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I know for a fact that when an object starts spinning, it can be described as an inertial frame. For the sake of this question, let's consider a disc with a person placed on the edges of it. Now, the disc is smoothly spinning in one direction, and the person feels an outward push (centrifugal force). But he can believe...
I am writing a javascript program (web page) that uses iterative simulation to show the motion and mechanics of a satellite in orbit around the earth. So far, using only circular orbits, it has been working perfectly. However, I am now adding arbitrary velocities to these satellites to see how that affects their moti...
I want to ask a question about a rather famous review paper on RG by Shankar. On page 92-93 of this paper, Shankar provides a version of RG for spinless fermions in $d=2$ dimensions with a soft cut-off (at $T=0$). This soft cut-off has completely baffled me. On one hand, it conforms to the intuitive expectation of allo...
Actually I have two questions. we know the efficiency of heat engine equal {1-(t/T)},where t is sink temperature and T is source temperature. Now, if two source and one sink reservior are connected by a heat engine(as shown in picture),then if T is taken as sum of two source temperature and that gives wrong answer. ...
I'm confused on the difference in results I'm seeing for the density of states for a free electron (for example, a conduction electron in a metal). For one textbook (Kittel), I'm seeing that the density of states depends on the volume of the system, whereas in another, the density of states does not depend on the volum...
I am interested in the time reparametrization. t is replaced by $\tau$. See how the infinite dimentional lie group Diff(R) is introcuced. t is a real number of R. and $\tau$ a function on R. To have them on an equal footing we will identify the variable t to the function t -> t (the identity on R). We considere $\tau (...
I was studying Lienard-Wiechert Potentials from Griffiths, where he wrote that electric charges cannot travel at the speed of light. Which led me to a rabbit hole of charges both magnetic and electric, wherein I stumbled upon the fact that the sheer existence of monopoles would require the removal of worldline from spa...
Background As someone who has just finished my first year of undergrad, I don't really have any experience with QFT but have some experience with quantum mechanics and the math behind it. I have taken college courses on Newtonian mechanics, special relativity, and electromagnetism. In the "Fields" episode of his "Bigge...
Everything I read about black holes—discussions using Penrose diagrams and Kruskal coordinates, etc.—seems to be based on vacuum solutions to EFE. Sometimes it’s said that all trajectories entering a BH must end (or not end, as you prefer) at $r=0$, where curvature is infinite. But my naive belief is that the mass-ener...
Imagine if two objects of identical mass are under two different gravitational field,let's say two different planets (with Different value of gravity) both of the objects are of same mass,but we can easily notice that one body will be easier to move as compared to another (the object which will be on the planet with le...
This question is a very basic one, We are told that that current is produced because of flow of electrons but it is stated that the flow of current is opposite to the direction of the flow of electrons if the electrons are the body which moves which further produces current then how can current move to the opposite dir...
This source is showing that solving the Schrödinger equation for a triatmoic linear molecule yields the same formula for the rotationaI quantum states $BJ(J+1)$ as for dipoles. For dipoles, the total rotational energy can be expressed as the total length of the molecule $R$ and a particle with reduced mass $\mu$ which ...
I'm studying Tensor calculus and I found this interesting problem: Show that: $$ \Delta F=\frac{1}{\sqrt{\vert g\vert}}\partial_i\left(\sqrt{\vert g\vert} g^{ik}\partial_kF\right)$$ Here's some attempts, hope it helps, even I find them useless! Well, we know that: $$\Delta F=\nabla\cdot \nabla F $$ And : $$\nabla \c...
If an atom flies long enough into deep space, without colliding any other matter or EM waves (purely thoughtful experiment), what does happen? Because velocity vector is unchanged, no EM waves are generated, so no energy is lost and atom continues the travel eternally. Electrons spin around nucleus and thus generate E...
Given question: A student uses simple pendulum of length 1 m and commits an error of Δl=1mm to determine g(the acceleration due to gravity). He uses a stopwatch with the least count of 1s for this and records 40 seconds for 20 oscillations. For this obervation which of the following statement(s) is(are) true? (1) Erro...
Can you please help me with this I'm stuck? A particle starts from rest at $t=0$ at the origin and moves in the XY plane with a constant acceleration of $a=( 2i+4j)\ \mathrm{m/sec^2}$ After a time of $3$ seconds has elapsed. find: the $x$ and $y$ components of velocity. the coordinates of the particle. the speed of ...
I know this is not the full equation but right now in this path of the course that what we learned so far. We studied that a wire along the $z$ axis produces magnetic field $\vec{B}=\frac{\mu_{0} I}{2 \pi \rho} \hat{\varphi}$ then for every closed loop that goes around the wire we can write $$\oint \vec{B} \cdot d \vec...
This is with regards to problem 3.19 from Goldstein's Classical Mechanics, A particle moves in a force field described by the Yukowa potential $$ V(r) = -\frac{k}{r} e^{-\frac{r}{a}}, $$ where $k$ and $a$ are positive. where I bolded the assumptions as this is the only information I can imagine helps me resolve this....
(The paper I'm referring to in this question is "Quantum simulations of one dimensional quantum systems") I've been trying to understand the paper above, specifically on constructing a matrix representation of the position operator, $\hat{x}$, in discrete real space (Equation (11)). In analogy with the CV QHO, we defi...
What is the mathematical or physical way to understand why the 4th and 5th components in the Georgi Galshow SU(5) model has the SU(2) doublet $(1,2,-1/2)$: $$ \begin{pmatrix} \nu\\e \end{pmatrix} $$ with left-handed $\nu$ in the 4th component and $e$ in the 5th component of $5^*$; while in the contrary, the SU(2) dou...
The Hamiltonian matrix of particle subject to a central potential is described by $$ H=\begin{pmatrix} H_{11} & H_{12} & H_{13} & H_{14}\\ H_{21} & H_{22} & H_{23} & H_{24}\\ H_{31} & H_{32} & H_{33} & H_{34}\\ H_{41} & H_{42} & H_{43} & H_{44}\\ \end{pmatrix} $$ where $$ H_{ij}= \langle\phi_i| H |\phi_j \rangle $$ and...
Even when we cast Maxwell's Equations in as coordinate-independent form as possible, $dF=0$ and $d \star F = J$, we still have to make use of the Hodge star $\star$ which is defined relative to an orientation. It doesn't look like the equations are preserved under orientation-reversal. But does space have an orientati...
I'm working on a problem in Kibble's Classical Mechanics (Chapter 11, Problem 12) and came upon a method for exploring the stability of an equilibrium point that I wasn't familiar with. The question basically says to explore the stability of one of the stable Lagrangian points in the restricted three-body problem by as...
From high school physics we know the heat energy $Q$ given to a mass $m$ rises its temperature by $\Delta T=\dfrac{Q}{mc}$. When there is a vacuum, $m=0$, like interstellar space how we define temperature rise due to a given heat energy?
I was going through the section on divergence and became confused on these examples. Griffith states in the textbook that (a) has positive divergence, (b) has zero divergence, and that (c) has again positive divergence. For (c), shouldn't the divergence be zero as all the arrows are pointing the same way? And if (c) ha...
What I mean is, suppose white light falls on a red object and is reflected, so when we see the reflected light reaches our eyes we see it as red (probably because its wavelength corresponds to red). But let's say that this reflected light falls on a purple object and then reaches our eye. What color would we perceive o...
Note:- Figure is the screen shot from https://www.youtube.com/watch?v=ofgusnhQ07Q Doubt regarding the application of Newton's second law in the radial direction. Left hand side of the equation consists of forces that are acting on the object. right? Why didn't he consider the centripetal force as a force acting on tha...
Let's say I have some Lorentz-violating theory. For concreteness we could imagine a scalar field \begin{equation} S=\int {\rm d}^4 x \left(-\frac{1}{2} (\partial \phi)^2 + V(x)^\mu \partial_\mu \phi\right) \end{equation} where $V(x)^\mu$ is some space-time dependent vector field (ie a non-trivial external current sourc...
Suppose that we have a particle moving at $0.8 c$ (or even a photon) and it is just, say $2 \times 10^{5} m$ away from the boundary of the universe (whatever that boundary be). Since the expansion speed of universe is less than that of our particle then it has to reach the boundary (right?), what happens then? Does it ...
From the videos I could find over internet, it is written that a liquid at high pressure always cools when throttled through a nozzle or restricted path(this is used in refrigeration). And that Enthalpy also remains constant. I have the Steady flow Energy Equation: $\delta Q + U_{1}+ K.E._{1} + P.E._{1} + P_{1}\nu_{1} ...
A quarter of all matter in the observable universe is Helium-4 while all Helium-4 atoms have a nucleus with a zero spin integer which is characterized by Bose–Einstein statistics. Does this mean that Helium-4 nuclei are not subject to the Pauli exclusion principle and likewise multiple Helium-4 nuclei can occupy the sa...
I've been trying to digest The Classical Mechanics of Non-conservative Systems by Chad Galley. It describes an approach to applying Lagrangian mechanics to non-conservative systems via variable doubling. The approach is basically to have one variable handling causal interactions with the environment, while the other ...
Note:This may look like a homework type question but this is just a doubt of mine in how much current flows from and Ideal wire. Let's take the circuit given below. Let's say current i flows in the circuit. Let's say the current divides into two parts $i_1$ and $i_2$. By symmetry we can say that same currents flows in ...
I read in the book that the normal force acting between two bodies during elastic collision is conservative, but I am not able to understand why this holds true because, if the normal force is non-conservative, then also the total work done by normal force on both the blocks will be zero and hence the kinetic energy of...
Let's say I have a particle in the quantum state $|+\rangle = \frac{1}{\sqrt{2}}(|0\rangle + |1\rangle)$, represented as a density operator (1st matrix) that went through a depolarizing chanel (2nd matrix). Let's call the depolarized matrix $D_p$. $$ \begin{bmatrix} .5 & .5 \\ .5 & .5 \end{bmatrix} \rightarrow \begin{b...
The Wikipedia page on the subject states: Galaxies are not distributed evenly throughout observable space, but are typically found in groups or clusters, where they have a significant gravitational effect on each other. Velocity dispersions of galaxies arising from this gravitational attraction are usually in the hund...
Water has a latent heat of vaporization equal to $2,260\ \mathrm{kJ/kg}$. While ethyl alcohol has a latent heat of vaporization equal to $846\ \mathrm{kJ/kg}$. Even though ethanol's latent heat is almost $1/3$rd as that of water, ethanol has a stronger evaporative cooling effect. In my understanding its because ethanol...
Are degenerate states stationary in quantum mechanics? I know that stationary state means single wavefunction corresponding to single energy. But, what will be in the case of several wavefunctions corresponds to single energy (e.g. degenerate states). are All of them stationary in that case? Can you pls give me expli...
The parabolic trajectory of a projectile has different radius of curvature at different points of time. Is there a way to find R of C for a simple projectile, thrown at an angle θ and initial velocity v0 from level ground.
Poincaré transformation consists of translation, rotation, and boosting. And by assuming the physical quantities are invariant and equations are covariant under the transformations, we build the models on particles. The invariance and covariance make sense if space is the same under the transformations. Space has symme...
A laser beam (a form of electromagnetic radiation) has various applications in laser cutting, drilling, welding etc. which is possible by melting or vaporization of target material by heat produced by laser. My question: How does electromagnetic radiation produce heating effect in a material?
My question is regarding the following graph, The $X$-axis is the $r$ coordinate of the $(t,r,\theta,\phi)$ system, and the $Y$-axis is the expansion $\Theta$ of a congruence of weakly bound, timelike, radial geodesics. There is only a physical (curvature) singularity at $O$. However after some calculations, I obtaine...
I am studying this paper which describes the metric of a Planck star, a state in the life of a massive star conjectured in the context of Loop Quantum Gravity: in a collapsing star, the pressure of quantum effect should be able to contrast and reverse the collapse of the star leading to an explosion; this stage is very...
When two identical bodies are brought into thermal contact, and both are surrounded by an isolation, does the fact that they have a finite temperature difference, which generates entropy, change their final temperatures. Are their final temperatures their arithmetic average
If a physical body leaves earth with 11.2 km/s escape velocity with a certain amount of Mechanical energy, then how can it be said that the body will have 0 Mechanical energy at a point at infinity without following the Conservation of energy?
Our fridge recently broke down, and now I'd like to turn the leftover compressor into an air compressor. I've also got an old tank from a water pump. This one has only 1 opening. All the air compressors I have seen, however, have 2 openings, besides the pressure release valves. One entrypoint, and one exit. Even tutori...
Can someone explain structure functions (proton structure functions)? I know they are used to study or understand the structure of protons , but does there exist a particular formula to calculate their value? Or are they measured from experiments? Is it a physical quantity?
There has been much media coverage of the paper Photonic Tensor Cores for Machine Learning: https://www.independent.co.uk/life-style/gadgets-and-tech/news/ai-machine-learning-light-speed-artificial-intelligence-a9629976.html https://www.sciencedaily.com/releases/2020/07/200721114731.htm https://techxplore.com/news/202...
I've been looking through different Pdfs /articles on strong coupling constant and nearly all of them involve cross section, I've understood what cross section is but not how is it connected to coupling constant?
A $170$ lb man carries a $20$ lb can of paint up a helical staircase that encircles a silo with radius $30$ ft. The silo is $80$ ft high and the man makes exactly four complete revolutions. Suppose there is a hole in the can of paint and $16$ lb of paint leaks steadily out of the can during the man's ascent. How much w...
These days I am spraying the leaves of my garden, to prevent insects, mixing strongly water and soya oil. The color has become all white. Soy oil has a relative density of $0.915 \div 0.925$ kg/dm$^3$ and the water is $1.000$ kg/dm$^3$. The white colour I believe is due to the strong mixing that breaks the bonds of so...
I was watching a "small overlap" car crash test video and I noticed that the car tended to rotate around to the right side during the collision (see the figure below). My question is why does the car rotate? This is the link to the video: https://youtu.be/dfG4SqPYcSA
According to wikipedia vapor supersaturation is relatively common (20-40% of the time) in the upper troposphere. Assuming perfect conditions (such as sufficient visual contrast and no wind), would it be possible to observe the mesmerizing patterns seen in a classic cloud chamber in the free atmosphere?
I have a hollow cylinder made of material A (eg. glass). Inside the cylinder I have some liquid (material B, eg. water). On the outside of the cylinder, wrapped around it, I have a metal wire (material C, eg. copper). We use the resistance of the wire with the appropriate current to generate heat. All parameters are kn...
I want to better understand what the path integral is and what it isn't. Even though I do this to learn QFT, this question is purely concerned with classical fields, no quantization is intended at all. Neither am I talking about classical particles with well-defined paths, though. Feynman introduces the path integral w...
Any electron in an atom is described as a standing wavefunction in a potential well. In multielectron atoms, when an electron in any orbital beyond 1S² is described, is it the resultant of interference of all other wavefunctions or is it calculated as if it's the sole electron in that atom?
The book says that oil spreads over water due to the greater surface tension of water as compared to oil, so the comparatively stronger water film stretches the oil surface and makes it spread... But if this is the case, doesn't that mean that the oil layer will go on spreading indefinitely(even if it gets one molecule...
I was listening to the Feynman lectures on physics Vol. 3, Ch.2 the other day, and he was talking about the relationship between light polarity and the electric field of light as it is transmitting through dense material. Suppose a medium is uniform and isotropic. Suppose light passes through the medium. Light is an e...
I have read this SE-Physics question and its answers, however, I could not find anything regarding the effect of Sun's $g$-field on the GPS clocks. When a GPS clock orbits earth, depending on whether it is in superior or inferior conjunction, the $g$-potential of the sun changes. In the traditional approach to the GPS-...
If I am breaking down a force $1$ N which is applied in one dimension on a mass. If the $x$-axis were collinear with the force vector, then the total force would be $1$ N along the $x$-axis and $0$ N along the $y$-axis. When you rotate the reference frame $30$ degrees, the force can become $(1$ N$)\,\sin30^{\circ}=0.5...
This content was taken from https://ecee.colorado.edu/~bart/book/contents.htm. In that they derive the diffusion current expression from this particular carrier density profile. Their derivation is as follows.(the explanation given is also theirs) The flux at x = 0 due to carriers that originate at x = -l and move fr...
It is commonly said that "elementary particles are indeed formed by strings." (from E Witten interview) Which equations of string theory show that elementary particles are indeed formed by strings (2d string worldsheets)? How to see elementary particles in equations of each version of string theory? In Type I? In Ty...
In the figure, Suppose the rod system(shown black) starts moving with some angular velocity say $\omega$ with the bob hanging to the string. So, after sometime the ball too rotates with the same angular velocity $\omega$ that of the rod system with the help of the string's tension(the rope making a constant angle wit...
If i have a block falling down a mobile inclined plane, would it work if I solve the problem as usual in the plane's frame of reference and use the relative acceleration formula $\vec a_{b|p}=\vec a_b-\vec a_p$? I'm concerned with whether the fact that the plane is moving would make the "gravity" value "less", and so I...
If two particle are neither approaching towards nor receding away from other then their relative velocity is non zero. How is this possible??
Since this is two-dimensional motion, why would $m(dv/dt)$ not have some directionality in addition to being the rate of change of the magnitude of momentum? Is Feynman assuming that the directionality doesn't change in infinitesimal time?
What are some of the explanations as to why the wave function of electrons collapses when interacting with an observer? Is there a specific reason why the wave function collapses, what are some of the proposed explanation. I read that it's because when observed an electron may hit the electron emitted thus causing the ...
I was going through a derivation and I came across a term in the kinetic energy of the Lagrangian that had both a velocity term and a rotational term. So I looked it up and I found these two links https://hepweb.ucsd.edu/ph110b/110b_notes/node19.html https://hepweb.ucsd.edu/ph110b/110b_notes/node20.html In the first li...
https://getpocket.com/explore/item/how-the-universe-remembers-information The memory principle might even solve the black-hole information paradox that Hawking discovered in the 1970s. In the usual analysis, black holes are pathologically forgetful. The only record they keep of the matter that falls in is its mass, sp...
If blue light is emitted from excitations below 500C for example potassium in a flame emits purple photons but only has to be 500C for it to do so, then how do we know if the sun is yellow hot or if it’s just an element inside causing it to be yellow when it could be much colder (or hotter)
Suppose there is a rope which is initially untaut, two people go and hold both ends of the rope and start running in opposite directions at constant velocity. Let person holding one end be '$A$' and the person holding other be '$B$', now when the rope becomes taut and the people try to move further, would there be a t...
I only did one QFT course so there may be something obvious I'm missing. Studying quantum fields, some of the easiest examples are bosonic scalar $\phi$ and vector $A_\mu$ fields, and fermionic spinor $\psi$ field. On the book from Peskin and Schroeder, it also mentions the (probable) bosonic tensor $g_{\mu\nu}$ for gr...
For any movement we need a force. Which force does push the gas coming fast out the bottle of cold coke drink when we open the lid especially for the first time?
The dipolar moment for the deuteron is $$\vec{\mu}_{d}=\frac{\mu_{N}}{2 h}\left\{\left(g_{s}^{(p)}+g_{s}^{(n)}\right) \vec{S}+\left(g_{s}^{(p)}-g_{s}^{(n)}\right)\left(\vec{s}_{p}-\vec{s}_{n}\right)+\vec{L}\right\}$$ we know could understad that $$\left(\vec{s}_{p}-\vec{s}_{n}\right)=0$$ in the deuteron if we suppose t...
I read about the teleportation in a simple explanation involving Alice and Bob. I understood the part where Alice and Bob are given one of the particle from an entangled pair. And then Alice measures state in Bell basis. And provides Bob with the operator to be operated. I did understand that, but I am still curious to...
I was watching an introductory video on general relativity and it said that according to Einstein the natural state of any object is free-fall motion. All objects naturally move through the shortest (geodesic) path through spacetime which can be described by a geodesic equation. If that spacetime happens to be curved d...
If I have a grounded conducting sphere with a cavity [radius $R$] that has a positive charge inside, using the image method to calculate the electric field I have to use an imaginary charge. My question is where is the charge located and why. The imaginary charge is placed inside the cavity or inside the conducting sph...
Although I hold a masters degree in math, I always struggled with physics, and I was relieved when I didn't have to study it any more. Now that I have been away from the academic scene for more than 25 years, I think I should give physics another go. I am looking for a single comprehensive volume that will teach me all...
The question has arisen as a result of working on part b of problem 3.19 in Goldstein's Classical Mechanics book. A particle moves in a force field described by the Yukawa potential $$ V(r) = -\frac{k}{r} \exp (-\frac{r}{a}), $$ where $k$ and $a$ are positive. Show that if the orbit is nearly circular, the apsides wil...
I am under the impression that topological insulators have a distinguishing characteristic where they have an odd number of Dirac points that intersect band gaps at the Fermi energy. However, this seems to violate the Nielsen-Ninomiya theorem which states there is an even number of states of opposite chirality. I take ...
https://en.wikipedia.org/wiki/Effective_potential In this wiki link, They write $$ E = \frac{1}{2} mv^2 + \frac{1}{2} mr^2 \omega^2 - \frac{GMm}{r}$$ Then they sub $$ L= mr\omega$$ Which turns the energy expression into, $$ E = \frac{1}{2} mv^2 + \frac{L^2}{2mr^2} - \frac{GMm}{r}$$ Now, at the end wiki writes that t...
When we write kinetic energy for orbital mechanics, we usually write $$ K= \frac{1}{2} m \dot{r}^2 + \frac{1}{2}m r^2 \dot{\phi}^2$$ I understand the first term is the tangent velocity along the ellipse but what is the second term? My direct interpretation of it would be the energy in rotating the velocity vector as t...
I've been analyzing "ball hits a rod in space" type collisions, where speeding ball transfers part of its kinetic energy during elastic collision to the motionless rod, making it gain linear and angular momentum. There are many videos explaining such a scenario, I think I understood basic concept. I tried to write a mo...
I was doing a propagation of uncertainty on the following numbers, and I got a lower error from the calculated quantity than the measured quantities. So why is it that my compounded error smaller than the individual errors it is made up of? The two measured quantities are $A = 1.0 \pm 0.2 \hspace{0.1cm} m$ and $ B = 2....
I have the following putative set of decays for the $\rho^0$ meson: $$\begin{array}{l} \rho^{0} \rightarrow \pi^{0} \pi^{0}:\text{STRONG} \\ \rho^{0} \rightarrow \pi^{-} \pi^{+}:\text{STRONG} \\ \rho^{0} \rightarrow \pi^{-} \pi^{+} \pi^{0}:\text{STRONG} \\ \rho^{0} \rightarrow K^{-} \pi^{+}:\text{WEAK}\\ \rho^{0} \righ...
A ceiling fan creates a vertical circular airflow. Does this airflow along a window or a door in the room reduce the airflow through them? I would guess air trying to flow into the room would face more resistance as the ceiling fan's speed increases. As an example imagine there's a window along the right-hand side I co...
I'm trying to proof the first Hohenberg-Kohn theorem using the Reductio ad absurdum, but I'm stucked in the last point. First, I know that the eletronic density is: $${ρ(r)=∑_{i=1}^n|χ_i(r)|²}$$ And, $$Ψ = ∑_{i=1}^nc_iχ_i(r)$$ The First Theorem states that the external potential $v(r)$ is determined, within a trivial a...
It is commonly shown that the magnitude of the band gap at the edge of the 1st Brillouin Zone is equal to twice the Fourier component of the potential energy for a one dimensional crystal. Also, the way the spectrum is plotted and compared to the free electron dispersion suggests that the split is symmetric. However, a...
Let us have a glass slab and we illuminate it by a light beam impinging normal to the slab and passing through it. Since the speed of light is slower inside the glass it loses its energy and when it exits the slab it gets up to speed of light in free space again. In this energy exchange the input side of the slab gets ...
With increase in cross sectional area the number of atoms with which electrons will collide will also increase in the same proportion. So basically the resistance shouldn't change with increasing wire thickness. Then why is it inversely proportional to cross sectional area?
This question is a spin-off from this related question: Why does the Born approximation for the scattering amplitude depend on the potential $V$ everywhere in space, unlike classical scattering? This question deals with a broadly similar topic, which is solving scattering problems "locally", i.e., without knowing the ...
I have read that symmetric potential has even bound ground state, but I don't know how to derive it? The only conclusion I can derive is for even potential I can take real wavefunction. I also want to ask, if odd bound ground state ever exist? I have never seen any.
What happens to the temperature of water when compressed? Enthalpy $H = U + PV$. $H$ is conserved in a closed system. By which I mean adiabatic and negligible external work applied. We compress a litre of water to 10 bar (say). This requires negligible work because water is almost incompressible. But $P$ goes up, $V...
What is the difference between classical particle and quantum particle? I was thinking that we can distinguish between classical mechanics and quantum mechanics by changing our length scale. But I don't understood in what way or on what parameter we differentiate between classical particle and quantum particle. you tak...
Intro On the topic of dynamical systems associated with 3-dimensional rotation of rigid bodies, you will always encounter singularities in the equations of motion that will produce computational errors at certain rotations. At least, these singularities will always occur if the following approach is attempted (see next...
My teachers use $B$ for representing magnetic field and the standard textbooks do so as well, but recently, one of my friends said that $B$ is magnetic flux density, and $H$ is used to represent magnetic field. I tried to look it up on the net and found both $H$ and $B$ are used for magnetic field. Can someone explain ...
I was browsing the Wikipedia page for "Magnometer" and saw the figure that a caesium vapour magnetometer has a sensitivity of $300 \rm\ fT/Hz^{0.5}.$ I understand femtotesla but I am confused about the meaning of square root hertz and the what the overall unit is truly measuring. I saw this post about square roots of u...
Let's say that we have defined a certain physical quantity from a particular relationship and then we find another relationship and define the physical quantity again. For example, $$v = u + at$$ $$\text{and }v = \sqrt{u^2+2as}$$ where $v$ denotes the final velocity, $u$ denotes the initial velocity, $a$ is the acceler...
The electric potential is zero on the equitorial plane of an electric dipole but there is an electric field at that plane anti parallel to the direction of dipole moment. Now what is the significance when we say that the electric potential is zero at a point in an electric field? Again, does the electric field exert fo...
If a car drives into a wall and energy cannot escape to the environment, does all that energy that went into the wall get transferred back into the car? If so, is that why the car gets damaged?