Potentials Definition and 244 Threads

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...

Homework Statement A charged particle (either an electron or a proton) is moving rightward between two parallel charged plates separated by distance d=2.87mm. The plate potentials are V1=-75.8V and V2=-49V. The particle is slowing from an initial speed of 90.0 km/s at the left plate. What is...

An alternative formulation of the second law is that the energy of the system U is minimised if the temperature and entropy of the system are held constant. However, dU= TdS -pdV which means that U is presumably constant if the volume V and the entropy S are kept constant. How then can U...

I have an understanding of Maxwell's equations and a vague grasp on potentials. I'm trying to do something different with the potentials. I'm using the Feynman Lectures on physics, http://www.feynmanlectures.caltech.edu/II_21.html#mjx-eqn-EqII2113, using the equations an potentials in a box...

In the weak field limit, we have dt = (1 + 2\phi)^{-\frac{1}{2}}d\tau where the usual meaning of the symbols applies. This means that in GR dτ < dt analogous to SR. Let suppose we measure the period dtS of a photon emitted at the surface of the Sun as well as the same photon, i.e. same atomic...

Greetings all, Trying to resolve a discrepancy with vector and scalar potentials with Maxwell's Equations, specifically Ampere's law. In my E&M textbook (Balanis, 1989, Eqn 6-17), Ampere's law with a magnetic vector potential and electric scalar potential can be expressed as E=...

Hello, I was wondering if anybody knew of any material (books, papers etc..) which considers a possible connection between longitudinal waves and vector potentials, at least mathematically. I have been scouting about, but failed to find anything substantial. I understand that there seems to be...

Homework Statement A solid has energy (for one mole): ##U_1 =\frac{S^2}{a_1}+b_1V(V-2V_0)## Write H, F, and G in terms of their proper variables. Homework Equations Maxwell's relations and H=U+PV F=U-TS G=U-TS+PVThe Attempt at a Solution [/B] H, for example: I have tried writing dV as a...

Homework Statement [/B] I recently retired and thought it would be fun to reread my old EM texts. I took Fields and Waves 35 years ago for my undergraduate electrical engineering degree, so I am more than a little rusty. This question is for my personal knowledge, not for a class, but seems to...

... why are there more nodes/zeros? If l = 0 then the angular momentum contribution to the effective potential is zero, and there is the coublomb potential only. So shouldn't it always go as ~ -k/r^2 (k = constant) like the n=1 s orbital? Why is it that for n = 2 is there 1 zero, n= 3 there...

Do the lienard wiechert potentials always give the same result as coulumb law+lorentz transformations?

In my intro to Quantum Mechanics course, my professor gave a little aside while exploring the analogy between the Schrodinger Equation and Newton's second law: in classical physics, energy is conserved when the potential energy is not a function of time. I wanted to try to answer this my self...

Hey guys, I have a question regarding fields. I hope you guys can guide me to the right answer! :biggrin: The question states: A charge Q = 42 nC is uniformly distributed over a half spherical shell of radius R = 48 cm. What is the potential at the center? I didn't learn Gauss's Law in class...

Tried searching for equivalent question but couldn't find it. Presumably, a potential (like a Coulomb one) comes from another particle, which has its own momentum/position uncertainty, but in the Schroedinger equation the potential is well-defined either in terms of some coordinate system or...

Hey everyone! I'm doing this simple exercice from Halliday's book, where I have to find some intensities at some points... anyway after solving it, I realized that only looking at point b,and using Kirchoffs loop rule, the voltage at the negative of E1 and the voltage at the negative of...

Hello, everyone... I'm starting a new thread (among numerous others) regarding quark confinement and propose a discussion (in case anyone finds it interesting) on some of my considerations. As we all know, the idea of confinement consists in forbidding free propagation of free color-chagres...

Homework Statement My question is how can one derive U(S(V,T),V) from the relation U(S,V,N).This is the beginning of a given solution which is not explained in more detail. Homework EquationsThe Attempt at a Solution I can understand U(S,V,N) as dU=TdS-pdV+μdN but not the transition...

I have a potential which is zero everywhere except at -2a , -a , 0 , a , 2a on the x-axis where there is an attractive delta potential at each of the 5 points. I know there is a maximum of 5 bound states. I know there can be no nodes for |x| > 2a and a maximum of one node between each delta...

Taken from my textbook: My understanding is that: One valence electron, 2 spin states -> Half-filled Brillouin zone Seeking inspiration from "Nearly Free Electron Model": gaps open up at zone boundaries States nearer to zone boundaries get pushed down in energy further Since a fermi...

So, a while back i read about this idea, but i can't find it anymore, so i was wondering if anybody else knows about it. here it is: We know that if a vector field is conservative, then there exists some surface whos level curves are perpendicular to the vector field. or inversely, that the...

Why is that large neurons have smaller threshold potentials than small neurons during external stimulation? My confusion is because the time constant should be larger, right? tau = (r_m) * (c_m). where r_m is membrane resistance and c_m is membrane capacitance Capacitance increases...

Hello readers, Given the potential V(x) = - 1/ sqrt(1+x^2) I have found numerically 12 negative energy solutions Now I want to try to solve for these using matrix mechanics I know the matrix form of the harmonic oscillator operators X_ho, P_ho. I believe I need to perform the...

Hi, I'm studying classical mechanics via Goldstein's book, but I don't get the chapter about velocity dependent potentials. He writes: 'Lagrange's equations can be put in the form \frac{d}{dt}(\frac{\partial{L}}{\partial{\dot{q}}})-\frac{\partial{L}}{\partial{q}}=0(eq. 1.57) even if there is...

Consider the following potential function: V=αδ(x) for x=0 and V=∞ for x>a and x<-a , solve the shroedinger equation for the odd and even solutions. solving the shroedinger equation I get ψ(x)=Asin(kx) +Bcos(kx) for -a<x<0 and ψ(x)=Asin(kx) +Bcos(kx) for 0<x<a is it...

I have a molecular dynamics code and I want to model the reaction of O with Mg to form MgO at arbitrary temperatures. I am a little confused, however, because oxygen will exist as the diatomic molecule O2. This seems to mean that O2 molecules will have one type of interaction with a bonded...

Let say we have charged conductor M and we know its potential energy function Vm(r) when M is isolated from any charges. We also have charged conductor N with potential energy function Vn(r) when it is isolated. Now we put objects M and N close together, the charges on their surfaces...

Conceptual question help--Electric fields, potentials, etc. Homework Statement 1) Assume that the electric field E is equal to zero at a given point. Does it mean the electric potential V must also be equal to zero at this point? If not, provide an example to prove your answer. if you think...

Suppose that we have the potential V=\frac{exp(-\lambda r)}{r} that \lambda is a constant. To calculate the charge density we have to calculate the \nabla^2V. We can calculate directly by the formula \nabla^2 V =1/r^2 \frac{\partial (r^2 \frac{\partial V}{\partial r})}{\partial r}without...

Homework Statement I'm working through the 3rd edition of Griffiths' Electrodynamics book and have gotten stuck on some details in example 10.2, which describes an infinite straight wire carrying a current I0 for t>0. The figure included with the example illustrates a wire in the vertical...

Homework Statement It's not a direct question, but it's an implied part of a larger question: can classical waves experience simple harmonic oscillator potentials, like a mass on a spring does? Homework Equations The Attempt at a Solution I'm thinking no, since I can't come up...

Problem - Find the potential difference between 2 pts given the electric fields at all points in the surroundings. Approach- Let one point be A and one point be B. Thus, Va - Vb=- integral from b to a(E vector. dr vector) Also I can write the opposite equation, that is Vb -Va = -integral from a...

I recently got a copy of Purcell's very excellent Electricity and Magetism book. In the chapter about moving charge, he states without proof that the electric field due to a moving charge points at where the charge is now, as if there is instantaneous action at a distance. This is of course...

https://dl.dropboxusercontent.com/u/22024273/vectorpotential.png In the above passage, can someone explain to me where (3.102) comes from?

Hi. So we all know that electricity requires a complete circuit in order for electrons to flow in a wire. It's my understanding that this is due to the charge differential at the positive and negative, creating an electric potential. So, given that (or correct me if my understanding is wrong)...

Am I right to think that the potential established at an electrode immediately when placed in solution is given by E = E° - R \cdot T \cdot log_e(Q_{surface}) where the potential E of the electrode results from the standard electrode potential (E°) of the reaction and the reaction quotient...

Hi guys, I'm having a bit of difficulty understanding Pourboix diagrams. The biggest problem at the moment is that I don't clearly understand what exactly the E° values on the y-axis are of. All the resources I've consulted haven't been especially clear about this. Sometimes they make it...

Could one always write the periodic potentials in the form: v(r)=Ʃf(r-G) where the sum is over G (reciprocal lattice vectors)?

Homework Statement Consider an imaginary substance which is characterized by thermal energy U=\frac{NS^2}{V^2} (a) Determine the Helmholtz free energy F(T, V). (b) Determine the Gibbs free energy G(T, p). (c) Determine the enthalpy H(S, p) Homework Equations F=U-TS (maybe dF = dU - sdT = -pdV...

Homework Statement A point charge q, moving with uniform velocity \vec{v} = v \hat{z}, in the laboratory frame called \cal{K}. The charge is in the origin of the system at time t=0. Homework Equations Find scalar potential \Phi and vector potential \vec{A} both in the frame in which the...

I am given 4 potential charges, 1V, 3V, -6V, and 5V, all arranged randomly around each other. There is a test charge located at infinity. No distances are given between the potentials.1. Where will a test charge of 2*10^-6 C travel? 2. What is its kinetic energy? 3. Find the capatinance of a...

What is the relation between Electrode Potentials and Redox reactions ? Can we determine the relative strength of reduction of a metal by looking just at the electrode potentials ? Here is a particular thing that confuses me : We know that the standard electrode potential of Lithium is...

Hello guys, I'm studying Thermodynamics and I don't totally see how you introduce the potencials using Legendre transformations. I have seen a non formal explanation showing how you can interpret them, but not a rigorous demonstration of how you get them via the Legendre transformations...

It's not hard to show that the function: g = \frac{1}{2} (c \times r) is a "vector potential" function for the constant vector "c". That is, that: \nabla \times g = c The calculation is straightforward to carry out in Cartesian coordinates, and I won't reproduce it here. However...

Homework Statement I have four questions based on this principal that I'm struggling with. 1. The Potential at the surface of a sphere of radius R is given by V = kcos(3θ). K is a constant. (Assume no charge inside or outside the sphere). a) Find the potential inside and outside the...

Homework Statement 1st question:A voltaic cell is made up of mg2+/mg half-cell and fe3+/fe2+ half-cell. Which of the following statement are correct? a.addition of water to the fe3+/fe2+ half-cell has no effect on cell emf. b.increasing the temperature has no effect on the cell emf...

Homework Statement I have to find the Lienard-Wiechert potentials \vec{A}=\frac{\vec{qv}}{R-\vec{R}\vec{v}/c} \phi=\frac{q}{R-\vec{R}\vec{v}/c} (both evaluated in t_r) with \vec{R}=\vec{r}-\vec{x}(t_r). \vec{r}=x\hat{x}+y\hat{y}+z\hat{z} is the vector asociated to the...

Hi, I have a doubt about a problem of classical electrodynamics (specifically for calculating the Lienard-Wiechert potentials). (t_r is the retarded time, and t the time). The position that has a particle is given by: x (t_r) = e cos (w t_r). The squared modulus of the relative position...

I'm trying to investigate molecular dynamics simulation for MgO, although this research is somewhat new to me. For those of you with university access, one of the papers I am following is Shukla et al. (2008, J. Nuclear Materials) here...

I'm trying to compile the first five IP's for Protactinium. I was able to find 1-3 on these two sites http://www.astro.lsa.umich.edu/~cowley/ionen.htm http://www.gordonengland.co.uk/elements/pa.htm But am coming up with nothing for the 4th or 5th IP. Does anyone have any possible...

Homework Statement What fraction of a beam of 8 eV electrons is reflected by a potential step up of height 6 eV? What fraction is reflected from a step down of 6eV? Homework Equations R=(\frac{k_{1}-k_{2}}{k_{1}+k_{2}})^{2} Exchange k_{1} and k_{2} for the step down potential...