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In Weinberg's Lectures on Quantum Mechanics (pg 31), he said that the commutator relation
$$[L_i, v_j]=i\hbar\sum_k \epsilon_{ijk}v_k$$
is true for any vector $\textbf{v}$ constructed from $\textbf{x}$ and/or $\nabla$, where $\textbf{L}$ is the angular momentum operator given by $\textbf{L}=-i\hbar\textbf{x} \times \n... |
If the electric field due to a point charge varies as $r^{-2.5}$ instead of $r^{-2}$, then would the Gauss Law still be valid?
I infer that the $r^{-2}$ term in the Electric field comes as a result of solid angle in 3 dimensions. Would this be valid in higher dimensions? The flux would depend on the spatial dimension... |
A beam of coherent unpolarised light is split into two. One is polarised horizontally, the other vertically. Will there be a phase difference between the two beams?
|
In a question, the left plate of a capacitor carried a charge Q while the switch was off;
When the switch is closed and the current stops flowing again, you're supposed to find the final charge on the right plate.
It's apparently done this way(say the electric field $= E$ ) ;
$$E = E_1 + E_2 \ \ \ \ \ \ \ \ \ \ \ \ $$... |
Consider a rigid wall somewhere in free space. Now imagine two balls of the same mass and same speed headed towards the wall from two opposite directions. Now they go on to hit the wall and rebound back with the same speed as before (elastic collision). The wall does not move cause of equal and opposite forces. Now if ... |
I fill coolers in my house with a pipe connected to a tap, as soon as it is full i place a thumb on the open section of the pipe effectively shutting off the outflow of water. Keeping my thumb in place requires force against the pressure exerted by the water, But i have noticed when i go to the tap and turn it off the ... |
Often when describing entanglement in an informal way, we talk about perfect correlation or anticorrelation of measurements of faraway particles, but I don't see how such correlation is particular to entanglement. Imagine I had a black ball and a white ball, I put them into two separate opaque boxes and I mix them up. ... |
I was looking at why fusion reactors need to get so hot and the internet said that it needed the momentum to overcome the repulsive forces of two atoms. Is heating the atoms the only way to give it enough momentum? Could we spin the two atoms In opposite directions instead and bring them close to let the angular moment... |
I have viewed the question : An electric dipole placed in a non-uniform electric field
But that is a different one from my query. I also viewed its answer.
My question is if an electric dipole is placed in a non-uniform electric field will it also do simple harmonic motion like an electric dipole does in a uniform elec... |
In the figure shown above, there's a block, lying on a smooth plank, with uniform distribution of mass and weighs 3 kg and is of length 30 cm. Pulleys and strings are ideal. The question asks for the force that the "10 cm part" of the block exerts on the "20 cm part". The question seems easy enough and we can find out... |
I am reading this paper, nature.com/articles/s41567-018-0347-x, which is about the generation of high-dimensional entanglement using two non-commuting variables, frequency-bin and time-bin.
On page 7 in this paper, they say that a time-frequency product is higher than the EPR limit of unity so both variables are allowe... |
I know in a ramp this isn’t true but there, the path is one dimensional.
However, here after the rolling ball goes off of the edge with a certain angular velocity, is the object's angular velocity constant? I think it is constant as no net torque is being produced.
So is it correct to say that a rolling ball and non r... |
How work function and surface and lattice binding energy are related in a metal?
I need to estimate with SRIM the changes of the work function of a gold slab after bombardment of ions, but SRIM reports the surface and lattice binding energy (see this site): how can I deduce the work function?
|
I am trying to prove that the angular momentum component operator ${L}_i$ commutes with any function of ${r}\equiv \sqrt{{\textbf{x}}\cdot{\textbf{x}}}$, i.e.
$$[L_i, f( r)]=0.$$
I first worked out that $L_i$ commutes with $\textbf{x}\cdot\textbf{x}$, i.e. $$[L_i,\textbf{x}^2]=0.$$
I then expanded $f(r)$ in terms of... |
I got a new LG 1.5 ton AC(Air conditioner) . It's summer time here and the temperature reaches approx 40 degree Celsius at peak time. And it's working quite satisfactorily. But in the last two weeks it rained twice lightly. After each rain the outside temperature dropped approx to 35 Celsius. Then I noticed that the AC... |
In the non-relativistic region of the space, with matter of mass $M$, and volume $V$ the density is given by
\begin{equation}
\rho=\frac{M}{V}
\end{equation}
If we encounter an equation, for example,
\begin{equation}
F=F(\rho,...)
\end{equation}
we simply substitute the first equation. However, if we want to consider r... |
I watched a documentary showing how NASA applied water droplets to absorb the huge amount of sound energy when the rocket is ignited at launch. So, how come billions of rain drops don't seem to mute or soften the sound of thunderclaps?
|
These two statements seems contrasting:
Electrons in the outermost shell are loosely held to the nucleus.
In a metal electrons move freely in all directions.
I am very confused as to its position.
How can it move freely when there is a complex system of protons, other electrons etc. around it?
Please explain.
Thank... |
I am told a $\mu$ meson with an average lifespan of $2 \times 10^{-6}$ is created in the upper atmosphere at an altitude of $6000m$. When it is created, it has a velocity of $0.998c$ in a direction towards the Earth.
What is the average distance that it will travel before decaying, as determined by an observer on eart... |
If we have a theory with gauge group $SU(3) \times SU(2)$ with a set of six complex scalar fields grouped in $\Phi=\begin{pmatrix}
a & d\\
b & e\\
c & f
\end{pmatrix}$, where, for instance, the fields b and f acquire a VEV, how can we write the mass terms for the gauge bosons?
I know that in the Standard Model this can... |
Suppose we have two different objects, one denser than the other. In short, what I mean is that one object is bigger than the other but they have the same mass. Now why does it take different efforts in raising those two objects to a same height from the same level even though the force required to lift the two object... |
Why does the partition function include current term in free scalar field
$$Z[J] = \int \mathcal{D}\phi \, e^{i \left(S[\phi] + \int d^4x \,J(x) \phi(x) \right)}~$$
|
I was dealing with a problem, which said that,
Supposedly Hamiltonian of a conservative system in classical mechanics is $\omega xp$, where $\omega$ is a constant, and $x$ and $p$ are the position and momentum operator respectively. The corresponding Hamiltonian in quantum mechanics is________.
To solve the problem,... |
What is the difference between toughness and hardness? I came to know about some materials that have low toughness but high hardness such as ceramic tiles and glass.
I want to know if it is true that high toughness also implies high hardness.
|
Systems with a gravity dual might experience the spontaneous breaking of a symmetry. In such a case, the dynamics of the dual QFT is determined by the Goldstone bosons.
But, what do the Goldstones look like in the gravity dual?
Take for example Sec. 3 of 1904.11445. Here translations along the $x_I$-direction are broke... |
I've been thinking about this question for a while and I didn't get to any conclusion yet.
When an aircraft flies faster than the speed of sound (specifically when it achieves it) a cloud of condensed water becomes visible. Like in the figure below:
I know that as the speed of the object increases to the sonic velocit... |
I've been wondering about this for a while. So let's assume a ship accelerates at 1 million G for an extremely short period of time, such that its total velocity change was (say) 1cm/s. Would the ship or its passengers suffer damage, and if so how much? Is there any level of velocity change where immense accelerations ... |
I have a question about Spin-Orbit Coupling, Zeeman effect and Fine Structure. I'll try to explain what I don't understand and want to know as good as I possibly can. This here is a sketch of how I understand orbital, intrinsic, and total angular momentum and their respective mangetic moments (and their components):
... |
I hope to compute a functional integral $Z=\int \mathcal{D}\phi\,\, e^{-S[\phi]}$ with an action
$$S[\phi]=\int d^2x \sqrt{g}\Big((\nabla \phi)^2+\frac{1}{\lambda}M^2(x) \phi^2\Big)$$
The scalar field $\phi$ is defined on a two-dimensional curved sphere. The mass-like term $\frac{1}{\lambda}M^2(x) \phi^2$ depends expli... |
I've stumbled across an interesting extra question in an old exam. In my own words:
Consider the Magnetization of the 1D Ising model $$H=-J\sum_iS_{z,i}S_{z,i+1}-B\sum_iS_{x,i}$$ at $T=0$. We know that for $B=0$ the magnetization $M_z$ is finite. How does the magnetization behave for large $B$?
It's obvious that all ... |
Equations of motions of
$$
\mathcal{L}[\phi,x]=\phi[x]
$$
where $\phi:\mathbb{R}\to\mathbb{R}$.
The Euler-Lagrange equations are:
$$\partial_\mu\frac{\partial \mathcal{L}}{\partial(\partial_\mu\phi)}=\frac{\partial \mathcal{L}}{\partial\phi}$$
Applying this to the $L[\phi,x]$, I get:
$$
\frac{\partial \mathcal{L}}{\par... |
I am working through VI Arnold "Mathematical Methods of Classical Mechanics". One of the first problems, after defining Galilean structures and Newton's equation of motion, it is to prove 'For a mechanical system of two points with initial velocity zero, the points will remain in the line that connected them in the beg... |
Dark matter does not interact with the electromagnetic force, however does interact with the gravitational force. Do we know if there are any big ‘clumps’ (like a star) of dark matter? If they exist (or could exist) would their collision with a black hole or neutron star give out gravitational waves?
|
I have been taking time this summer to try and understand what "reasons" some flat earthers offer for their beliefs for a "science and the public" class. One of the oldest and most obvious observations that proves a sphere-like earth is the "sinking ship." In order to verify this observation, modern experiments (see h... |
Say you have a charged black hole solution in General Relativity. I am wondering if the variation of the electromagnetic action with respect to the induced boundary metric is $0$?
I am asking because if this is the case then the electromagnetic action does not contribute to the Brown-York quasi-local stress tensor.
Cou... |
I'm just going through old protocols of oral exams students wrote up. One student writes that he was supposed to derive the "non-linear limit" of the Dirac equation during the exam.
Is there a nonlinear limit of the Dirac equation, that I've never heard before, or is the student just referring to the well-known non-rel... |
Let's say I have a pendulum hanging from a bar that's fixed to the wall of an elevator. Assume that there's no air or anything inside the elevator, that the string of the pendulum is very light and that the bob of the pendulum is more or less a heavy point mass. After setting the pendulum in motion, the elevator starts... |
For the harmonic oscillator we have $\sigma_x \sigma_p = \hbar(n+1/2) $ and by the uncertainty principle $\sigma_x \sigma_p \geq \frac{\hbar}{2}$.
In one of the exercises I was doing I was asked to comment on this result. This makes me think that I am missing something special, as the most I can say is that
there is s... |
I was reading about black holes and I've found part saying that black hole is a point and anther saying that black hole can rotate. However the points are dimensionless, so they can't rotate - How can black hole rotate then? Can non rotating black hole start rotating?
I rather don't know too much about physic so even b... |
I don't understand how astronomers estimate the redsfhit of a cluster. As far as I understand a cluster of galaxies is something really "big", so I expect that different galaxies in the cluster have different redshifts.
The redshift of the cluster is some average of the redshift of every galaxy in the cluster?
|
Lets say the temperature is Y, and we want to observe an electron but if we do we will use a high energy light wave which will make it act more like a particle, so why dont we just lower the temperature to X where after the high energy light wave touches it, it would be like an un-observed electron at temperature Y
Was... |
In a textbook I read the following (emphasis added):
Division of amplitude is a method of achieving interference using two waves that have come from the same point on a wavefront. Each wave has a portion of the amplitude of the original wave. In order to achieve interference by division of amplitude, the source of lig... |
I am aware of two definitions of canonical transformations which I state below.
Definition $1$ We go from old set of $\{q_i,p_i,t\}$ of $2n$ phase space variables to a new set $\{Q(q_i,p_i,t),P(q_i,p_i,t),t\}$ of $2n$ phase space variables such that the determinant of the Jacobian of the transformation is $+1$ and the... |
The law of reflection (that the angles of incidence and reflection are equal) can be derived directly from Maxwell's equations, or from Fermat's principle. However, reflection gratings completely defy this law, and from light incident at a fixed angle comes a whole diffraction pattern - light reflected at a range of di... |
Drawing parallels between electrons and holes in semiconductors, and electrons and positrons in Dirac equation is certainly useful in the context of learning/teaching the quantum field theory methods, since it allows drawing parallels between the nearly identical formalisms. I am wondering however, how far/literally th... |
In the following book (page 19 / equation 2.7 --- part of the free preview at google-books), we have the parametrization general volume element, defined as
$$
d\mu_p=\sqrt{-\det G_{\alpha\beta}}d^{p+1}\sigma
$$
where
$$
G_{\alpha\beta}=g_{\mu\nu}(X)\partial_\alpha X^\mu\partial _\beta X^\nu
$$
For instance, if $p=0$, ... |
Can a non rotating black hole start rotating? Intuitively it is not possible, but intuition often leads to wrong conclusions.
I have only basic physic knowledge, however I like to wonder about relativity, quantum mechanics e.t.c, so even not comprehensive answer would be great for me.
|
Problem: A rope wraps an angle θ around a pole. You grab one end and pull with a tension $T_0$ . The other end is attached to a large object, say, a boat. If the coefficient of static friction between the rope and the pole is $\mu$, what is the largest force the rope can exert on the boat, if the rope is not to slip... |
I have a old toy helicopter which is currently not working. It has coaxial blades in order to lift it. It has a fixed shaft. Both blades have separate motor which helps them to rotate. I have very little knowledge about this field but while doing my research on this i found on Radio-controlled helicopter (wikipedia) t... |
Earlier people used to be obsessed with thermodynamics and laws describing behavior of gases, electric current, gravity. Cavendish,Kelvin, Newton and etc etc etc. But now in every movie, I see physics as being referred to as parallel worlds, alternate reality blah blah which has perhaps created this interest. Will they... |
I am unable to get the maths and neither the physics behind how gravity affects clock rate.
Note- As far as possible I was able to express and clear I have understood.
"Suppose if we keep spatial components to be zero, the clock runs at different rates in gravity."
My sir showed me the proof by sending a radiation beam... |
Suppose air is flowing from west to east and door is facing north . Now, I know using Bernoulli's equation the air outside is flowing at higher speed when compared to air inside which creates a pressure difference and that's why doors and windows open.
Now what I don't understand is, if air is flowing from west to eas... |
Let's say that we have two homogeneous spherical balls - one with mass $m_1=1000m$ and radius $r_1=1000r$ and second with mass $m$ and radius $r$. Distance between centers of this balls is $R>1100r$. The balls are not moving(Their relative velocities are equal to $0$). Can equations of relativity theory be applied to p... |
Fermions with antiperiodic boundary conditions have momentum in the form $$\frac{n \pi}{L}$$ where $n=-(L-1)...-1,1,...(L-1)$, i.e. odd integers. I am dealing with a Hamiltonian in momentum space with an interaction term of the form $\sum_{k_1, k_2,q}V_0(k_1,k_2,q)c_{k_1}^{\dagger}c_{k_2}^{\dagger}c_{k_2-q}c_{k_1+q}$.N... |
Suppose i have a point mass which is moving in a circular path.Since the point mass can only have transnational motion, kinetic energy due to it will be $\frac{ mv^²}{2}$. But what if i observe the motion from the centre of circle, I can write it's kinetic energy as $\frac{I\omega^²}{2}$ which is also equal to $\frac{... |
The classical radius of electron is obtained from the electrostatic energy of a sphere of radius $r_e$ which is: $U=\displaystyle\frac{e^2}{4\pi \epsilon_0r_e}$. For the electrostatic energy of a sphere of radius $R$ I obtain that $U=\displaystyle\frac{3e^2}{20\pi\epsilon_0R}$ by using the formula $U=\displaystyle\frac... |
In the book "Superconductivity, Superfluids and Condensates", they write down the macroscopic free energy to be
$$ F_s(T) = F_n(T) + \int\left(\frac{1}{2m^*}\left|\left(\frac{\hbar}{i}\nabla + 2e \boldsymbol{A}\right)\psi\right|^2 + a|\psi|^2+\frac{b}{2}|\psi|^4 \right) d^3r + \frac{1}{2\mu_0} \int B(\boldsymbol{r})^2... |
What is the meaning of Killing vector field? I know that if $ \textbf{X}\in\mathfrak{X}(\mathcal{M})$, let $(\mathcal{M},g)$ be a pair who define my riemannian manifold, The killing vector fiels is defined by $\mathcal{L}_{\textbf{X}}g=0$. So i think that $g$ is invariant under the flow of the integral curves generate... |
Electrons show a banded distribution at the end of a double-slit experiment set-up. This banded pattern shows that wave interference prevents many electrons from reaching areas where probability is lowest.
My question is about how an electron can pass through both slits without dividing because electrons are detected i... |
$$F=mg$$
Why is the acceleration constant? Shouldn't it change as it is thrown upward as the distance from the earth increases.I know the effects would be very negligible but is there any equation to account for this change? How can we apply it to real life?
$$\frac{dg}{dr} =\lim_{h \to 0} \left[ \frac{Gm_{earth}}{(r+... |
TLDR:
Given a Lagragian $\mathcal{L}$ depending on some fields $\{\phi_a\}$, which contractions between the fields are permissible?
Example to illustrate my problem
Consider the following Lagragian
$$\mathcal{L}_{\mathrm{SQED}}=-\left(D^{\mu} \phi\right)^{*} D_{\mu} \phi-m^{2} \phi^{*} \phi-\frac{1}{4} F^{\mu \nu} F_... |
In the circuit representation of a capacitor, why is the internal resistance of the capacitor, caused by the dielectric medium between its plates, taken to be parallel to it?
|
I was trying to figure out how far can a sound of 103 dB can be heard, so I converted it in W/m$^2$ (it gave me about $0.0200$ W/m$^2$) and then I used the formula “$I=P/4\pi r^2$” to find the maximum distance the sound can be heard, thus replacing the I of the equation by $10^{-12}$ W/m$^2$, so that I would have 10$^{... |
I have some basic doubts about current density vector $\vec J$, which is defined as "the vector whose magnitude is the electric current density, and whose direction is the same as the motion of the positive charges" (Source: Wikipedia).
Let's consider a cylindrical conductor like this:
Current may be found through thi... |
Disclaimer: I may seem to be using strange terms because although I know English rather well, it is not the language I learn physics in.
Consider a cylinder (with mass $m$ and radius $r$) on an inclined plane (incline is $\alpha$, an angle in radians).
As far as I know this is a valid way to calculate its acceleration ... |
I was studying for my electrodynamics exam and came across two questions which seemed to require conflicting models of how power is transferred in a current carrying wire.
The first question:
A straight cylindrical wire of length $L$, radius $R$ and cross-sectional area $A$ has a potential difference of $V$ across it a... |
Statement: I understand similar questions have been asked; however, none of them really helps me.
The detailed version of my question is as follows:
Why do unconstrained and unfixed objects always rotate about the lines passing through their CMs when a constant tangential forces are applied to them? I understand that i... |
Given a qubit in the state $|0\rangle+\exp(2πi/2^n)|1\rangle$, is there a quantum mechanical operator to multiply the phase of the qubit with $2^k$ (where $k \leq n$). Such that:-
$$|0\rangle+\exp(2πi/2^n)|1\rangle \quad \mathrm{becomes} \quad |0\rangle+\exp(2πi/2^{n-k})|1\rangle$$
|
In both theories of galactic formation, top-down and bottom-up, we understand that galaxies become increasingly structured as they age. By increasingly structured, I mean they are more spiral or more elliptical and less amorphous. Since the speed of light is finite, the further you look into space the younger the str... |
I am reading the experiments about Electrification in Part I Chapter I in "A Treatise on Electricity & Magnetism". There are few experiments on Electrification by friction, induction and conduction described in the book.
Description
The demonstration of the experiments can be shown below.
By friction
Firstly, the glas... |
The higher the energy of the particles, the higher their polarization.
I just cut-and-pasted the above statement from the chirality-and-helicity section of the Wiki article on 'Beta decay'.
What does it mean, exactly?
Are lower-energy negative beta decays more likely to result in a right-handed electron and left-handed... |
I am just confused how a person or a particle can move with non uniform centripetal acceleration along a circle. Take the case of non uniform circular motion. The magnitude of centripetal acceleration is given by $a=\frac{v^2}{r}$. So if $v$ is changing, $a$ must also change, but $a$ is the rate of change of direction ... |
I understand how a basic interferometer works, and how Michaelson used an interferometer to more-or-less disprove the “luminiferous anther”, but, analytically, how would one go about using an interferometer to measure distances?
|
I've found a formula for photon density which states:
$$
\rho_\gamma = \frac{a_B\, T_0^4}{c^2}$$
What is the name of the $a_B$ constant? I'm going to guess the 'b' is Boltzmann, but I need the official name.
|
How does one go about rigorously deriving special relativistic dynamics (both relativistic mechanics and electrodynamics) from quantum electrodynamics? Is this even possible from the mathematical structure of QED?
|
We have this water tank ($R$) that is pumping water to the end of pipe ($E$) in this figure.
When I say geometric information I mean things like: area of the pipe section, height of the reservatory relative to the ground or other things like that. Can we determine the water flow rate that $E$ has in this project? How?... |
I am a mathematician who specialises in algebraic geometry and algebraic topology. I am looking for a good textbook on the standard model that gears towards readers with more of a math rather than a physics background. Any suggestions?
|
Using these two definitions of work:
Work = Force * Distance
Work = Change in a particle's kinetic energy
When a skydiver hits terminal velocity, their change in kinetic energy is basically fixed for the rest of their path after that point (before they land). So using the second definition, it would seem that the w... |
The vacuum functional for the fermionic oscillator is given by
$$
Z[0] = N\int\mathcal{D}\overline{\psi}\mathcal{D}\psi \exp\left(i\int_0^Tdt\left(i\overline{\psi}\psi-w\overline{\psi}\psi \right)\right).
\tag{5.80}$$
Using Weyl ordering and discretizing the time integral, it is claimed that this could be written as
$... |
I was reading this Wikipedia article which describes how Planck’s Law of blackbody radiation is derived. Letting $B(v,T)$ represent the energy emitted at frequency $v$ and temperature $T$, the article states that we may “[equate] the integral of spectral radiance in per unit wavelength to that of per unit frequency” li... |
Has anyone considered using the excited meta-state of Rh 102 to create a gamma-ray laser?. I see an advantage in favor of using Rh 102m extracted from nuclear waste over Hf 178m2.
While Rh 102m has a reasonably long half-life of 3.7 years, this is also much longer than the half-life of the ground state with a half-life... |
Kitaev's one-dimensional p-wave superconductor Hamiltonian${}^\dagger$ is
\begin{equation}
{\cal H}_{JW}=-J\sum\limits_i(c_{i}^\dagger c_{i+1} + c_{i+1}^\dagger c_{i} + c_{i}^\dagger c_{i+1}^\dagger + c_{i+1} c_{i} - 2gc_{i}^\dagger c_{i}+g)
\end{equation}
After Fourier transformation ($c_k=\frac{1}{\sqrt{N}}\sum\l... |
I could only find some articles talking about radios used to communicate with submarines and a few now-defunct transmission towers for ELF. I would think this would be something that was studied to see if anything produced such frequencies in the universe but I couldn't find anything.
Do we see emissions in the electro... |
I thought that spin was an intrinsic property to electrons and protons that related to characteristics of an atom, so I'm not clear as to how applying an electromagnetic field, such as in the case of an MRI, to change the alignment of protons does not have an impact on the atomic structure of the hydrogen making up the... |
It's only a hypothetical example.-
What will be the time dilatation effect in the following cases. Suppose the video length is 1 hour(with earth) then how long is the duration of these videos on saturn-
Playing a youtube video on saturn that was made on earth
Playing a youtube that was made and played on saturn
Live vi... |
In the "Molecular dynamics" entry of 2018 version of Wikipedia (it have been removed for the current version), there is such a synthetic molecular motor:
You can also find this image by searching "MD_rotor_250K_1ns" for image on Bing.
(1) Any references about this synthetic molecular motor?
(2) According to the animat... |
If the second law of thermodynamics is about statistics, there's a chance of a specific microstate of a very unlikely macrostate happen, so the entropy would be reversed. So, the Universe could return to it's initial macrostate spontaneously? I know it's very very very unlikely but still possible probabilistically, rig... |
I heard that $F=-bv$, where $F$ is the drag force, $b$ is the damping coefficient, and $v$ is the velocity of an object, can be used to calculate the drag force exerted on an object moving at a moderate velocity.
What range is this moderate velocity referring to?
Does $b$ in the drag force formula $F=-bv$ have to be ... |
Here the author has done numerical calculation and has plotted energy spectrum and wave function for Kiteav Chain whose hamiltonian is given by
$$H=-\mu\sum_n c_n^\dagger c_n-t\sum_n (c_{n+1}^\dagger c_n+\textrm{h.c.}) + \Delta\sum_n (c_n c_{n+1}+\textrm{h.c.})$$
I was wondering how can we also do the same using mathe... |
I am confused in questions of fluid flow involving boundaries. Let's say, there is a source of fluid of strength $m$ at $(0,0)$ i.e origin. And both y-axis & x-axis are rigid boundaries. Is this system equivalent to a source of strength $3m$ at $(0,0)$ but without boundaries?
|
We use cross product of vector to find out area of a parallelogram and we end up with a vector.
As a learner, I know that area is nothing but the measure of the surface. So how can it have a particular direction?
Area does not seem to have directions like force, velocity, etc.
|
In Feynman Vol. 1, I have read:
If we blow on the water so as to maintain a continuous preponderance in the numbers evaporating, then the water is cooled.'
My question is, how does the continuous preponderance help molecules to keep evaporating?
|
For a particle in a central potential, the orbital angular momentum magnitude operator $\textbf{L}^2$ commutes with the Hamiltonian operator $H$, i.e. $$[\textbf{L}^2,H]=0.$$
I read that one way to prove this is to first note that $$[L_i,\textbf{L}^2]=0,$$ where $L_i$ is the orbital angular momentum component operator... |
My book says that the speed of sound wave in a gas is always lesser than the r.m.s. speed of the gas at the same temperature. I understand that speed of sound is given by:
$$v_s=\sqrt{\frac{\gamma RT}{M}}$$
and r.m.s. speed is given by:
$$v_r=\sqrt{\frac{3RT}{M}}$$
Then my book says, "since $\gamma$ is always lesser th... |
The friction coefficient between an athlete's shoes and the ground is $0.90$. Suppose a superman wears these shoes and races for $50 m$. There is no upper limit on his capacity of running at high speeds. a) Find the minimum time that he will have to take to complete the $50 m$ starting from rest. b) Suppose he takes e... |
This talks about "Afterglow" of a Gamma-Ray Burst. What exactly is an Afterglow? And how do we use these to detect GRBs(Gamma-Ray Bursts)?
|
While I was selfstudying capillary rise I came to a point thinking how the meniscus in both ends of a water drop in a capillary tube would appear if it were falling under gravity then I built my hypothesis. but no idea whether it's correct. Please, someone who's interested in regards of this, kindly explain us how it h... |
In adiabatic expansion, gases expand when heating so volume and pressure also increase. How can I convert into work?
|
How can I understand that " In photon gas, particle number is not conserved"
|
If light is an electromagnetic wave how does light move in a line? Especially laser light. I thought that electromagnetic waves (as well as sound waves) can only expand in all directions as a sphere. Does that also mean that radio waves and sound waves can be turned into lasers?
|
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