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Context I'm studying statistical mechanics using Huang's Statistical Mechanics [1]. Huang writes, Empricially $U$ is an extensive quantity. This follows from the saturation property of molecular forces, namely that the energy of a substance is doubled if its mass is doubled. I searched for saturation property and did...
In deriving the 1/$\sqrt{N!}$ normalization factor the first step is looking at the one particle state (see image below). I am confused about how we got from the first line to the second? Maybe I am very rusty on QM... But how did the commutator get in there?
I've had the idea to try and code a ray tracer that obeys laws of special/general relativity. In order to predict the motion of objects in the scene I'd need to compute geodesics with a user specified metric. How can I do this in the most efficient way. Lets take the Schwarzschild metric for example. Assume the observe...
In the case of angular momentum in quantum mechanics, a common exercise is to derive the spectrum for $J_z$ and $J^2$. I follow most of this argument, but I get a bit lost at the end. To my understanding the logic is as follows: Create an eigenstate of the operators we are searching for the spectrum of. Call this $\ver...
The $q=3$, $d=3$ ferromagnetic Potts model has a first-order transition on varying temperature. I recently learned that at small $h>0$, where $h$ is a field favoring one of the three colors, there is still a first-order transition on varying temperature. I hadn't appreciated until now that first-order transitions could...
In the theory of electromagnetism in 1+1 spacetime dimensions (one temporal and one spatial coordinate), one can define the 2-potential vector (analogous to the 4-potential vector in 3+1 spacetime dimensions): $$A_\mu=\left(A_t,A_r\right)\equiv\left(\phi(t,r),A_r(t,r)\right)$$ given those potentials we can express the ...
The magnitude of torque is defined as the product of the perpendicular (to the object) component of the force I apply and the distance between the axis of rotation and the point of application of the force. Now, this is a definition, and it does not have a proof. However, it is motivated through the fact that $\tau\pro...
Relative Kinetic energy is given by K.E = ($\gamma$-1)$m_0$c²; where $m_0$ is rest mass but can it also be given by this K.E= $\frac{1}{2}\gamma m_0v²$; where v is velocity of particle can it?
Suppose I'm in a rotating space station (that is somewhere in free space) and there is no other force. Now how am I supposed to fall to the circumference of the station if nothing pulls me? I will certainly be at the same point at all the times since there is no friction, neither attractive nor repulsive forces. Then h...
I would like to track the motion (actually, I am more interested in the velocity) of an object in a 2D plane (typically 4m x 4m). The object speed is typically 10cm/s, but the mouvement may be chaotic (no predictible pattern). Additionally, the object may rotate. I've thought of several options but they all have a prob...
Can we induce antisymmetric stretching vibration in carbon dioxide molecules by collision with nitrogen molecules in air at standard temperature and pressure?
If a concave lense is covered half with a piece of a paper and used to look at an object, is the object completely visible or is some part of the object not visible?
When a body falls from a height $h$ it loses some energy to the surroundings, is it the energy that is lost to the surroundings that increases its temperature on the remaining energy that is stored in that object that increases its temperature?
Is there a way of characterizing entanglement between states in a path integral formalism? If so, does this shed some light on the apparently non-local effects of quantum mechanics?
In different books (one example is Statistical mechanics of learning, by Engel and Van Der Broeck) I stumbled upon an idea which should be elementary, but to me it is not easy to grasp. Entropy can be interpreted as the negative of the expected fluctuation of energy around its typical value. My own way to convince myse...
I'm a pure mathematician and I was doing some physics for fun. I was trying to obtain the equations of motion of a particle moving along a curve $y(x)$ under the effect of gravitational force which constant $g$ depends on the heigth from the $x$ axis, ie $g=g(y)$. I take $q=x(t)$ as the generalized coordinate, and used...
I haven't looked into Anderson localization before. A quick review of the available information gives the impression that this phenomenon has mainly been studied for the case of a discrete random Schrödinger equation. Therefore, I have the following question: does localization of the wave function take place for the on...
In, An Introduction to Thermal Physics, Schroeder states It’s not obvious why a rotational degree of freedom should have exactly the same average energy as a translational degree of freedom. However, if you imagine gas molecules knocking around inside a container, colliding with each other and with the walls, you can ...
I was studying Hilbert spaces to understand quantum mechanics, and I came across these two properties of such vector spaces. I couldn't understand how these two properties are useful in quantum mechaincs.
The NIST atomic spectra database has atomic energy levels well documented. I understand that discrete energy levels in gases can be identified using emission and absorption spectroscopy, due to the presence of isolated atoms. However, I'm curious about how we can experimentally identify the discrete energy levels in me...
I'm trying to work through problem 5.4 of Schwartz (QFT and the Standard Model), which involves calculating the spin components of the matrix corresponding to the $e^+e^- \rightarrow \mu^+ \mu^-$ cross section. The problem starts by assuming two incoming electrons $e^-$ and $e^+$ as before, with momenta $p_1^\mu = (E, ...
I have a confusion about something in the following question. An ideal diesel engine has a compression ratio of 20 and uses air as the working fluid. The state of air at the beginning of the compression process is 95 kPa and 20°C. If the maximum temperature in the cycle is not to exceed 2200 K, determine (a) the therm...
I was reading the paper SISAR Imaging for Space Debris based on Nanosatellites, in which the Fresnel-Kirchoff diffraction formula is applied for a scenario in which the receiver, transmitter and target are moving. The author arrives to the following equation, defined as the complex profile function (CPF): $$ H(x') = \i...
If we see into the past with light and distance travelling so we can’t see things how they are currently, only how they were in the past; and James Webb took a photo from the beginning of the universe theoretically. But if we are seeing it as it was 13.8 billion years ago is there a possibility that the universe has al...
In classical electromagnetism, the EM field can be described by a 4-potential $A^\mu$. This potential describes two different phenomena. Static fields: A static charge $q$ at fixed position $r_0$ will have attached a Coulomb field $A^0=\frac{q}{\|r-r_0\|}$. Radiative fields: These are wave solutions to Maxwell's equatio...
I don't know if this topic is studied at all but I'm looking for good references for closed string collisions on a finite number of fixed type mutually intersecting football orbifolds with D-branes at the orbifold singularities where the D-branes are configured in a symmetrical way (for example the D-branes coincide wi...
I am trying to understand the formula for mass and field renormalization in QED from the book Gauge theory by Bohm, Denner, pp $202$. They use renormalized perturbation to rewrite the Lorenz gauge fixed Lagrangian with $$A_\mu^0=Z_A^{1/2}A_\mu,\; \psi_0=Z_\psi^{1/2}\psi, \;e_0=Z_ee,\;, m_0=Z_mm,\;\xi_0=Z_\xi\xi,$$ wher...
What I am going to speak about may not be a paradox but i see a contradiction here so I used used the word "paradox". To begin with, let there be 2 charges A and B which are stationary with respect to each other and their separation is one light year in a frame which is stationary with respect to them. Then some change...
If the number of degrees of freedom is the minimum number of independent variables necessary to describe the system, does this mean that this number is always equal to one? For example, if, as it seems to us, we need $\mathbf n$ variables to describe the system, then we can always put 1 variable in accordance with thes...
From Introduction to Superconductivity; Second Edition; A.C. Rose-Innes and E. H. Rhoderick; Page 3 Electrons have, of course, a wave-like nature, and an electron travelling through a metal can be represented by a plane wave progressing in the same direction. A metal has a crystalline structure with the atoms lying on...
In the theory of phase transitions, the upper critical dimension (UCD) is the dimension of space above which the phase transition is well captured by mean-field theory. For instance, it is well known that the UCD of the classical O(N) model is 4. The intuitive reason is that (for a lattice model), the number of neighbo...
In my solid state course, I was taught that Van Hove singularities can be explained because the DOS follows: $$\mathrm{DOS} \propto \frac{1}{\nabla_k E} .$$ However, the DOS of a 3D system is proportional to $\sqrt{E-E_0}$, therefore, at the bottom of the band where $E=E_0$, it has a minimum. Does this mean that the ab...
Say I have a laser traveling at the stationary observer at relativistic speed, so the laser wavelength gets blueshifted. To conserve total energy emitted, according to the observer, the laser emits smaller number of bluer photons. Is this how energy is conserved in special relativity settings?
What determines the direction (i.e. angle) at which an emitted photon travels? Are very flat surfaces more spatially-coherent (i.e. the photons travel in a parallel manner, akin to a laser beam) or perhaps can be made so? Or is the thermal radiation completely scattered?
Is it possible to arrange two off axis parabolic mirrors (OPAs) to transform the emitted rays of a point source into a collimated beam, as in the figure below? That is, similar to a Keplerian telescope, but achieved with mirrors and not lenses. EDIT: I want to desing an optical system that takes a point souce and coll...
By considering a particle on a ring, the eigenfunctions of $H$ are also eigenfunctions of $L_\text{z}$: $$\psi(\phi) = \frac{1}{\sqrt{2\pi}}e^{im\phi}$$ with $m = 0,\pm 1,\pm 2,\cdots$. In polar coordinates, the corresponding operators are $$H = -\frac{\hbar^{2}}{2I}\frac{d^{2}}{d\phi^{2}}$$ $$L_\text{z} = -i\hbar\frac...
What is a good formula for air density (kg/m^3) given temperature (°C), pressure (hPa), and relative humidity? I tried implementing the formulas from here as follows: import math def air_density(temperature, pressure, humidity): psat = 6.1078math.pow(10,7.5temperature/(temperature+237.3)) pv = humidity*psat ...
This answer explains how the Coulomb-potential can be calculated as the energy shift of the (photon) ground state for 2 charges fixed in place. This calculation has been done for a covariant "quantization" of the electromagnetic field, where one has 2 transverse photon degrees of freedom, and one longitudinal and one t...
When a single photon is emitted as a result of an electronic transition, it will have a defined energy and wavelength. However, its amplitude is not constant over infinite space and time; instead, it is a disturbance of the electromagnetic field originating from the electron. According to Fourier, this wave therefore c...
Suppose I have a hamiltonian of the form $$ H(q,p) = H_0 + \epsilon H_1(q,p) $$ In perturbation theory we approximate the solution to the equations of motion as a power series in $\epsilon$: $$ q(t) = q_0(t) + \epsilon q_1(t) + \epsilon^2 q_2(t) + ... $$ (and similar for p). In the Fokker Planck approximation we obtain...
I am only focusing on non-relativistic quantum mechanics in this post. My current understanding is that a particle of spin $\ell$ can be described as an element of the tensor product $L^2(\mathbb{R^3}) \otimes V$ where $V$ is a vector space of dimension $2\ell + 1$ carrying a representation of the Lie group $SO(3)$. I ...
Edit: After writing a Python code to numerically solve the constraint problem on the coefficients with Gauss-Jordan elimination, it seems that the biggest problem was that I was treating the coefficients $C$ and $D$ as identical for wave functions on each side of the well. This simply isn't true for solutions of any pa...
For example we work with 1+1D massless free boson, in canonical quantization we allow creation operators at any momentum so the Hamiltonian has continuous spectrum. But if we conformally map to a cylinder, the Hamiltonian has discrete spectrum. Why they are different?
I was working on desmos drawing transfer trajectories between the earth and moon. I managed to draw both the trajectories but i noticed something rather odd. The transfer orbits were different ellipses with the same apogee and perigee. My question is why and how are the orbits different even though the final destinatio...
The concept of the Grassmann number makes me confused. It is used to describe fermionic fields, especially path integral quantization. Also, it is used to deal with the classical field theory of fermions. To reduce my confusion, I want to ask the question only focusing on the classical field theory. Let us discuss the ...
In collision momentum always remains conserved that is total initial momentum is equal to total final momentum. Now suppose first object is ball and the second object is very very heavy like a floor. So the velocity of floor remains zero before the collision and after the collision. Now if I apply the concept of conser...
I have been trying to construct a charged object (not a conductor carrying any current) that can behave simultaneously as an electric and magnetic dipole and then calculate the electric and magnetic forces of interaction between two copies of this object at a large distance, and possibly associate an energy of interact...
In Elliot and Lira's Introductory Chemical Engineering Thermodynamics on p.134, the authors derive the entropy generated from an ideal gas expanding from a volume V to 2V, by the removal of a partition (no work or heat). They substitute the equation from the previous page $ p = N!/m!(N-m)! $ Which is the formula for th...
" The true physical significance of the concept of electric field, however, emerges only when we deal with time dependent electromagnetic phenomena. Suppose we consider the force between two distant charges q1, q2 in accelerated motion . Now, the greatest speed with which a signal can go from one point to another is c...
Dear fellow physicists! I come to you with a question regarding the definiton of the Hall current. The only sentence close to definition of this concept, I have found after extensive search on the internet was the book "Hall Effect Devices" by Popovic. Popovic says only this: "We shall see that this change in the termi...
we know that something travelling faster than the speed of sound creates a continuous sonic boom because the air cant get of its way fast enough but if we consider smaller particles which can travel much faster they cannot create a sonic boom because they are not ;arge enough and do not interact with the air particles...
Asuuming the vacuum has zero mass (negligible ZPE of the vacuum) and since Black holes generate gravity without the presence of mass (i.e. singularity at the center of a Black Hole) does this mean that the vacuum is gravitational? If yes, because free space vacuum is isotropic and homogeneous we would not feel its grav...
Hi almost every student knows the rotating bucket with a fluid problem as described here: Fluid in a rotating cylinder I wanted to do the same for a rotating fluid in free fall (like in the ISS) to show that it will take the shape of a sphere. Then we also consider by a symmetry of the final result that we can guess th...
Since the volume of a sphere $v(r)=\frac{4}{3} \pi r^{3} \left[m^{3}\right]$, its derivative relative to the radius is: $$ \frac{dv}{dr} =4\pi r^{2} \left[\frac{m^{3}}{m}\right] $$ Which is also a formula for the area of the sphere surface. While mathematically the expressions are identical, can we actually simplify th...
From my understanding, the coefficient of restitution, $e$, between two colliding particles, $A$ and $B$ is given by: $$e = \frac{ \big\vert \vec{v_A} \cdot \hat{I} - \vec{v_B} \cdot \hat{I} \big\vert}{\big\vert \vec{u_A} \cdot \hat{I} - \vec{u_B} \cdot \hat{I} \big\vert}$$ where $\vec{u}$ and $\vec{v}$ represent the i...
Light has no mass. So simply assuming F = M x A Will generate a zero answer. However, in slowing down light there is a reduction in energy. Energy cannot be lost only transformed. People have theorised about solar photon sails in outer space. If they were giant and made of this new concept, would there be any resultant...
I know that is a silly question but i cant figure it out. Suppose we have $$ \textbf{R} = A i + B j $$ and want to find the radial acceleration. We know that the radial acceleration is $$ \ddot{r} - r\dot{\theta}^ 2 $$ I tried to write x and y hats of the $$ \ddot{R}=\ddot{A}i+\ddot{B}j $$ in spherical unit vectors(...
I cannot grasp what should be a simple gas problem (last time I worked with gas formulas was 40 years ago). Values I provide here are just for the sake of explanation. There is a thermically isolated container of volume V=1m³. It contains compressed air with pressure P=5bar and T=300K. I make a hole on a side of the co...
I need to measure an acute angle in a right triangle. There are $2$ methods. Use a protractor with precision to $1^\circ$ to measure the angle. The result is $5^\circ$. Use a ruler with precision to $1\mathrm{ mm}$ to measure the opposite leg of the angle $a$ and the hypotenuse $c$, and calculate $\arcsin\frac ac$ ...
In rocket designs such as VASIMR, superconducting nozzles are frequently used to focus the resulting plasma jet. This leaves out the question of TVC control mandatory in chemical rocket engines, and an obvious way to do this is to adjust the magnetic nuzzle's field strength, e.g. make it slightly stronger on one side a...
In the book Quantum Mechanics by Cohen-Tannoudji, the author explains that the solutions of the Schrodinger equation of a free particle in one dimension are plane waves: $$\psi (x, t) = A e^{i(kx-\omega t)}$$ And that every linear combination of such plane waves that satisfy $$\omega = \frac{\hbar k^2}{2m}.$$ Will also...
So I have a problem with the intrinsic Fermi Level because by definition it is in the middle of the gap energy, and knowing that Eg=(Ec-Ev), we should have Ei=(Ec-Ev)/2. But when we follow the mathematical logic of the electron and hole densities in the intrinsic semiconductor we find the Ei=(Ec+Ev)/2. So does anyone h...
Twenty-five years ago I came across this question on a physics olympics exam and I've never really worked out a satisfactory answer... How much longer does it take to thaw an elephant than a chicken? I got as far as making the following simplifying assumptions: They are both frozen spheres of meat at a uniform -1°C "m...
How can I relate the Temperature distribution in a solid of simple geometry, like a cylinder, to the mechanical stress due to thermal expansion? I understand that using the linear expansion coefficient and Hook's law I could arrive at the expression: $$\sigma=E\alpha\Delta T$$ Where E is Young's modulus, $\alpha$ is ...
Consider a turbulent rotating flow. You are interested in its average features so you use the Reynolds-averaged Navier-Stokes equation. Now, conservation of angular momentum implies the viscous stresses are symmetric. But isn't that valid only for the total flow? In other words, is it possible that there could be a sit...
I am studying rigid body dynamics and am currently exploring the paper "Analytic determination of wrench closure workspace of spatial cable driven parallel mechanisms". In the paper, the derived dynamic model is: $\mathrm{Q}$ is a 3x3 matrix which maps the euler angle rates $\dot{\Theta}=[\dot{\psi},\dot{\theta},\dot{...
I noticed this while I was cooking pasta: The oil forms globules which viewed from top to down seem as perfect circles floating on the surface of water. How does this happen? Is there some elegant physics explanation behind this?
I am sorry about the probably naiive nature of this question (I am a software eng, not a physics student): I (think I) understand the popular curved "trampoline" model of 2-dimensional space, curved by a mass in the center ("bottom") of the trampoline. A free-falling particle will orbit the center, and if the velocity...
Game developer here. Most problems about objects sliding down sloped planes with friction are about the object sliding in the natural downward sliding direction of the slope. But how would you calculate the frictional forces on an object sliding in some arbitrary direction on a sloped plane? My initial thought is to ca...
Often when physics students are introduced to the HUP for position and momentum, the interpretation is that you aren't able to measure position and momentum for a particle to arbitrary precision at the same time. However, a better interpretation that works conceptually even without talking about measurements, is to acc...
I have read all of the question related to "bra-ket" but no one seems to take the same perspective as I am going to try to give. I know it might be a rather simple and short question, but I need to understand this to continue studying quantum mechanics (I'm new to this subject). Here's how I understand it: In my head, ...
I am reading up on the detection of the Higgs-Boson at the LHC and more specifically at CMS. I found the following graphic: I understand that the peaks correspond to the mass of the Higgs-Boson but I struggle to interpret all the aspects of the graph in general. The CMS site itself did not yield a satisfactory answer....
If one is heading towards the source of a constant amplitude EM wave at a speed that makes the frequency twice that of another observer, then the amplitude of the E (electric field amplitude) will double relative to the other observer. The power will be 4 times as great relative to the other observer, since power is pr...
I am intrigued about the physics behind these paintings, which are created by swinging a bucket with a hole filled with paint from a rope (here it is another example). In principle, it seems to be a spherical pendulum, whose lagrangian and equations of motion in spherical coordinates are $$L=\frac{1}{2} ml^2\left( \do...
I read that quarkonium is a "flavourless" meson. However what does it mean for a meson to be flavourless? I thought composite particles don't have "flavour" in the first place, and flavour just means the species of an elementary particle
I’ve been pondering a thought experiment related to quantum mechanics and photon detection, and I’m curious about the theoretical outcome and whether any similar experiments have been conducted. Imagine we have two setups designed to detect single photons emitted from a laser that’s been attenuated to ensure, on averag...
I'm stuck on the contents of a side box in "QFT for the Gifted Amateur", chapter 4, dealing about field operators. The side box sets the scene about the use case the section will be exploring, i.e. particle-in-a-box scenario. Under the assumption of a box of volume $V$ and using periodic boundary conditions, it's easy ...
This question has bothered me for some time couple of years ago, so here is the main problem: Suppose that an object of mass $m$, is thrown with horizontal velocity $v$ on a horizontal, frictionless, flat surface. There is air friction, so the only force acting against this object is air friction, which is the functio...
I was looking at this question on Mathematics S.E, as I would like to know the origin of the signs in the gauge transformations of the scalar and vector potentials components, $\phi$ and $\vec A$, of the four-vector potential $A^\mu=\left(\phi, \vec A\right)$: $$\phi\to \phi-\frac{\partial \lambda}{\partial t},\quad \v...
I am applying the method that Gibbons presents in this article, and it consists of dimensionally reducing a four-dimensional Lagrangian using Kaluza Klein in $S_1$, to a three-dimensional one and after some calculations, applying a magnetic transformation to the three-dimensional Lagrangian , but I can't find informati...
In discrete bais, we can express a vector as $$ \|\psi\rangle=\sum_{i} c_i\|e_i\rangle $$ with orthonormality $$ \langle e_i\|e_j\rangle=\delta_{ij}.$$ $\delta_{ij}$ is usual kronecker delta. If we promote the basis to continuum basis, we use dirac delta function instead, i.e., $$ \langle x\|x'\rangle=\delta (x-x').$$ My q...
As light strikes the emitting electrode, electrons are ejected. But not all of the ejected electrons are collected at collecting electrode since they don't all get ejected in the same direction. Increasing the positive potential of the collecting electrode attracts these electrons to it (the collecting electrode has a...
We know that the reflective coefficient in total internal reflection is 1, which means that all energy is reflected. But we also know that for evanescent wave, Poynting vector in the direction parallel to the reflecting surface is not zero. Isn’t this contradictory to the statement that all energy is reflected? Also, e...
There are some models that postulate the existence of graviphoton. What is the Lagrangian for the interaction of graviphoton with matter?
Let two concentric hollow charged conducting spheres of radius R1 and R2. If charge on inner sphere is Q1 and for outer it is Q2, wouldn't the resulting electric field due to the whole system be '0' inside inner sphere because charges at the surface of inner sphere will rearrange themselves to do so... because it's the...
My high school textbook briefly touched the topic of black holes, and this is how it defined them: "Consider a spherical body of mass $M$ and radius $R $. Suppose,due to some reason the volume goes on decreasing while the mass remians the same. The escape velocity from such a dense material will be very high. suppose ...
The books are stacked horizontally against each other. Each book weighs 1kg(10N). The coefficient of static friction between hand and book is 0.6 and between book and book is 0.4. Each hand gives a normal force to the books of P=120N. The prof. explained it as 2 cases, one where all the books are taken as a single body...
I am looking at Weinberg, The Quantum Theory of Fields, Volume 1 page 66. In this table, the author mentions various little groups of the Lorentz group. Orthochronous Lorentz transformations must leave $p^2$ and the sign of $p^{0}$ for $p^{2} \leq 0$ invariant. Shouldn't (c) and (d) then be $(\kappa,0,0,\kappa)$ and $...
When we calculate lower and higher frequency such that power becomes half in LCR circuit we end up with two value. For a complete derievation please see here. I have copied relevant information below: Resonant frequency: \begin{align} X_L &= X_C \\ \omega_r L - \frac{1}{\omega_r C} &= 0 \\ \omega_r &= \frac{1}{\sqrt{L...
I have a red laser and BS. Can I make MZI at the lab? I heard that is very difficult to achieve the calibration. What is expected to be seen after BS2? A dark spot at centre with fringes around? I searched a video on net but they very unpleasant and in one they said they can not arrange it because the paths difference ...
I've been studying fluid statics, and im getting stuck all the time trying to understand things that seem contradictory for example the hydrostatic paradox or how a small force can be magnified in Pascal's law. Anyway, i wanted to ask about the hydrostatic pressure in Torricelli's experiment at container 2 compared t...
I am trying to understand the basic concept of observable and state. Say that we have a state $\|\psi>=\|0>$ which is $(1\ \ \ 0)^T$, we have an observable $\sigma_x= \begin{bmatrix}0&1\\1&0\end{bmatrix}$.I would like to know what do I get if I measure $\sigma_{x}$ on this state? Should we simply apply the observable on...
It is on the basis of Principle of Least Action, that Lagrangian mechanics is built upon, and is responsible for light travelling in a straight line. Is its the classical equivalent of Schrodinger's equation?
w = fringe spacing $\lambda$ = wavelength D = horizontal distance between slits and screen s = slit spacing d = slit spacing $\theta$ = angle between central maximum and the ray at the nth maximum $\lambda$ = wavelength I am an A Level physics student in the UK. The book I am referring to later on is the 'Advanced PH...
I am reading a paper and it uses a notation I am not too familiar about. Although I saw it used elsewhere, I don't remember the meaning of it and I don't want to misinterpret it and realize after having done the computations. The topic is a velocity induced by a dipole of forces in a Stokes flow, and given $U_S (r,k)$ ...
Hello I'm trying to solve the following problem as I'm preparing for physics olympiads: The solution they gave involves finding the forces acting on the cylinder and hence finding acceleration, which allows us to figure out distance and time. However, I tried to find the distance it takes to stop using energy conserva...
A ferromagnet is inside a solenoid. When the current in the solenoid flips its direction, the solenoid magnetic field flips. As a consequence, the ferromagnet magnetization flips. What determines the timescale for the ferromagnetic response to the flipping of the external field? I imagine that the temperature plays a ...
There should be some relationship between them due to the nature of FSC, but I could not find anything about it.
Considering the equation $F(t) = ma(t)$, I'm trying to figure out if the following is also always true: $$F(x(t)) = m\cdot a(x(t))$$ I.e.: $F$ as a function of $X$ (the position, which itself is a function of time) is equal to the mass times the acceleration (which is a function of $X$). It seems mathematically to me l...
There is something that always puzzled me with perturbative approaches. To my understanding perturbative approaches are often qualified in terms of the order of the perturbation considered. For example in the context of cosmological perturbation theory several quantities are perturbed: metric, density, pressure... In t...

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