Potential Definition and 1000 Threads

Time indepedendent Schrödinger equation for a system (atom or molecule) consisting of N electrons can be written as (with applying Born - Oppenheimer approximation): $$ [(\sum_{i=1}^N - \frac {h^2} {2m} \nabla _i ^2) + \sum_{i=1}^N V(r_i) + \sum_{i < j}^N U(r_i,r_j)] \Psi = E \Psi $$ Terms in...

Hi, I'm wondering if I have an expression for the scalar magnetic potential (V_in) and (V_out) inside and outside a magnetic cylinder and the potential is continue everywhere, which mean ##V^1 - V^2 = 0## at the boundary. Does it means that ##V^1 - V^2 = V_{in} - V_{out} = 0## ?

Ion traps are very complex, but one of my Physics Olympiad textbooks presents a simplified model of a resonating charged particle in an ion trap A tuned circuit consists of an inductor and a parallel plate capacitor (capacitance C and plate separation d). It has a resonating frequency ##\nu...

V1 = Q/30 In parallel: C = C1 + C2 V2 = Q/(60 + 90) V1/V2 = 3 V1 = 3V2

The removed mass is ##\frac{1}{8}M## My idea is to find ##g## from large sphere then minus it with ##g## from small sphere (because of the removed mass): ##g## at A = $$\frac{GM}{R^3}\left(\frac{1}{2}R\right)-\frac{G\left(\frac{1}{8}M\right)}{R^2}$$ Is this correct? Thanks

I encountered a problem regarding the appropriate sign needed to be taken for the work done on a dipole when it rotates in a uniform electric field and would appreciate some help. The torque on a dipole can be defined as τ=PEsinθ The work done on a dipole to move it from an angle ##\theta_0##...

- Change DV to velocity and measure it with motion sensor - create separate table/graph of friction coefficient using velocities and other information

I tried solving the part (a), and got I =1.82 A for the current value using Kirchoff's law. Next, I want to use Ohm's law to calculate the voltage at point a. Va = IR In this equation, will resistance R correspond to 4.4Ω or 8.8Ω? How do you determine which resistance to use when solving this...

I have derived the Coulombian potential as an effective potential between two spinless charged particle taking the non-relativitic approach on the scattering amplitude obtained in terms of the Feynman rules in SQED. The scattering amplitudes are: I'm using the gauge in which xi = 1. How could...

According to theory I should be able to get the Electric Field (E) from its pOtential (V) by doing the grad (V) so E = -grad(V), however, V is contant V = k*lambda* pi which results having E =0, but this is not right. What I am missing?? see figure below The answer should be Ex = 2*k*lambda / r...

I considered the capacitor as two capacitors in parallel, so the total capacitance is ##C=C_1+C_2=\frac{\varepsilon_0\varepsilon_1 (A/2)}{d}+\frac{\varepsilon_0\varepsilon_2 (A/2)}{d}=\frac{\varepsilon_0 A}{2d}(\varepsilon_1+\varepsilon_2).## Since the parallel component of the electric field...

I feel that this problem can be directly answered from the E>0 case of the attractive Dirac delta potential -a##\delta##(x), with the same reflection and transmission coefficients. Can someone confirm this hunch of mine?

Considering a reference frame with ##x=0## at the leftmost point I have for the leftmost piece of wire: ##\int_{x=0}^{x=2R}\frac{\lambda dx}{4\pi\varepsilon_0 (3R-x)}=\frac{\lambda ln(3)}{4\pi\varepsilon_0}##. The potential at O due to the semicircular piece of wire at the center is...

So I have been given a uniform electric field ##\vec{E}=20 V/m## in the direction as show in the image. I have been told to calculate the potential difference ##VC - VA##. According to the teacher (on YouTube) the potential difference ##VC - VA = -10\sqrt{2}V##. But I say it's ##-20 V## as...

When the pendulum is released, the Kinetic Energy should be 0. When the pendulum is at the bottom/hits the rod, it should have 0 potential energy. However, I don't quite understand what happens after it hits the rod.

Hello everyone, I've been struggling with this problem for 1 hour so far. homework-and-exerciseselectric-cir

In the initial position the spring is previously compressed, then the block adds a force, and the spring is again deformed. I think the energy balance is incorrect; the potential energy of the spring is repeated.

e=QxV t=Q/I p=(QxV)/(Q/I) =V/I The expression I came up with for a) is the potential difference divided by current to get power but I have no idea if that is even right if someone could just prompt me in the right direction that would be greatly appreciated

My attempt: Let ##M_e## be the mass of the Earth and ##M_m## be the mass of the person. Let ##D_{EM}## be the distance from Earth to Mars and let ##R_e## be the radius of the earth. Defining these constants (leaving off units for brevity): Masses in Kilograms (G is not a mass but I'll leave...

u = (9*10^9)(1.61*10^-19)^2 * (1/[3*10^-15 ]- 1/[2*10^-10]) u = 7.68*10^-14 J but here the question. I have been taught that W= -U so shouldn't the answer be negative?? When i look up at the solution all other sources say that the W = U and therefore the answer is in postive.

I don't understand this statement about potential energy V(x) from Griffiths Intro to Quantum Mechanics, 3rd Ed. Problem 2.1c: If V(x) is an even function (that is V(-x)=V(x)) then psi(x) can always be taken to be either even or odd. psi(x) refers to a solution of the Time Independent...

hi guys I am trying to calculate the the potential at any point P due to a charged ring with a radius = a, but my answer didn't match the one on the textbook, I tried by using $$ V = \int\frac{\lambda ad\phi}{|\vec{r}-\vec{r'}|} $$ by evaluating the integral and expanding denominator in terms of...

Hi, not really a homework question just a quick question regarding FET-transistor. If the gate potential is -4V does that mean that in the figure below that uGS is -4V. If not, what does it mean and how do you use it in a bigger circuit problem?

Each spherical shell will contribute to potential on the surface of inner shell and the same will apply to outer shell. Due to inner shell ##V_1 = \frac {kQ} {{r_1}}## and due to outer shell ##V_1 = \frac {-kQ} {r_1}##. Therefore potential on inner surface is zero. But the answers are ##V_1...

I am totally confused about the task. Any help will be nice. Thank you so much

[Mentors' note: This thread was split off from https://www.physicsforums.com/threads/system-potential-energy-and-nonconservative-forces.1009237/] This is not a particularly helpful way to think about things; For a general mechanical system, you usually split the specified forces into external...

Hello, I am trying to get my head around the idea of nonconservative forces doing work and changing the potential energy of a system. First of all, forces acting on a system can be: a) internal and conservative b) internal and nonconservative (friction, pushes, pulls, thrust, etc.) c) external...

please help me

Hello everyone, I'm looking for help for the problem 3 of the chapter III. Schrödinger's equation, §25 The transmission coefficient of the Volume 3 of the Landau-Lifshitz book (non-relativistic QM). In this exercise Landau considers a smooth potential wall $$\frac{U_0}{1 + \exp{\left(-\alpha x...

A question to physicists: What sort of real world scenario / image would *best* depict the increase in gravitational potential energy in a radial field? Would a rocket traveling through the Earth's atmosphere suffice or are there better alternatives? This image would have to be relevant to the...

hi guys i am encountered with a question that is : two protons in a helium atom stand close together,approximately at a distance of 2 fm. what is the potential energy of this system ? i can understand the concepts that are potential of a particle or potentail of a object etc but can't...

hi guys I came across that theorem that could be used to check if a surface represented by the function f(x,y,z) = λ could represent an equipotential surface or not, and it states that if this condition holds: $$\frac{\nabla^{2}\;f}{|\vec{\nabla\;f}|^{2}} = \phi(\lambda)$$ then f(x,y,z) could...

Hello, any answers appreciated: 'Two spheres are 5 m apart. Sphere 1 has a charge of -20 mC and sphere two has a charge of -50 mC. (a) Find the strength of the electric field at the sphere's halfway point. (b) Find the electric potential at the halfway point

Does fermi level (in metals) depend on the density of states? I am asking this because from fermi-dirac distribution it seems like that fermi level is non-dependent of DOS, but there is chemical potential in fermi-dirac distribution, which is said to be dependent of DOS.

I'm studying nuclear physics in a text, but at one point that is said: "Both the Coulomb potential that binds the atom and the resulting electronic charge distribution extends to infinity" , I don't understand what is that "resulting electronic charge distribution extends to infinity" what they...

This problem is from David Morin's classical mechanics textbook: I am having trouble with Part b. Here is the textbook's answer: I do not understand why large particle energies lead to capture. I would think that smaller energies would lead to capture because the particle wouldn't have enough...

The Schrodinger equation: $$-\frac{\hbar^2}{2m} \frac{d^2\psi}{dx^2} + \hat V\psi = E\psi$$ $$\frac{1}{2m}[\hat p^2 + 2m\hat V ]\psi = E\psi$$ The ladder operators: $$\hat a_\pm = \frac{1}{\sqrt{2m}}[\hat p \pm i\sqrt{2m\hat V}]$$ $$\hat a_\pm \hat a_\mp = \frac{1}{2m}[\hat p^2 + (2m\hat V) \mp...

So Kirchoff's Loop law states that, The sum of all the potential differences encountered while moving around a loop or closed path is zero. Ok so that is basically a statement of energy conservation. So I see why in the TYPED solution, they related all voltages in the circuit equal to zero. I...

Hello, To first clarify what I want to know : I read the answer proposed from the solution manual and I understand it. What I want to understand is how they came up with the solution, and if there is a way to get better at this. I have to show that, given a vector field ##F## such that ## F ...

I know the math behind these, and I'm happy to use more precise language if needed, I just wanted to get some input on this sweeping generalization that entropy is the conversion of potential to kinetic energy. A brief summary of two important branches of entropy: 1) thermodynamics - the total...

So I started with b) and it there was no q2 this would seem reasonable I was wanted to ask , what effect does q2 have on potential of these two charges? Because it has to be given for a reason.

My solution for the vector potential ##A=2Cln\frac{x^2+y^2}{z^2} \hat{z}## is: a) I used the following formula to calculate the magnetic field $$ \mathbf{B} = \nabla \times \mathbf{A} = \left( \frac{dA_z}{dy} - 0 \right) \hat{x} + \left( 0 - \frac{dA_z}{dx} \right)\hat{y} + 0 \hat{z} =...

So I know that E = -ΔV/Δs. If I wanted to solve for change in potential I could rearrange this equation and get Δ = -E*ds. With that information I believe I can solve the problem below. But in both solutions provided below, the negative sign goes away. Now I know I can pull the E out because it...

Hi, I'm new here, so I don't know how to write mathematical equations, and I may not be fully aware of the rules here, so I'm sorry if I made a mistake. I know how to calculate the electrostatic potential energy of a countable number of charged particles, but I don't know how to calculate the...

Hi! I tried to solve it by using the equation of the electric potential above and as we see it requires the electric field, but the electric field at the center of the ring is zero. Then I tried by using the equation [text] V = \frac{1}{4\pi\epsilon_0r} \int \lamda dl [\text] and I got [text] V...

I have been having a hard time understanding Electric Potential and believe I finally have a grasp on what is trying to say. I wanted to right out my understanding here and hopefully have someone confirm what I am saying is somewhat accurate as I feel like when you write stuff out you tend to...

I am unsure how to solve the problem and would appreciate any suggestens on how to start solving the problem.

I read about a proposal for storing potential energy by hoisting heavy weights that can be dropped when needed to generate electric power. So using the numbers from a hydraulic turbine from Hoover dam, how heavy would a hanging weight have to be to generate 178,000 horsepower as it descended...

I set up an equation for the sum of all the potential energies and when cancelling out ##k## and ##q^2##, I got ##\frac{1}{0.05}-\frac{1}{x}-\frac{1}{0.05-x}=0##. However, this has no solutions, so I must've gone wrong somewhere. Could someone just give me a hint, not a solution, that would put...

Using the generating function for the legendre polynomial: $$ \sum_{n=0}^{\infty} P_{n}(x) t^{n}=\frac{1}{\sqrt{1-2 x t+t^{2}}} $$ It's possible to expand the coulomb potential in a basis of legendre polynomials (or even spherical harmonic ) like this: $$ \begin{aligned} &\frac{1}{\left.\mid...