendicular to one loop of wire with an area $A = 10\textrm{ cm}^2$. The magnetic field is$B= 7.2\times10^{-5}\textrm{ T}$.
You turn the loop and the flux decreases with 30%. Calculate the angle at which the turn is turne... | It is $\cos \alpha$, if the angle through which the loop is turned wrt to the initial plane of the loop is $\alpha$. So, if the angle between the final plane and initial plane of the loop is $\alpha$, so is the angle between the final normal and initial normal. The final flux is therefore initial flux X $\cos \alpha$,... | {
"language": "en",
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Confused about magnetic and geographic north I'm slightly confused about the "north-seeking" pole of a magnet: does it point towards magnetic north, or is it towards geographic north?
I ask because I've been finding different explanations in different places.
| You must have seen this image of the earth mapped on a globe before, this one shows a satellite orbit:
The axis of the earth's rotation points to the north pole star and navigation calculations use its location on the celestial sphere to define latitude.
Since ancient times people defined north by the polaris star d... | {
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What exactly are we doing when we set $c=1$? I understand the idea of swapping from unit systems, say from $\mathrm{m\ s^{-1}}$ to $\mathrm{km\ s^{-1}}$, but why can we just delete the units altogether?
My question is: what exactly are we doing when we say that $c=1$?
| While the more careful approach is indeed to say the units are still there, we just don't write them as such, I prefer to think of it as DJBunk suggests:
By using certain ("god-given") constants, we are able to express the concept of time in meters just as well as seconds: Rather than say "something takes 10s", you mig... | {
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Current without Voltage and Voltage without Current? At school I've always learned that you can view Current and Voltage like this:
The current is the flow of charge per second and the Voltage is how badly the current 'wants' to flow.
But I'm having some trouble with this view. How can we have a Voltage without a curre... | When you think electricity think water.
Let's use a waterfall as an example for this analogy:
Water traveling from the high point to the low point of the waterfall is like electrons flowing through a conductor. That is the current: current $\equiv$ flow.
Voltage by definition would be the "difference of the potentials"... | {
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Ways to create controlled small bubbles in water within plastic tubing What is a practical way in an engineering or physics laboratory to create bubbles of a specified size in water within plastic tubing? The tubing is a few mm inner diameter. We'd like to make bubbles smaller in size than the diameter, for example 1/... | Bubble nucleation is largely controlled by the surface features of the material, the type of gas being used, impurities, temperatures and partial pressures. A quick search came up with this reference, which explores bubble formation in order to understand the process well enough to prevent formation. My immediate thou... | {
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Could negative dimension ever make sense? After some quick check I found that negative dimensions are not used. But we have negative probability, negative energy etc. So is it so likely that we won't ever use negative dimension(s) ?
Update
I understand there're also dimensions that are not integers e.g. dimension 1½ (?... | The infinite lattice is a fractal of negative dimension: if you scale the infinite lattice on a line 2x, it becomes 2x less dense, thus 2 scaled lattices compose one non-scaled. If you take a lattice or on a plane, scaling 2x makes it 4x less dense so that 4 scaled lattices compose one non-scaled, etc.
| {
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Is it possible for a physical object to have an irrational length? Suppose I have a caliper that is infinitely precise. Also suppose that this caliper returns not a number, but rather whether the precise length is rational or irrational.
If I were to use this caliper to measure any small object, would the caliper ever ... | If you are talking about real, physical objects, then your question collapses completely, because such objects are composed of particles which have no definite positions and momenta according to Heisenberg's uncertainty principle.
So lets stick to a stick in classical mechanics, then your caliper can return irrational... | {
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Finding orbital eccentricity I have this problem: They give me, from a satellite that is in orbit in earth, a value for the period, and the closest height to earth surface, the ask me what the eccentricty of the orbit is. I have no idea how to do this. I've tried using Binet's equation, and the equation that comes for ... | You're trying all of the right things, but the problem is actually much simpler---you just need to use better relations for this problem. In particular, think about kepler's law of orbital periods; and some of the general ellipse equations, like:
$r(\theta) = \frac{ a \, (1 \, - \,e^2) }{1 \, - \, e \cos \theta}$
(whi... | {
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Why can I add the Atomic form factors in the calculation of the Diamond Structure factor When trying to calculate the structur factor for diamond I came across the calculation on the wikipedia. In the calculation they just add up the atomic form factors of alle the atoms in the unit cell to calculate the structure fact... | We need to get some terminology straight first: "Diamond structure" in solid state refers to a way of arranging atoms in a crystal. That does not necessarily mean that the compound we are talking about is diamond, the carbon compound. For example, silicon also crystallizes in the diamond structure.
When atomic form fac... | {
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Can low-gravity planets sustain a breathable atmosphere? If astronauts could deliver a large quantity of breathable air to somewhere with lower gravity, such as Earth's moon, would the air form an atmosphere, or would it float away and disappear? Is there a minimum amount of gravity necessary to trap a breathable atmos... | Gravity is a major factor in planets retaining atmospheres over the eons. But there are other factors that must be taken into consideration to consider the volatility of an atmosphere.
Solar wind is the main factor of erosion on any atmosphere. But a healthy magnetic field can deflect most of the solar radiation and de... | {
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Equivalence principle question I understand the equivalence principle as "The physics in a freely-falling small laboratory is that of special relativity (SR)." But I'm not quite sure why this is equivalent to "One cannot tell whether a laboratory on Earth is not actually in a rocket accelerating at 1 g".
| The best entry level introduction to the equivalence principle I have found to date is found here. As it explains in the article, one of the key items that is general not well understood about the equivalence principle and its relationship to the concept of tidal forces.
If one can imagine a freely falling elevator ... | {
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Theoretical power limit of nuclear bomb Is there any limits of power or power to mass (or any other) limits for nuclear bombs?
I found this wiki article: Nuclear weapon yield: Yield limits. Is the information provided is correct? If yes, from where this limits come from?
| The sun and all other stars are in effect thermonuclear bombs. If they get heavier than about 10 times the mas of the sun they eventually blow up as a supernova, so there is a limit to the size but it's a lot larger than anything we will ever build.
In the wikipedia article, the yield limits have to do with deliverabil... | {
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Wick Rotation, interpretation of $\bar{p}^2$ vs the usual $p^2=m^2$ Suppose we use the metric $(+,-,-,-)$ thus the momentum squared is
$p^2 = p_0^2-\vec{p}^2 = m^2>0$
Defining $p_E:=\mathrm{i}\cdot p_0$ and $\bar{p}:=(\,p_E,\vec{p})$ with Euclidean norm $\bar{p}^2 = p_E^2+\vec{p}^2$.
Here's my question:
If we plug ... | Yep. You've defined $\bar{p}$ such that $\bar{p}^2$ will have the opposite sign from $p^2$. Notice for instance that the spatial components of momentum, $\vec{p}^2$, have a negative sign in your definition of $p^2$ but a positive sign in your definition of $\bar{p}^2$.
Of course, the sign doesn't change whether somethi... | {
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Falling Electron Suppose there are two objects in the universe. Earth, with a gravitational acceleration of g = 9.8m/s/s, and a typical electron.
The electron is dropped from a certain height, say 1000m above the Earth's surface.
The initial energy of the electron is only the potential energy, $mgh = m_eg\times1000$... | A falling electron is basically a miniscule electric current, and will create a circular magnetic field, which can be calculated using Ampere's Law.
As the electron accelerates this magnetic field also grows, generating a perpendicular electric field, which can be calculated using Maxwell's Equations.
At this point you... | {
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Electric Field due to a charged sphere Suppose we have a spherical surface with a surface charge density varying as $cos(\theta)$. Apparently one can find the electric field both outside and inside such a spherical surface by superposing the fields of two slightly offset charged spheres with uniform volume charge densi... | To be honest, I just learned about all this myself in the last months, so I am not sure whether this is actually correct.
Since you have this spherical symmetry, I think that you need spherical harmonics. They are orthogonal functions, think of them as a Fourier series on the surface of a sphere.
Your charge density $\... | {
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How to get "complex exponential" form of wave equation out of "sinusoidal form"? I am a novice on QM and until now i have allways been using sinusoidal form of wave equation:
$$A = A_0 \sin(kx - \omega t)$$
Well in QM everyone uses complex exponential form of wave equation:
$$A = A_0\, e^{i(kx - \omega t)}$$
QUESTION... | As user1104 commented, you use Euler's identity:
$$ e^{ix} = \cos(x) + i \space \sin(x) $$
so:
$$ \sin(kx-\omega t) = \frac{ e^{i(kx-\omega t)} - e^{-i(kx-\omega t)}}{2i} $$
But we wouldn't normally proceed by replacing sin by this expression. Both the sin form and the exponential form are mathematically valid solution... | {
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Why does gravity assist transfer twice the planet's velocity? In orbital mechanics and aerospace engineering a gravitational slingshot (also known as gravity assist manoeuver or swing-by) is the use of the relative movement and gravity of a planet or other celestial body to alter the path and speed of a spacecraft, typ... | If you analyse the situation from the planetary frame of reference (which will essentially be the centre-of-mass frame), then the incoming probe has a velocity $U+v$ if it then does any sort of "elastic bounce" off the planet - i.e. if it loses no energy and goes back in the opposite direction - then the planet will no... | {
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Would a magnetic rod through Mars shield it from solar wind? Would a magnetic rod going all the way through Mars shield it from solar wind?
| You needn't necessarily run a rod all the way through. A wire wrapped around the circumference of Mars would do the job as well.
Since a magnetic dipole (which is basically what a bar magnet is) can be thought of as a current loop, wrapping a wire around Mars would achieve the same thing.
I have to point out though, ... | {
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How to comoving volumes depend on the evolution of the Universe? I'm reading a paper which states that
Neutron star binary merger rate at redshift $z$ per unit observer time
interval per unit volume is $\dot{n}_{m} = \dot{n}_{0} (1+z)^{2}
(1+z)^{\beta}$, where $\dot{n}_{0}$ is the local neutron star binary
merger... | In astrophysics processes that are not well understood are often modeled as power laws and that is what I believe the authors are doing here. First of all $1/(1+z)\ $ is the scale factor $a(t)\ $ from the FRW metric that describes the evolution of the universe. The case $\beta = 0$ is assuming there is no evolution Of ... | {
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In Noether's theorem, what is a "classical solution of the equations of motion"? I'm reading a book which states that:
for each generator of a global symmetry transformation, there is a
current $j^{\mu}_{a}$ which, when evaluated on a classical solution
of the equations of motion $\phi_{cl}$, is conserved. I.e.
... | The classical equation of motion can be find solving the Euler-Lagrange equation for the Lagrangian of the system $L=L(q,\dot{q})$, then EL equation states $$\frac{\partial L}{\partial q_i}-\frac{\text{d}}{\text{d}t}\frac{\partial L}{\partial\dot{q}_i},\text{ }i=1,\dots,n.$$
The conserved current $j_a^\mu$ come from t... | {
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What is mass of free up and down Quark?
*
*Quarks combine to form composite particles called hadrons, the most stable of which are protons and neutrons, the components of atomic nuclei. Due to a phenomenon known as color confinement, quarks are never directly observed or found in isolation.
*Color confinement, often... | Confinement precludes free quarks so the question is ambiguous. If you mean invariant mass the answer I think is it depends. It can’t be directly measured. In QCD quark mass as a parameter of the Lagrangian is a re-normalized quantity. The momentum scale and re-normalization scheme scale affect the answer.
| {
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What is movement through time? In general, when I think of movement through space, I think of this:
$$\frac{dx}{dt}$$
But in special relativity, we also have a concept of relative duration, which means that $t$ must have a rate of change, but with respect to what?
$$\frac{dt}{d?}$$
| This is a near duplicate of What is the speed of time? and Terry has given a comprehensive answer there. However there is one point that wasn't made in the previous question.
In special and general relativity there is an invarient called proper time, $\tau$, which is is the time measured by a freely moving observer, an... | {
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Shoot object into the Sun using minimal energy Say I want to shoot a cannonball into the Sun with minimal energy (minimal initial velocity relative to Earth).
In which direction do I shoot it?
Let's neglect Earth's gravity, if that would make things very complicated.
| If we only neglect earth's gravity, then you still have the gravity of the sun. Then you have a rotating ball alround the sun.
What you are saying is the same as if you say there is no earth, only a cannonball or another model would be: Which how much energy would you 'shoot' earth, so that it leaves the orbit and fall... | {
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How to judge whether a symmetry will be spontaneously broken while only given a Hamiltonian preserving this symmety As asked in the title, is Hamiltonian containing enough information to judge the existence of spontaneously symmetry breaking?
Any examples?
| In general, you should look to solve the potential for a function that gives a minimum. Does this minimum of the potential respect the symmetry? If not, you are very likely to find an anomaly. The classic example of this is the minimum of the higgs potential not respecting the gauge invariance of the SU(2) x U(1) fi... | {
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Why and how does symmetry work in circuits? Why symmetry work in circuits? In my book there is no mention explanation as such for symmetry arguments and circuits. But there are circuits that are very difficult to solve without symmetry. Also I have heard that they save a lot of time. Can anyone please tell me why symme... | Imagine you have an electric circuit which is in the form of a square mesh ABCDA $4\times 4$ say, and in each branch you have a resistor of value R. Then you connect a battery of emf =E at two diagonally opposite points such as A and C, say. If you draw the diagram yourself you will have a picture of it. Here is an e... | {
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What's the exact gravitational force between spherically symmetric masses? Consider spherical symmetric$^1$ masses of radii $R_1$ and $R_2$, with spherical symmetric density distributions $\rho_1(r_1)$ and $\rho_2(r_2)$, and with a distance between the centers of the spheres $d$. What is the exact force between them? I... | For spherically symmetric bodies the point-mass approximation is actually exact as a description of the centre-of-mass force on the spheres. This is due to Gauss's law in its gravitational form: the flux of the gravitational field through a concentric spherical surface is proportional to the mass inside it, or mathemat... | {
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Is velocity quantized? If velocity is not quantized, then do moving objects have 'infinitely decimal place' velocities which we just can't measure to infinite decimal places? From my understanding the quantization of velocity in Bohr's model is just a consequence of the quantization of angular momentum.
| Let us talk about the first question, first: Can "moving objects have infinitely decimal place velocities?"
Most certainly yes!! The simplest example is the motion of a particle on a circular orbit of radius R. Let us assume the radius of the circle is $R=10m$ exactly (as exact as we can make it,) and let the partcle ... | {
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Difference between torque and moment What is the difference between torque and moment? I would like to see mathematical definitions for both quantities.
I also do not prefer definitions like "It is the tendancy..../It is a measure of ...."
To make my question clearer:
Let $D\subseteq\mathbb{R}^3$ be the volume occupie... | Torque is $\vec{F} \times \vec{r}$ but in this case $\sum{\vec{F}}$ may not be equal to zero. Where as in case of moment the two equal force acts in tow different side, So $\sum{\vec{F}} = 0$. I think this is the difference.
| {
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Please explain this statement about Lorentz transformations I'm reading Sternberg's Group Theory and Physics. I have a question about chapter 1.2 Homeomorphisms.
Background:
A Lorentz Metric is defined as $||{\bf x}||^2=x_0^2-x_1^2-x_2^2-x_3^2$
And a Lorentz Transformation $B$ as one which satisfies $||B{\bf x}||^2=||... | If $C$ doesn't change the time component then it is just a spatial rotation!
To show this mathematically we can use $\boldsymbol{e}_{0}$ to construct a projection operator that projects down to the space orthogonal to $\boldsymbol{e}_{0}$:
$$ \Pi = \mathbb{I} - \boldsymbol{e}_{0} \otimes \boldsymbol{e}_{0} $$
Then the ... | {
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How are X-rays focused? Specifically in XRD. Well do they even focus X-rays in XRD? I read in a government website that reflecting an x-ray from a parabolic mirror followed by a reflection from a hyperbolic mirror results in focusing the x-ray, but this was for astronomical purposes. I was wondering if in x-ray diffrac... | Technology has evolved a bit compared to what was described by Martin Beckett. Many powder diffractometers still use the setup he describes, but mirrors are becoming more and more common at laboratory powder diffractometer sources. However, these mirrors do not aim to focus the beam, they collimate the beam (try to mak... | {
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Does gravitational force attract bodies with mass or with energy? On my textbook is written that gravitational force is the force that attracts bodies with mass. But I've seen on a book that It actually attracts bodies with energy. I'm having a class tomorrow and I would like to know some argumments to use with - again... | In Newtonian gravity (what your textbook is talking about), the gravitational field couples to mass density, $\rho$. This is seen in the Poisson equation:
$$\nabla^2 \phi =4\pi G\rho$$
where $\phi$ is the gravitational potential. The argument you heard about energy comes from General Relativity, which is a more advance... | {
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Why doe we not get a shock on induction cooker? In induction cooking, eddy currents in cook-pot cause heat to be produced. But why do we not get a shock?
Also, why is it that current is converted to heat while it has a good conductor(say, steel) to flow through?
I went through Why is the lid of the cookware kept on in... |
why do we not get a shock?
Because the electric resistance of a human body is by orders of magnitude higher than the resistance of the steel pot.
why is it that current is converted to heat while it has a good conductor(say, steel) to flow through?
According to Maxwell–Faraday equation, changing magnetic field crea... | {
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Equivalence between QFT and many-particle QM My understanding from my QFT class (and books such as Brown), is that many-particle QM is equivalent to field quantization. If this is true, why is it not an extremely surprising coincidence? The interpretation of particles being quanta of a field is -- at least superficiall... | It took a lot of work to show that the computational power of topological quantum field theories and the computational power of quantum computers were equivalent. See Friedman, Kitaev, Wang and Friedman, Larsen, Wang. If your book's claim had been mathematically rigorous, this equivalence would have taken one line.
In... | {
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Why is electric potential scalar? I can't conceptually visualize why it would be so. Say you have two point charges of equal charge and a point right in the middle of them. The potential of that charge, mathematically, is proportional to the sum of their charges over distance from the point ($q/r$). But intuitively, my... | From a more general point of view, electric potential is not a scalar, but a component of a 4-vector (http://en.wikipedia.org/wiki/Electromagnetic_four-potential ) - it is not invariant with respect to boosts.
Edit: in answer to question:
Well the potential is just one component of the four-vector. Not the four-vecto... | {
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Constructing a Toffoli gate with 2-and 1-qubit gates? I'm looking through Nielsen & Chuang's book on quantum computation and information and in part of it he says that any $C^2(U)$ gate can be constructed from two qubit and one qubit gates. I can't figure out how to do this, or how to verify it (fig 4.8 in his book)
I'... | Quantum gates act linearly, so the operation of these two circuits on any input qubits is a linear combination of their operation on the eight basis qubits $|000 \rangle,|001 \rangle, |010 \rangle \dots|111 \rangle$. To verify that these two circuits are equivalent, you only have to show that they have the same effect ... | {
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Would Oscars made of pure gold bend? Since gold is often considered "soft": If the Oscars were made of pure gold (instead of gold-plated britannium), would they bend (deform) over time?
| Solid metals are crystals, not liquids.
The way any crystal plastically deforms is by motion of crystal dislocations.
Every crystal obeys a stress-strain curve, where stresses up to a certain amount do not result in permanent deformation.
Higher stresses do result in permanent (plastic) deformation because dislocations... | {
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How to make a non-grounded conductor have equipotential? I'm studying the Method of Images and I seemed to have come to a conundrum. Method of Images takes advantage of grounded objects, (I am currently studying spheres), to set boundary conditions. However, how would one use the idea of MoI to set the potential of a c... | Regardless of whether it is grounded, if there were a nonzero electric field inside a conductor, it would push the charge carriers around until there were no longer forces on them.
Thus: A perfect conductor, grounded or isolated, will have a surface (and volume) of equal potential, and the electric field inside will be... | {
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Definition of Free field or Noninteracting field In QFT we can write a Hamiltonian operator for a free field. So, what is a free field/ noninteracting field?
| A quantum field theory is defined by the connected n-point functions of its observables. (One can recover the n-point functions from the connected ones, and from the n-point functions you can reconstruct the Hilbert space and all the operators.)
A field is free if its connected $n$-point functions vanish for $n > 2$. ... | {
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Empirical bound on sum of electron and proton charge Followup to "Why do electron and proton have the same but opposite electric charge?".
It is argued that even a tiny residual charge would result in huge amounts of electricity in bulk matter, everything would be different, etc. I do not find that a convincing answer:... | In $\beta$ decay a neutron turns into a proton, an electron and an electro antineutrino. So if the proton and electron charge were not the same either the neutron must originally carried a net charge or the antineutrino must carry a charge.
For the neutrino current limits are reported by the particle data group as less... | {
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Estimate number of hairs on human head A technique of vital importance at all levels in physics is estimation. This is obvious from the first chapter in any introductory physics textbook, but is also related to the working physicist. Checking orders of magnitudes during research presentations is common practice - I've ... | I'll take a go at it - as with the piano tuners in Chicago, I take the approach as if I have "no facts to go on". Your head has a surface area of $4\pi r^2$, the fraction of it which is covered with hair is $\gamma$. The density of hairs per unit area is $\sigma$, and the number of hairs is then
$N=4\pi r^2 \gamma \sig... | {
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Foucault pendulum The equations of motions for a Foucault pendulum are given by:
$$\ddot{x} = 2\omega \sin\lambda \dot{y} - \frac{g}{L}x,$$
$$\ddot{y} = -2\omega \sin\lambda \dot{x} - \frac{g}{L}y.$$
What are the equations describing $\dot{x}$ and $\dot{y}$?
| If I had to take a reverse-engineering guess, I would say that you want to solve the system by creating an autonomous system. It goes like this:
Define $u=\dot x$ and $v=\dot y$ (similar to a substitution). Then, your equations read:
$$\dot{u} = 2\omega \sin\lambda v - \frac{g}{L}x$$
$$\dot{v} = -2\omega \sin\lambda u... | {
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Observable (in principle) signal of a bubble collision in eternal inflation Assuming a scenario of eternal inflation with a lot of "bubble universes" expanding, Lenny Susskind explains here that a potential signal of a collision of our universe with another bubble could be a spot of warmer or colder temperature in the ... | See http://arxiv.org/abs/0810.5128 for the gory (and they are very gory!) details.
Basically, it's unlikely that the inflaton field has the same value in the two bubbles. When the bubbles collide, the bubble with the lower energy inflaton field will see the collision as a hot spot, and the bubble with the higher energy... | {
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Why can't we store light in the form of light? We can store cold (ice), heat (i.e. hot water bag) and electrical charge (batteries). We can even "store" a magnetic field in a magnet. We can convert light into energy and then, if we want, back to light. But we can't store light in form of light in significant amounts. ... | We can store light - just for very small amounts of time. I'm no physicist though, so perhaps this link isn't what you intended?
http://news.bbc.co.uk/1/hi/sci/tech/3308109.stm
| {
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What causes insects to cast large shadows from where their feet are? I recently stumbled upon this interesting image of a wasp, floating on water:
Assuming this isn't photoshopped, I have a couple of questions:
*
*Why do you see its image like that (what's the physical explanation; I'm sure there is an interesting ... | *
*The mechanism at play here is surface tension. The cohesion of the molecules of water is what keeps the wasp afloat. Due to this cohesion, the surface of the water behaves like a membrane and is curved inwards. The light rays that would be refracted from the perfectly flat surface are now incident at an altered ang... | {
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Gamma Ray LASER Theory and Technology I am aware that a similar question has been asked by someone else in the past, but in a very general form. Due to the physics interest and technology, in this question I put emphasis on the detail of the physics part and the question becomes very specific.
We know the power of vis... | For gamma-ray wavelengths a much better alternative are Free Electron Lasers, since their gain medium is the Bestrahlung and synchrotron electron radiation inside the undulators. They also have the benefit of not being constrained to a nuclear energy state, and they can operate on a range of wavelengths
| {
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Conservation of energy in Lenz's law When we bring opposite poles of two magnets together, they attract each other (or vice versa). Now, we can say that the kinetic energy gained by the magnets is due to the attractive force.
Similarly, we say in Lenz's law that if the north pole of magnet is moved towards a solenoid (... | Lenz law actually is that induced current always tends to oppose the cause which produce it.So in order to do work against opposing force we have to put extra effort. This extra work leads to periodic change in magnetic flux hence more current is induced. Thus the extra effort is just transformed into electrical energy... | {
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What was the first ionization radiation? While trying to make somewhat of a timeline of the history of ionizatig radiation, i am wondering about the following questions:
The first photoelectrical effect was found 1839 by Alexandre Becquerell - the photoelectrical effect and therefore UV-light, would be the first ioniza... | X-rays were discovered in 1895, a year before Becquerel discovered Uranium's radiation (1896). And, while it is not ionising, Hertz worked on radio waves as early as 1886, following theoretical work by Maxwell in 1861.
Here are some links:
A list of the discovery dates of particles (or rays, before they were considered... | {
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Why is electrical energy so difficult to store? Does anyone know a general answer to these questions? (I've asked them together because they're all pretty related, it seems.)
*
*Why is it that we find electrical energy so difficult to store? Do we just find energy difficult to store generally? (...surely not, we can... | Yes, electrical energy is difficult to store.
In my opinion for the following reasons:
It dissipates fast with explosive reactions in specific situations since it depends crucially on conductivity which can easily be affected by weather or accident. The more electrical energy is stored, the greater the possibility of ... | {
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nuclear fission and half life Why is the alpha, beta or gamma decay of an unstable nucleus unaffected by the chemical situation of an atom, such as the nature of the molecule or solid in which it is bound? The chemical situation of the atom can, however, have an effect on the half life in electron capture. Why is this ... | The cross-section for electron capture depends (among other things) on the likelihood that there is an electron in proximity to a proton.
Orbital states with angular momentum other than 0 (that is all states except s-states) have a node at $r=0$ and because the nucleus is several order of magnitude smaller than a typic... | {
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Finding the force of friction of a moving object and its change when it accelerates to a constant speed If an object is moving at a constant speed the force of friction must equal the applied (horizontal) force, and for it to be accelerating or decelerating, the force of friction and the applied force must be unequal. ... | The object will continue accelerating to just below light speed (speed limit of the universe), but only in a vacuum. Unfortunately I only know a little about air resistance, but apparently the faster an object travels the more the atmosphere tries to resist the object. This is where aerodynamics comes in.
I'm sure you... | {
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Bat hitting a ball When a bat hits a ball, consider two cases:
1) The batsman goes for a defense, and stonewalls it, to reduce its speed.
2) the batsman goes for a shot, e.g. a home-run, etc.
in which case will the bat have the highest chance of breaking due to the impact?
And am I right in assuming that the force on t... | A good swift swing of the bat changes the ball's momentum the most. Recall that force F = change in momentum. According to plain simple Newton's laws, this puts the greatest force on the bat at the point of contact. As fast as interatomic forces can convey stresses and changes of motion, that impact along with other... | {
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Are two waves being in phase the same as saying that the two waves are coherent? If two waves are coherent, is it the same as them being in phase? Please correct if I'm wrong.
| Let's place your question in the frame of a Mach-Zehnder interferometer so we can define some important variables. Here is a hastily drawn Mach-Zehnder from MS Paint.
The electric field $E_{i}$ incident on the first beam splitter $BS_{1}$ is split into electric fields $E_{a}$ and $E_{b}$. If we assume the mirrors are... | {
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What fraction of peak horsepower do typical 4 door passenger vehicles use? I was surprised when I looked at the power rating of the engine used on a Humvee. It's only ~190 horsepower, which is exceeded by many sedan engines.
So an obvious question is why doesn't my Camry SE burn more gas than a Humvee and I think it's ... | Find a long straight hill, take your foot off the gas and see what terminal speed you reach.
From the rate of descent and the slope you can work out the power (in this case potential energy) required to maintain that speed.
For my typical modern aerodynamic small car I think it worked out at around 30-35HP to maintain ... | {
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Schriffer Wolff Transformation - for first order change in eigenvalues Step 1
Let me formulate the problem to convey my notation.
I have a matrix $A$ which is hermitian - and is diagonalisable by a transformation
$$ U_A A\,\,U_A^{-1} = A_{diag}$$
Now the matrix is changed, using the small parameter $\lambda$. Therefor... | The Schriffer Wolff transformation was developed to remove the effect of the effect of the perturbation term to the first order by performing a similarity transformation on the hamiltonian. $\tilde{H}=SHS^{-1}$. I am giving you a paper where it was first developed...
http://link.aps.org/doi/10.1103/PhysRev.149.491
| {
"language": "en",
"url": "https://physics.stackexchange.com/questions/56748",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "2",
"answer_count": 1,
"answer_id": 0
} |
Potential Inside Conducting Cube A cubical box with sides of length L consists of six metal plates. Five sides of the box { the plates at $x=0, x=L, y=0, y=L, z=0$ - are grounded. The top of the box (at z = L) is made
of a separate sheet of metal, insulated from the others, and held at a constant potential $V_0$. Find ... | You have to solve the Laplace equation with the given boundary conditions. In cartesian coordinates, the solution has the form V = X(x)Y(y)Z(z).
| {
"language": "en",
"url": "https://physics.stackexchange.com/questions/56806",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "4",
"answer_count": 3,
"answer_id": 1
} |
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