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A Brief Explanation of the Issue
A common problem type for vector calculus students or introductory physics/engineering students is tension problems. For instance, if a mass of $10$ kg is suspended from two taut cables of length $3$ m and $5$ m at angles of $52^\circ$ and $40^\circ$, respectively, then the correspondin... |
Interaction between 'nearly free' or 'bound' electrons is what leads to bands. I understand this but why specifically at Brillouin zone boundaries?
|
Let's consider a discrete quantum system such as the harmonic oscillator or the hydrogen atom. According to quantum mechanics, when a measurement of the energy of the system is made the wave function collapses to one of the eigenfunctions of the hamiltonian operator. But if we consider instead a non-discrete system, su... |
A small marble is rolling without slipping in a circular track (pic enclosed) in a vertical plane. Marble has enough energy to reach the top and not fall and complete the full track. I am trying to understand the motion and hence trying to find direction of friction at various points on it. I have depicted what I thin... |
I know that current is same in a series circuit becuase the current only has one path to flow but I'm confused on how resistors work in series. From what I've read is that current is the same before and after a resistor (Eg. if 500ma flow into a resistor 500ma flow out of the resistor) so what is the resistor actually ... |
I have read that the incompressible Navier Stokes equation is preserved by the scaling
$$x',y',z'=\lambda x, \lambda y, \lambda z$$
$$t'=\lambda^2 t$$
$$u'=(1/\lambda) u$$
As I understand it, fluid energy is given by
$$\int u^2 dv$$
I am trying to understand what is meant by the claim that the fluid energy is invariant... |
In solid state physics, it is helpful for some analytical results to assume that $\boldsymbol{k}$-space is a continuum and perform the replacement
$$ \sum_{\boldsymbol{k}} f\left(\boldsymbol{k}\right) \rightarrow \frac{V}{\left(2\pi\right)^3} \int_\Omega \mathrm{d}^3k\ f\left(\boldsymbol{k}\right) \tag{1}$$
for $\bolds... |
Physically speaking, does it make sense to talk about the "speed of sound at some pressure"? Is this a coherent concept?
|
A uniform electric field of 2000 $(\frac V m)$ exists through all space (the field is in $+x$ direction). An electron is moved from the origin to the location where $x = -2.00 (m)$ and $y = +3.00 (m)$. What is the change in potential energy and change in electric potential respectively?
I calculated the electric pote... |
If I have an open tap such that there is a continuous stream of water falling through height $h$, is the flow rate the same at every point on $h$?
|
I am dealing with a problem where I'm given an ungrounded spherical conductor with radius $R$ which is centered at the origin, the sphere is charged with a total charge $Q$. Besides the spherical conductor, there is a charge $q$ located at $h\hat{z}$ and a charge $-q$ located at $(h+d)\hat{z}$ where $h>R, d>0$. I am as... |
After using google and my textbook, I keep getting contrary view in which where the direction of magnetic field lines would travel.
Does the magnetic field lines travel from SOUTH to NORTH or NORTH to SOUTH?
Based on the following snippet from hyperphysics:
it seems that the magnetic field is directed from SOUTH to NO... |
I was wondering, how can I calculate the decelerations of an object due to friction - and therefore find the maximal distance it can reach?
For example, if a car suddenly brakes in the middle of a road, how can I find how long it will take it to fully stop, its deceleration, the distance it will reach before stopping?
... |
Quantum spin liquid ([QSL])1 is usually defined as a kind of phase that
(1) no long-range order,
(2) has long-range entanglement and
(3) hosts emergent gauge structures or fractionalized excitations.
I am wondering is there any principle ensures that properties(2) and (3) imply (1)? Or actually we can have a phase that... |
I am reading a book on aircraft dynamics (Blakelock Aircraft and Missiles) where the author presents the following system on page 408:
Lagrange's equation is given by:
$$
\frac{d}{dt}\left(\frac{\partial T}{\partial\dot q_j}\right)-\frac{\partial T}{\partial q_j}
+\frac{\partial F}{\partial\dot q_j}+\frac{\partial U}{... |
I am a bit confused regarding a commonly cited definition of proper time. For example, in Spacetime and Geometry, Sean Carroll writes:
the proper time between two events measured the time elapsed as seen by an observer moving on a straight path between the events
Similarly, in Gravity, James Hartle writes:
proper ti... |
Sometimes plasmons are defined as collective plasma oscillations of the free electron gas in a metal. Therefore, plasmons must be a periodic modulation of electron charge density in the metal. But sometimes, plasmons are defined as electromagnetic waves that exist on the surface of metals and decays inside. What is pla... |
In Weinberg's Cosmology, the FRW metric is
\begin{equation}
d\tau^2=dt^2-a^2\left[d\vec{x}^2+K\dfrac{(\vec{x}\cdot d\vec{x})^2}{1-K\vec{x}^2}\right]
\end{equation}
with $g_{ij}=a^2\left(\delta_{ij}+K\dfrac{x^ix^j}{1-K\vec{x}^2}\right)$. From this, the final Christoffel symbol is
\begin{equation}
\Gamma^i_{jl}=K\wideti... |
In my book it is given that for the formation of hydrogen molecules, hydrogen atoms come closer due to net attractive forces.
It is written that initially when the atoms were approaching towards each other from a distance the magnitude of attractive force was greater than that of repulsive force and hence they come cl... |
Why does moment of inertia dependent on square of radius and can this be derived by some means? If so then how? or only can be proved experimentally?
|
What is the basic difference between static, dynamic and hydrostatic head in bernolli equation?
Is static pressure gauge pressure or thermodynamic pressure?
|
i am a beginner in physics and am currently studying electrical engineering. I was wondering when the excess electrons move to equalize themselves, can it result in some atoms being positively charged due to the spacing between the electrons causing the majority of the electrons to be outside the atoms.
An example woul... |
My textbook had an example question:
"A loop of irregular shape carrying current is located in an external magnetic field. If the wire is flexible, why does it change to a circular shape?"
And the answer reads:
"It assumes a circular shape with its plane normal to the field to maximize the flux since, for a given perim... |
Wheeler's delayed choice experiments demonstrate that extracting "which path" information after a particle passes through the slits can seem to retroactively alter its previous behavior at the slits.
Quantum eraser experiments demonstrate that wave behavior can be restored by erasing or otherwise making permanently una... |
I encountered expressions such as "3 x 2 surface reconstruction" or "6 x 2 surface reconstruction" while studying.
I understand surface reconstruction refers to the movement of atoms on the surface such that the atomic structure on the surface is different from that of the rest of the crystal.
But what does the precedi... |
I have a hard time understanding why does earth have magnetic fields.
My textbook reads:
"The Earth's core is very hot and molten, and the ions of iron and nickel are responsible for Earth's magnetism.
But how did it manage to create such huge magnetic fields?
|
why does the speed of light in vacuum never change? Under any circumstances, The speed of light in vacuum never change, why?
|
Suppose a football is racing towards you at some speed $v$. What you are gonna do is try to stop it. There are two scenarios:
1.Suppose you hit it with your closed fist in the direction opposite to the ball's motion. The ball will rebound as a result.
2.You try hitting the ball,but this time with your palm open and fac... |
My question is in regard of the following snippet provided by my textbook.
So why is the electromotive force (EMF) highest in the loop when $\theta$ = $90$ or $270$?
So the magnitude of the induced EMF will be determined by the rate at which the loop is rotating, according to Faraday's Law. EMF will be maximum when th... |
So I was just watching some YouTube videos on a spinning wheel that seemed to "defy" gravity. The creator made two videos on it, the first showing the wheel, and the second with an attempt to explain it. There are the names of the videos:
"Anti-Gravity Wheel?" by Veritasium
"Anti-Gravity Wheel Explained" by Veritasium... |
I am Studying Electron self-energy using Ryder's textbook, In page 334 we can see
Defining $k'=k-pz$ and avoiding the term linear in $k'$(because it integrates to zero) gives
\begin{equation}
\Sigma(p)=-ie^2\mu^{4-d}\int_0^1dz\gamma_\mu({\not} p-{\not}p z+m)\gamma^\mu\int\frac{d^dk'}{(2\pi)^d}\frac{1}{[k'^2-m^2z+p^2z... |
What is the Gauss law in any arbitrary dimension "n" and how can one derive it?
|
from this morning I think about the third law of Newton and the force of buoyancy and I can't solve it. I know that I misunderstood something, but I can't find out what is it. And sorry if my questions are ambiguous, but I'm too tired, I want to find out where I'm wrong. these are my questions:
Why the Buoyancy Force=... |
The youngs modulus relation is given by,
$$ Y= \frac{F}{A} \cdot \frac{ L}{\Delta L}$$
According to wiki,
The 'A' is the area on which the force is applied and $ \Delta L$ is the length along which the material is stretched... but now which length are we talking? I am confused because a single force can causes stretch... |
I have another question about the third law of Newton (if you can check the last one that I posted) :
Why is it that the gravity that pushes me on the Earth is so powerful, but the reaction force (normal force) is so weak (I feel a force only on my foot, but even if I jump, gravity keeps me on the Earth). Newton says t... |
For the description of a chiral multiplet in Supersymmetry there are 2 formalisms, the one I am used to presented for instance in the Supersymmetry Primer of SP Martin which is based on 2-component (Weyl)-spinors and another one which apparently tries to avoid the intricateness of the Weyl-spinor formalism.
For instanc... |
I have some conceptual doubts to clear up, in terms of piecing together what we learn of a vertex operator algebra (VOA) in conformal field theory, and how it is defined by a mathematician, say from Kac's book. In particular:
Because of the state-field correspondence, can we equally think of $V$ as a space of fields, ... |
I am a middle school student and I want to learn more about physics from A - Z but I don't know any book or website that is useful. Can you share me some suggestions?
|
I'm working on researches in the area of Special and General Relativity (SR/GR) focused on time dilation and I have a question to pose.
Lorentz transformations (LT) introduce a time transformation such that two events occurring at same time in one frame not being at same time in another frame (relative simultaneity).
... |
I know that in calculating phases of materials it is standard to choose a pressure $p$ and temperature $T$ of interest and then, keeping these two quantities fixed, find the mixture of phases that minimizes the Gibbs free energy. This then has to be the themodyanimcally stable mix of phases.
But naively, you could make... |
I just want to make sure I understand what I am doing. Let me write down how I think things should work, and please spot any mistake in my thought process once I make any.
Say I have some state
$$
\langle \psi_1 | \hat{A} | \psi_2 \rangle
$$
and I want to insert $\mathcal{T}^{-1} \mathcal{T}$ in the matrix element, whe... |
In a 1974 Pati and Salam published the paper "Lepton Number as the Fourth Color", which suggested the gauge group $\rm SU(4)\times SU(2)_L\times SU(2)_R$ could be the fundamental symmetry group, rather than $\rm SU(3)\times SU(2)\times U(1)$.
An important property of any such candidate is that it can reproduce the stan... |
When I explain QM to non-physicists, I sometimes say that quantum effects are typically noticeable on very small scales. For example, a QM particle in the harmonic potential behaves mostly classically, up to effects of order $\hbar$ (think of the spread of coherent states!), which becomes especially clear if the partic... |
I am trying to derive the formula for Torque on a circular current loop inside a magnetic field.
I know the formula is:
$\tau = IAB\sin{\theta}$
Where I is the current, B is the magnetic field and A is the Area.
My attempt so far:
$d\vec{F} = I\,d\vec{s}\times \vec{B} = IB\,ds\cdot\sin{\alpha}$
Now, if the formula for ... |
A random question struck my mind. If $|\phi_n\rangle$ be an eigenstate of Hamiltonian H (s.t. $H |\phi_n\rangle =E_n|\phi_n\rangle$), so is $e^{i\delta_n}|\phi_n\rangle$ for any real $\delta_n$. This is true for any n. These phases aren't global but relative, as they depend on $n$. Would these ambiguous phases that cou... |
When talking about bicycles, it is usual to measure their gears by the number of teeth they have. This measure is then used to calculate the gear ratio: the ratio between the number of teeth of the front gear and those of the back gear. This in turn is calculated for each front-back gear combination available on a bike... |
I'm reading this introduction to string theory by Mariana Grana and Hagen Triendl and I have understanding problems around the method of compactification in string theoretical sense. The compactification scheme works as follows (see pages 14/15):
The ten-dimensional (or say abstractly $n$-diml) spacetime is divided i... |
Imagine a car $S'$ with a velocity $ v = c $ in the +x direction. Now if someone fires a photon from the back of the car opposite to it's the direction of motion, that is $ u = -c $. Using the velocity addition formula, the velocity of photon observed by a stationary observer is
$$ u' = \frac{u + v}{1+\frac{uv}{c^2}} $... |
Let's think of the Planck constant as of the slope of the electromagnetic field dispersion relation, $E=\hbar \omega$. Planck constant is not independent of the electron charge, both can be rescaled as long as the fine structure constant remains unchanged. Still, it's oftentimes convenient to use both.
As we start lear... |
I know that according to textbooks $⟨p⟩ = −iℏ∫ψ^{*}(x)\frac{dψ(x)}{dx}dx$, but why? Knowing that $I = ∫|x⟩⟨x|dx$
I get $⟨p⟩ = ⟨ψ|p|ψ⟩ = ∫⟨ψ|p|x⟩⟨x|ψ⟩dx = ∫(−iℏ\frac{dψ(x)}{dx})^{*}ψ(x)dx$,
but also $⟨p⟩ = ⟨ψ|p|ψ⟩ = ∫⟨ψ|x⟩⟨x|p|ψ⟩dx = ∫ψ(x)^{*}(−iℏ\frac{dψ(x)}{dx})dx$.
Now I would expect that $∫(−iℏ\frac{dψ(x)}{dx})^{*}ψ... |
Let’s say, as a thought experiment, that we drilled a hole straight through the Earth and out the other side. Let’s ignore things like heat and what a massive undertaking this would be.
We would have a hole with no bottom. If you could look through the hole and somehow see out the other side clearly, you would see the ... |
Why can the Hamiltonian
$$
H = \frac{1}{2m}\left(\vec{p}-q\vec{A}\right)^2+q\Phi + V
$$
be transformed to
$$
H = \frac{1}{2m}\vec{p}^2 - q \vec r \vec E + V
$$
in the dipole approximation, in which the vector potential $\vec{A}$ (and, as a consequence, the electric field $\vec{E}$) are assumed to be constant in space?
... |
Let's say I have a star 20x the mass of the sun. At the end of its life, it collapses into a black hole. Now correct me if I am wrong, but as it collapses it rotational speed dramatically increases doesn't it? So does the singularity continue spinning as it forms? Can something spinning so rapidly actually become a... |
I have watched a few videos about naked singularities, and it is my understanding that one is a singularity without an event horizon. My question, is could you ever have that with anything larger than a Planck mass black hole?
|
As far as I know, in physics, calculus is approached using nonstandard analysis in which $dx$, $dy$, etc. (infinitesimals) are treated as fixed, extremely small quantities rather than the standard analysis approach using limits where they are treated as something that approaches $0$.
I understand that the nonstandard a... |
When we derive the expression for particle flux/probability current, we find that it is directly proportional to the Wronskian of $\psi$ and its conjugate and deduce that it is constant when particle current is constant.
Is it just a coincidence that the Wronskian shows up, or does the have some noteworthy implications... |
I understand that superconductivity mainly occurs due to the formation of the Cooper pairs in which electrons, instead of repelling each other, actually attract because one electron actually attracts the positive charges nearby which further attract the the other electron thus establishing a Cooper pair. And since the... |
Our teacher told us today:
Suppose a satellite is moving around the earth in a circular orbit of radius $r$. Suddenly an external agent stops its motion so that its kinetic energy becomes zero but its gravitational potential energy remains the same. Assume there is no air friction or drag. The satellite starts to fall... |
If a vehicle were to move horizontally through solid stone by separating it into pieces, moving the pieces behind it, and reassembling them precisely as they were, the net change in energy ought to be zero. The actual cost of boring a hole appears to depend on the immense inefficiency of grinding up material through f... |
What makes silver the best conductor of electricity?
I want to know in terms of electrons. Although, Cu and Ag and many other metals have only one electron in their valence shell. Then what makes Ag the best conductor?
|
I thought of this question from watching the trailer for the new movie "Greenland" with Gerard Butler. Essentially in the trailer a huge comet falls towards the earth, apocalypse, etc.
However, that got me thinking: what if in such a situation (meteor strike), the World Governents sent a huge nuclear missle (or many mi... |
Suppose you have a solid sphere of m, where m is an element with freezing point of 0 degrees Celsius.
In one scenario, you place your sphere in a (“static”) 25 degree Celsius environment and measure time, t, until melting. The sphere is fixed and cannot be displaced.
In the other, you place your sphere in environment w... |
Planck developed his black body radiation theory assuming that atoms treated as simple harmonic oscillators can stay in states of very much defined energy. If normal frequency of such oscillator is $\nu$, then the energy levels are the multiples of $h \nu$ (that is $E_n = n h \nu$, forgetting about zero-point vibration... |
Can someone explain to me what effective gravitational acceleration is from a kinetics perspective?
I understand what it is (the acceleration of gravitation felt by an object in another accelerating object, or, at least that is my basic understanding, if I am wrong here, do correct me) but I am not able to prove it to ... |
Let us suppose I have a particle in a 1D infinite potential well of length $L$ which is in the ground state. The energy is given by
$$E=\frac{\hbar^2\pi^2}{2mL^2}.$$
Now I decrease the size of the well gradually to lets say $L-x$. This means that particle is still inside the 1D well, since it can't escape infinite pote... |
So, for E field boundary condition, we know the vertical part of the incident field
$\varepsilon _{1}E_{1\perp } = \varepsilon _{2}E_{2\perp }$
and the tangential parts are same from both side.
That basically means a larger $\varepsilon$ leads to a smaller vertical part. put that into a figure as following
As shown in... |
I know extremely high temperatures can generate plasma, but I've heard that high voltages can too, does anyone know how a high voltage ionises gas?
|
I am not sure if I am asking a metaphysical question but I really have a problem understanding the core of this concept of energy and its ability to drive almost everything we see in the universe, whether it be cells in the body, electrons in atoms, movement of everyday objects upon mechanical force.
Like what it is ab... |
Background
The quantum relative entropy is defined for any quantum states $\rho, \sigma$ as
$$D(\rho\|\sigma) = tr(\rho\log\rho) - tr(\rho\log\sigma)$$
For arbitrary choice of $\rho,\sigma$, the quantum relative entropy can take any nonnegative value. Consider some bipartite state $\rho_{AB}$ and let its marginals be $... |
(Rigorous theorists will have to forgive my phrasing on this question, I’m new to GR and most of my physics training is in quantum mechanics)
In non-Euclidean geometry, we can speak of a spherical space as in an intrinsically curved space. In a spherical space, “parallel” lines converge to a point. I read on Wikipedia ... |
I'm holding two very massive, dense objects, one in each hand at arms length. I fall through the event horizon of a very large black hole. The tidal forces at the event horizon are not large, so I survive.
Now inside the event horizon, I bring the masses that I hold together. This should affect the shape of the event h... |
I know it's a big and confusing title, if someone could improve it I would appreciate.
My question is a thought experiment.
If kinetic energy is relative to other objects and the total energy of a system doesn't change, what would happen if in a completely empty universe, besides the existence of a simple rocket, this ... |
If I were to do an experiment measuring the magnetic field strength (in tesla) of an iron core solenoid magnet, how would I determine the value for the dipole moment in the formula displayed in https://en.wikipedia.org/wiki/Dipole#Field_of_a_static_magnetic_dipole?
What does the metre squared represent?
|
The Unruh effect is a well-known example in which two Hamiltonians $H$ and $\hat H$ associated with different timelike Killing vector fields both have a lower bound, in the same Hilbert-space representation, even though they are not related to each other by any spacetime isometry. This question asks about a generalizat... |
Suppose you are inside a closed box which is moving with a constant speed with no acceleration whatsoever. You cannot see outside the box. If you are given all the instruments you need, what experiment could you perform to ascertain that you are, in fact, in motion?
This was a question asked in an interview for admis... |
Today while I am driving my car this question came to my mind but I cannot figure it out. Sorry I am not in physics related major that this question is not expressed professionally.
When you drive a real car you gets less acceleration while at higher speed. But let's say there an engine that get thrust by pushing small... |
What is the potential energy of an arrangement of eight negative charges on the corners of a cube of side $b$, with a positive charge in the center of the cube? Suppose each negative charge
is an electron with charge $−e$, while the central particle carries a double positive charge, $2e$?
This question is an example ... |
Why can toe kick cause greater change in the ball's momentum than kicking with the whole instep in contact with the ball? Perhaps it has something to do with how the foot's momentum is transferred in the two cases..... What's that?
|
In the above picture of the microscope experiment, I am considering that the observer is situated at the eyepiece. The observer is a rectangular 2D grid of square-shaped detectors, each detector with a side length of $s$. The experiment is done with a single photon. If a photon encounters one of these square-shaped de... |
When an electron passes into the valence band, is it no longer useful for conduction?
|
I was trying to calculate the electron cyclotron frequency under earth magnetic field which has a horizontal and a vertical component.
Now when I consider the initial motion of the electron in all three directions and magnetic field along two-direction (x and y) I get 3 equations:-
$m\frac{dv_x}{dt} = -v_zB_y$
$m\frac{... |
We know that when a system gains heat energy from the surroundings through conducting walls of the container , then the temperature of the system also increase till it reaches an equilibrium value .
Whereas in an adiabatic compression of a gas where temperature increases but the change in heat energy of the system is z... |
I was trying to read about 3+1 decomposition of spacetime from section 12.2 of Padmanabhan's book Gravitation Foundations and Frontiers. However, other sources can also provide the context for my question.
Once the coordinate system $(t,y^\alpha)$ has been adopted on the spacetime from the foliation, $x^a=x^a(t,y^\alph... |
The Hubble law says that if an object is at a distance $r$, it should have a velocity $Hr$ and therefore any light signal from that object will be correspondingly redshifted. However, the light reaching me from the object was emitted a long time ago when the distance was much less than $r$. So why should the signal be ... |
In the book "An Introduction to Thermal Physics" by Daniel Schroder, I got the following expressions Helmholtz free energy : F = U - TS
and Gibbs Free energy : G = H - TS = U + PV - TS
The author explained the intuition behind Gibbs free energy the following way
I found in different places (Chemistry StackExchange, W... |
Suppose a ball of mass $m$ is thrown vertically upwards from the ground. I understand that the speed-time graph would be somewhat like a distorted parabola. But what about the velocity- time graph (considering air drag or viscosity)?
According to me it would attain a kind of terminal velocity while falling down. But I ... |
I am following Sidney Coleman's lectures of Quantum Field Theory (World Scientific).
For the renormalization of QED, he considered the following Lagrangian (Eq 33.54 in the book)
\begin{equation}
\mathcal{L} = -\frac{1}{4}F_{\mu \nu}^{2} + \bar{\psi}(i \gamma^{\mu}\partial_{\mu} - m - e \gamma^{\mu}A_{\mu})\psi - \frac... |
So I was thinking of brakes in a car the other day. When brakes are applied, the forward force is converted to heat in the brake disks. When brakes are cool (at the beginning) they have the ability to absorb a lot of heat and have more braking power. But as the brakes heat up, their ability to absorb more heat should d... |
In a projectile motion, consider the projectile to be launched from $(0,0)$ as traced to be on cartesian axes. Then the trajectory is given by
$$y=x \tan \theta \big(1-x/R)$$
where $\theta$ is measured from $x$ axis , and gravity acts along $y$ axis, $R$ stands for the maximum range which may vary with the initial velo... |
If most mass from a proton comes from the nuclear force's bonding energy between quarks that make-up this proton, why wouldn't most mass from a galaxy come from the gravitational force's bonding energy between all traditional matter that make-up the galaxy?
|
If at high temperatures atoms are more intensely interacting with each other or emitted photons that also could make the core vibrate. Is in these circumstances the radioactive material more likely to fission faster? Can this be used to get rid of radioactive garbage?
|
In Padmanabhan's book Gravitation Foundations and Frontiers, the following equation can regarding the extrinsic curvature of a hypersurface can be found in section 12.2 (see just above equation 12.19 in that book),
\begin{align}
K_{\alpha\beta}=-\nabla_\alpha n_\beta=-N\Gamma^0_{\alpha\beta}.
\end{align}
According ... |
Let's assume that there is inertial frame of reference $S$, and the observer is at the origin of this frame at time (associated with this inertial frame) $t = 0$. The observer has own frame of reference $S'$ (with proper time $\tau$), which coincides with inertial frame at $t = \tau = 0$. From the perspective of this i... |
In this stack and this other stack which I had asked, there was discussion on when you can apply momentum conservation in collisions. The conclusion was that you can do it if time period of collision is small.
However recently I came across a question in which momentum conservation is not obeyed even if time period of... |
I was studying how the Lorentz transformations are derived, and found this table in Special Relativity for The Enthusiastic Beginner by David Morin. The primed frame $S'$ is taken to have a velocity solely along the positive x-direction of the unprimed $S$ frame.
I justified the four conditions to myself as follows:
... |
Suppose that I superimpose two waves travelling in a string of area of cross section $s$ and density $\rho$. The two waves are
$$
y=8\sin(\omega t-kx)\quad \text{and}\quad y'=6\sin(\omega t+kx).
$$
I need to find the energy between two consecutive nodes. The resultant wave ($y+y'$) can be taken as a combination of a pu... |
I've often seen spin 1/2 commutation rules as a principle valid for every angular momentum. In some text books there is a derivation from symmetries principles.
My question is, if I have a spin $1/2$ particle, which measurements should I perform to know which are the commutation rules of $S_x, S_y, S_z$?
|
I attended a lecture on theoretical electrodynamics, and there we exclusively used the combination of E and B to fundamentally describe electromagnetism. They contain no approximation for material behaviour and use the exact charge density and current density (including the bound charges and bound currents in materials... |
Consider an (active) infinitesimal Lorentz transformation:
$$ x^\mu \rightarrow x^\mu + {\omega^\mu}_\nu x^\nu, $$
so that any scalar field is transformed as
$$ \phi(x) \rightarrow \phi'(x) = \phi(x) - {\omega^\mu}_\nu x^\nu \partial_\mu \phi(x) + O(\omega^2). $$
Now consider a Lagrangian density function $\mathcal{L(\... |
Can I connect my digital ammeter in parallel to a battery to check the maximum current It can supply? Will it burn my ammeter or its fine?
I have tried it and nothing happened so is the ammeter being damaged slowly from inside?
|
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