Potentials Definition and 228 Threads

I have an observable denoted by C, related to a complex potential B by : ## C= \bar{B}B ,## where ##B## is a complex potential. I know that ## \left. C \right|_0 =C_0 ##, a known constant, where the evaluation at ##_0## denotes an equilibrium \ reference state. From this, I can not make any...

I am struggling with Hamiltonian formulation of classical mechanics. I think I have grasped the idea of canonical transformations, including the idea of angle-action variables and invariant tori in phase space. Still, few points seem to elude my understanding... Let's talk about a particle...

I noticed that ##V(\phi)## has nonzero minima, therefore I found the stationary points as ##{{\partial{V}}\over{\partial\phi}}=0##, and found the solutions: $$\phi^0_{1,2}=-{{m}\over{\sqrt{\lambda}}}\quad \phi^0_3={{2m}\over{\sqrt{\lambda}}}$$ of these, only ##\phi^0_3## is a stable minimum...

Hi Pfs i am interested in spin networks (a pecular lattices) and i found two ways to define them. they both take G = SU(2) as the Lie group. in the both ways the L oriented edges are colored with G representations (elements of G^L the difference is about the N nodes. 1) in the first way the...

Can the magnetic and electric potentials (A and φ) be fixed to zero, or at least some constant value in a region of space? Naively, I'd think something like this might work (a hollow conducting sphere connected to a voltage source connected to ground, would the potentials inside the sphere be...

In a problem of an oscillating electric dipole, under appropriate conditions, one can find, for the potential vector calculated at the point ##\vec{r}##, the expression ##\vec{A}=\hat{k}\frac{\mu_0I_0d}{4\pi}\frac{cos(\omega(t-r/c))}{r}## where: ##\hat{k}## is the direction of the ##z-axis##...

Ion traps are very complex, but one of my Physics Olympiad textbooks (this is not homework) presents a simplified model of a resonating charged particle in an ion trap which according to me is wrong, there is either something missing or something overspecified here. A tuned circuit...

My solution in shown on the attached files. The overall reaction between Mn02 is 0.81 Volts The overall reaction which shows the reformation of the MnO2 catalyst is .27 Volts. The first reaction is more positive which shows that the MnO2 can work as a catalyst.

Goldstein writes "only if ##V## is not an explicit function of time is the system conservative"That means ##V(r,\dot{r})## is a conservative potential, however I think that only potentials of the form ##V(r)## are conservative potentials. Could you please tell me where I'm going wrong. Thank you.

We have a scalar potential $$\Phi(\vec{r})=\frac{q}{4\pi\epsilon_0} \left( \frac{1}{r} - \frac{a^2\gamma e^{-\gamma t}\cos\theta}{r^3}\right)$$ and a vector potential $$\vec{A}(\vec{r})=\frac{a^2qe^{-\gamma t}}{4\pi\epsilon_0r^4}\left(3\cos\theta\hat{r} + \sin\theta\hat{\theta} \right) .$$ how...

What I tried to do was using the fact that the wave function should be continuous. Asin(kb)=Be^{-\alpha b} The derivative also should be continuous: kAcos(kb)=-\alpha Be^{-\alpha b} And the probability to find the particle in total should be 1: \int_0^b A^2sin^2(kx) dx + \int_b^{\infty}...

The equation of motion for a particle in a gravitational field is ai = -Γijk vj vk In inertial coordinates the Lorentz force is mai = qFij vk So it seems like F corresponds to Γ. Just like F is expressed in terms of the derivatives of A, the christoffel symbols are expressed in terms of...

For part (a), I used this formula where where the i's represent the substance being used and mu_i^0 represents some reference potential. However, to my knowledge this simply calculates the change in chemical potential from one state to another which is not of much help in finding the relative...

Hello, PFI'm studying electromagnetism, delayed potentials, and I've been wondering about a few things. My understanding of the delayed potential is that the information from a moving charged particle at a given time travels through space at the speed of light to reach the observation point, so...

The Dirac equation for an electron in the presence of an electromagnetic 4-potential ##A_\mu##, where ##\hbar=c=1##, is given by $$\gamma^\mu\big(i\partial_\mu-eA_\mu\big)\psi-m_e\psi=0.\tag{1}$$ I assume the Weyl basis so that $$\psi=\begin{pmatrix}\psi_L\\\psi_R\end{pmatrix}\hbox{ and...

I think the right choice is c. I'll pass on my reasoning to you: We can think that if the formula of the potential is V(r)=\dfrac{kq}{r} If r tends to infinity, then V(r)=0. But the correct answer is d).

This is the diagram in mind Some of my assumptions like the particle q will be moving with some initial velocity V1 in the circle of radius of r1 and when it moves to the circle of radius r2 its velocity will be V2 ( > V1) since its potential energy is decreased. The amount of work done by...

Consider the cell ##Pt | H_2 | H^+ || Ag^+ | Ag##. I’ve sketched the electric potential against distance across the cell: I would think the electrode potential of the ##Ag+/Ag## electrode is ##V_{Ag+/Ag} - V_{H^+/H_2}##, which I’ve labelled on the right. We set ##V_{H^+/H_2} = 0## as per...

I have been trying to understand angle potentials such as described in this website, https://lammps.sandia.gov/doc/angle_style.html . Supposing two bonds have a certain angle they have to adhere to, what does this mean for that one atom being bound to, that only x amount of atoms can bind with...

My teacher insists that the reverse reaction has a negated electrode potential (oxidation potential?). This doesn’t make sense to me, since I am under the impression that the electrode potential is a property of the half cell at equilibrium and not of either of the reactions in a particular...

I tried looking for the other charge using the equation k|q1||q2|/r^2 but it tells me that my answer is wrong

What's the most used type of electromagnetic potential? Is it the retarded potentials?

"of the two types of solutions which the Maxwell equations yield for the wave equation, the retarded and advanced potentials, only the retarded field seems to have a physical meaning," let's start please with basic (and detailed as possible for the knowledgeable layman! p.s-which equation is...

Lorentz gauge: ∇⋅A = -μ0ε0∂V/∂t Gauss's law: -∇2V + μ0ε0∂2V/∂t2 = ρ/ε0 Ampere-Maxwell equation: -∇2A + μ0ε0∂2A/∂t2 = μ0J I started with the hint, E = -∇V - ∂A/∂t and set V = 0, and ended up with E0 ei(kz-ωt) x_hat = - ∂A/∂t mult. both sides by ∂t then integrate to get A = -i(E0/ω)ei(kz-ωt)...

There are 3 regions, to which I split the function as follows. I can derive the solutions myself. However I need to verify whether I am using them properly. There are two principles/ideas that I am not sure if I am misinterpreting. 1) Anytime a wave is incident on a discontinuity(such as when a...

Let ##Q## - charge of one of conductor, ##\phi_1## --- potential of charged conductor, ##\phi_2## --- potential of uncharged conductor. For the charged conductor: \begin{equation} \phi_1 = D_{11}Q , \end{equation} for uncharged conductor: \begin{equation} \phi_2 = D_{21}Q \end{equation}

This page shows solutions for Maxwell's equations of the electric and magnetic potentials (Eqn.s (509) and (510)): http://farside.ph.utexas.edu/teaching/em/lectures/node50.html They are derived with the aid of a Green's function: http://farside.ph.utexas.edu/teaching/em/lectures/node49.html...

Hello, Quick question on the relative refractory period in neurons. I understand it is caused by the slow closing of voltage gated K+ channels, which leads to hyperpolarisation. This means a larger than normal stimulus is required to bring the membrane to threshold. However, after reading my...

In Mathematical Methods for Physicists, 6th Edition, page 44, Example 1.8.2, the curl of the central force field is zero. 1. Why are central force fields irrotational? 2. Why are central force fields conservative? Any help is much appreciated...

Suppose there is a screen. This screen has been divided into a very large number of pixels. Each pixel has a material, that has the capability of producing a potential difference when light falls on it. The potential difference for different wavelengths should be different. Say, over a range of...

Homework Statement The textbook says to find the electric potential due to a point charge by moving a test charge from R to infinity, and integrating using the equation below. But when I integrate from infinity to R, the sign switches. Why is that? Both times, electric potential at V is 0...

and Lorentz Gauge. Manipulating Maxwell equations and introducing ##\vec A## vector and ##Φ## scalar potentials the following equations are obtained: ## \nabla^2 \vec A+k^2 \vec A=-μ\vec J+\nabla(\nabla⋅\vec A+jωεμΦ) ~~~~~~~~~~(1)## ## \nabla^2 Φ+k^2 Φ=- \frac ρ ε -jω(\nabla⋅\vec...

Homework Statement using Laplace principle find potential inside an uncharged spherical shell of finite width. shell is placed in an electric field E in z-axis direction. Homework Equations in this equation u is potential. equation is called 2-D Laplace’s equation. The Attempt at a Solution...

Homework Statement In hydrogen atom ionization H→p+e show that ##μ_H=μ_p+μ_r## Homework Equations G=μN (N is the number of particles) The Attempt at a Solution (1) I think the question should say "Find chemical potential relation AT EQUILIBRIUM", don't you think? (2) My professor said that...

Homework Statement Given circuit is a circle, force is a central force[/B] Ueff(r)=U(r)+L^2/2mr^2 Homework Equations the problem i find is, the angular momentum is a function of r however, the solution when differentiate the effective potential, just treat angular momentum as a constant. That's...

Consider the scenario where there are two parallel conducting pipes of radius R separated by a distance d, with pipe 1 at a potential of -V and pipe 2 at a potential +V. I have seen from many sources that there is a very easy method of images solution to the potential outside the pipes, given...

For a Dipole and a Torad (or a Solenoid) I need to find the scalar Potential,phi, Charge Density,rho, and then 4-Electromagnetic Current,J(rho*c,j) where A and J are 4-vectors and a and j are 3-vectors. -grad^2(phi) + 1/c^2*d/dt(phi) = rho/epsillon0 where grad(A(phi/c,a)) = -1/c^2*d/dt(phi)...

Hi, friends! Under particular conditions on ##\phi:\mathbb{R}^3\times\mathbb{R}\to\mathbb{R}## - I think, as said here, that it is sufficient that ##\phi\in C_c^1(\mathbb{R}^4)##: please correct me if I am wrong - the following equality holds$$\frac{\partial}{\partial r_k}\int_{\mathbb{R}^3}...

Hello, friends! I know, thanks to @Hawkeye18 who proved this identity to me, that, if ##\phi:V\to\mathbb{R}## is a bounded measurable function defined on the bounded measurable domain ##V\subset\mathbb{R}^3##, then, for any ##k\in\{1,2,3\}##, $$\frac{\partial}{\partial r_k}\int_V...

Homework Statement Consider a charge distribution which has the constant density ##\rho## everywhere inside a cube of edge ##b## and is zero everywhere outside. Let ##\phi## zero at infinity, ##\phi_0## at the centre of cube and ##\phi_1## at one corner of the sphere. Determine the ratio...

Hi, I need to teach a lesson on electrons in periodic potentials for Bachelor Physics students in just 20 minutes Any ideas on how to organize the lesson (pre-concepts they should know, relevant message and consequences) would be very much appreciated

According to responses at: http://physics.stackexchange.com/questions/93390/field-of-moving-charge-lorentzlienard-wiechert The Lorentz contraction of the electric field of a charge with uniform velocity is supposed to be symmetric across the plane pi/2 radians from the velocity vector of the...

Homework Statement My questions are just related to part a of this problem. Homework EquationsThe Attempt at a Solution I know that potential inside a conductor is equivalent to potential on the surface of the conductor and potential at any point is an algebraic sum of potential...

I'm studying for my electrodynamics exam and one of the past exam questions is: From the scalar and vector potentials, derive the homogenous wave equations for E and B fields in vacuum. I did derive the wave equation for the B field by simply taking the curl of the homogenous wave equation for...

Hi, I am a bit confused about rotational and irrotational flows, in this way: When I do exam questions/problems, there is often a bit at the start of a question on flows about why you can treat the velocity as the gradient of a potential. The only information it gives you is that it is...

What exactly are the problems with a path-dependent potentials? (e.g. magnetic scalar potential, normal electric potential over a changing electric field) I came up with this question, but can't be sure. The problems with such potential seem to me may be multivalued, as well as making the...

Consider a particle moving near the ground with the ground surface as the zero-point potential reference. If at time t we apply an electric field, say parallel to gravity force, where we should consider as a zero-potential reference point? Does the energy remain conserved (Is the energy equal to...

Hi. I'm wondering how different potentials, such as the Dirac-Delta potential, linear potential, quandratic potenial, etc., are implemented experimentally. I only understand how the Schrodinger equation is solved if these are the potentials and I'd like to have a better understanding of quantum...

If I took a charged particle and accelerated it, that acceleration would have an effect on charges potentials, allowing for the radiation of electromagnetic waves. This acceleration would be local to a point in spacetime and the observed potentials would depend on the frame of reference of the...

These are Maxwell´s equations in potential formulation: ∇2φ = DIV(grad(φ)) . Am I right? ∇2A = ROT(ROT(A))=ROT(B)=grad(DIV(A))-Laplace(A) . Am I right? In coulomb gauge in every point and at any time DIV(A)=[PLAIN]https://upload.wikimedia.org/math/4/4/1/44131cc26bd9db464d0edb7459ccca84.png...