Questions tagged [potential]

Scalar and vector potentials in electromagnetism. The scalar potential is potential energy per unit charge. For potential energy, use the potential-energy tag.

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1D Infinite Square Box Discrete Energy levels but Continous Momenta?

In the 1d particle in the box the energy of the particle should be completely determined by the momentum of the particle that you observe correct? So how can you have discrete energy levels and a ...
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Potential of arbitrary charge distribution

Imagine this: You have a sphere of air where you have no charge and around this sphere you have a charge distribution $\rho(r,\theta,\phi)$. (For instance, this could be $\rho(r,\theta,\phi)=e^{-r}$)...
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Finite, square, potential well

Lets say we have a finite square well symetric around $y$ axis (picture below). I know how and why general solutions to the second order ODE (stationary Schrödinger equation) are as follows for the ...
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279 views

Alternative definitions of potential?

I hope this question is simple and can be quickly cleared up. In a 1D conservative dynamical system, I've always been taught that the potential function is the function $V(x)$ such that: $$F=-\frac{...
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Does this example contradict Earnshaw's theorem in one dimension?

This is basically a continuation of the post here. Consider electrostatics in $1$-dimension (say, the $x$-axis). Now consider a positive charge $+q$ located at $x=0$, and two equal negative charges $...
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Electric potential and field due to a continuous charge distribution

(1) The electric potential due to a continuous charge distribution is: $$\psi=\int_V \dfrac{\rho}{r}\ dV$$ To calculate this integral $\rho$ must be continuous over $V$. But $\rho$ is discontinuous ...
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Is it possible to draw a potential landscape for this system?

Attention: The question was modified for numerical solution. (see Update 2) I have the following system of differential equations: \begin{align} \dot x & = -x+F(a\,y+b),\\ \dot y & = -y +F(...
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What does electrical potential at a point mean?

From my understanding, potential difference (or voltage) between point A and point B is the difference in electrical potential at the two points. The potential difference is also, the work done per ...
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487 views

Why is voltage described as potential energy per charge?

Voltage is often called an electromotive force since it causes a flow of charge. However, it is described in terms of Joules per Coulomb or Potential Energy per Charge. Question: How does the ...
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How does the Particle in a box model help research/understanding of physics?

With my complete non-formal education on physics (meaning I read things around) I am having trouble to understand how the particle in a box model helps the further understanding of physics. ...
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602 views

Physical meaning of multipole moment

Is there a physical interpretation for multipole moments? For a quantity governed by the Laplace equation ($\nabla^2 \omega = 0$), I understand that the general solution is given by the multipole ...
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Why is the Taylor expansion of the gravitational potential cut off after first term?

In this answer to a question on this site, the gravitational potential of the Earth is expanded as $$U(r) \approx U(r_0) + \left.\frac {dU(r)}{dr}\right|_{r=r_0}(r-r_0),$$ keeping only the linear term....
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What is the relation between ‘Electric Potential’ and ‘Electric Potential Energy’?

What is the relation between ‘Electric Potential’ and ‘Electric Potential Energy’?
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Locally every force admits a potential?

I have a little doubt about a force being or not conservative. Well, as I understood, some forces cannot be expressed as exterior derivative of some scalar potential because the work done by the force ...
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Why do two ends of a long conducting wire have the same electric potential?

I am not seeing the "big picture" here. If I have two conducting spheres separated by a long conducting wire, why would the spheres share the same electric potential? I think of the spheres as point ...
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Time-Dependent Potentials in Quantum Mechanics

A potential that depends on time is usually solved using the time dependent perturbation theory in standard undergraduate textbooks in quantum mechanics. The reason usually mentioned is that time ...
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Can Quantum Mechanical Potential have a Probability Distribution

I am currently in my second semester of undergraduate quantum mechanics. We have recently starting discussing two particle systems, usually in relation to spin interactions. In all of our calculations,...
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Interpretation of the magnetic potential ($A$-field) in the quantum mechanical probability of current

The probability of current in quantum mechanics when the is a magnetic potential, A, is defined as: $$\boldsymbol j=\frac{1}{2m}(\psi^*\hat{\boldsymbol p} \psi-\psi\hat{\boldsymbol p}\psi^* -2q{\...
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Why doesn't the Standard Model have a whole Potential Zoo?

Is there any strong argument which stops us from including potential terms (may be polynomial or not) for other standard model fields besides the Higgs potential? In other words, why isn't there a ...
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How can current remain in a super-conducting loop without any applied emf?

Okay, let's say we have a circular wire loop in which there are no positive nuclei for the electrons to collide to. There are only electrons, no force between electrons, neither can they colide with ...
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Two conducting spheres connected by a wire

There are two conducting spheres of different charge and a conducting wire. After they are connected by the wire, charge flows between the spheres. The charge distributes itself so that the spheres ...
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What is an “Interaction Hamiltonian”

I'm an undergraduate reading up on some quantum physics so that I can help out more in the lab that I'm working in this summer. In the book I'm reading (Shankar's "Principles of Quantum Mechanics") I ...
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291 views

In $\textbf{f} = -\boldsymbol{\nabla} u$, what is $u$?

I know that force is the negative gradient of the potential: $$\textbf{f} = -\boldsymbol{\nabla} u$$ where force $\textbf{f}$ is a vector and $u$ is a scalar. This is a relatively soft question, ...
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Velocity-Dependent Potential and Helmholtz Identities

I'm currently working through the book Heisenberg's Quantum Mechanics (Razavy, 2010), and am reading the chapter on classical mechanics. I'm interested in part of their derivative of a generalized ...
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Why do we assume simply connected domains and continuously differentiable fields in electromagnetism theory?

In many textbooks, including Griffiths', they erroneously claim that a field is irrotational if and only if it is conservative (there exists a scalar potential). This is true only if the domain of ...
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General solution of Poisson's equation [closed]

How to find general solution of Poisson's equation in electrostatics. $$ \nabla^2V=-\frac{\rho}{\epsilon_0} $$ Where, V = electric potential ρ = charge density around any point εₒ = absolute ...
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Physical meaning of gauge choice in electromagnetism

In electromagnetism, it is often referred to gauges of the electromagnetic field, such as the radiation or Coulomb gauge. As far as I know, the definition of a gauge helps us to redefine the problem ...
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Intuitive explanation of difference in $r$-dependence between dipole and monopole

For an electric monopole, its potential scales with $\frac{1}{r}$, where $r$ is the distance from the point of interest to the charge. However, for a dipole, its potential scales with $\frac{1}{r^2}$. ...
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Solving quantum radial equation for infinite potential spherical annulus for $l=0$

There is a mass $m$ in a potential such that $$ V(r) = \left\{ \begin{array}{lr} 0, & a \leq r \leq b\\ \infty, & \text{everywhere else} \end{array} \right. $$ ...
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Potential Difference Between Capacitors in Series

I am struggling to find an answer to this, hopefully relatively simple, question. I had a search on stackexchange but couldn't find anything helpful. We are learning about capacitors in Physics and I ...
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How to calculate time evolution of a wave function in an 1D infinite square well potential?

A particle in an infinite square well has an initial wavefunction $$\psi (x,0) ~=~ Ax(a-x) \qquad \mathrm{for}\qquad 0\leq x\leq a.$$ Now the question is to calculate $\psi (x,t)$. I have ...
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Determining potentials at points in a circuit with multiple batteries

I am asked to find the potential difference across the points $P$ and $Q$. Using Kirchoffs second law, I calculated the 'resultant' emf as being $E$. The p.d across each resistor would then be $\frac{...
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Potential for chasing/pursuit problems

There are many interesting kinematics problems, where the velocity vector of one moving body points towards another moving body. For example, consider the well-known problem of a dog chasing a rabbit (...
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Potential well for gravitational waves

Can one consider the gravitational field of a gravitating body such as a planet or a star as a potential well for gravitational waves? In other words, would it be possible for such a gravitating body ...
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WKB Approximation on an linear + harmonic potential

I have a quick question: I have performed the WKB approximation to find the energies of bound states in symmetric potentials (Square, harmonic, ...). To do this I just find the "turning points" by ...
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Tricky particle in an infinite potential well question

For a particle in an infinite square-well potential in an energy eigenstate, the probability distribution relating to outcomes of position measurements vanishes outside the square well and takes a ...
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745 views

How do we find the number of bounded states in this potential?

for the potential $$V(x)=-\frac{1}{1+\frac{x^2}{m^2}}$$ we can approximate the wave function and bounded state accurately for $x << m$ as simple harmonic oscillator, so what are we gonna do if ...
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What does a hexadecapole look like? [duplicate]

Two dipoles can form a quadrupole, two quadropoles an octopole. The textbook by Griffith then says ' and so on'. So how would a hexadecapole really look like? My impression was that the construction ...
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Why do electric field lines point in the direction of decreasing electric potential?

Why do electric field lines point in the direction of decreasing electric potential? I came across this sentence in my school book but am trying to understand this ever since. I know that dV=-E.dr ...
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Potential of an infinitely long cylinder

Suppose I have an infinitely long cylinder with radius $R$, charged with longitudinal density $\lambda$. I want to calculate the potential outside the cylinder. The field induced by the cylinder is $...
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Current in a fluorescent tube that is not in a circuit

In Walter Lewin's 8.02 Electricity and Magnetism course, he places a fluorescent tube pointing radially outwards from a large Van de Graaff (VDG) generator. Due to the VDG's E-field, this causes a ...
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Transmission + Reflection coefficients >1 For Potencial Barrier with Negative Complex Part Contradicts Paper

I am studying reflection and transmission coefficients for a barrier consisting of a a step potencial defined by: $$V(x):=\begin{cases}0&{\rm if}\,|x|>a/2 \\ V_0+iW_0 & {\rm if}\,|x|<a/...
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Deriving the Lorentz force from velocity dependent potential

We can achieve a simplified version of the Lorentz force by $$F=q\bigg[-\nabla(\phi-\mathbf{A}\cdot\mathbf{v})-\frac{d\mathbf{A}}{dt}\bigg],$$ where $\mathbf{A}$ is the magnetic vector potential and ...
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Electric potential of sphere

(a) I am a little confused about this part. The point at A to B isn't radial. The electric field is radially outward, but if I look at the integral $$\int_{a}^{b}\mathbf{E}\cdot d\mathbf{s} = \int_{a}...
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Relation between the propagator and probability for the infinite well

This may be an easy question, but I am really confused about it. For the infinite square well, the (time-dependent) energy eigenfunctions are (inside the well):$$\psi_n(x,t) = \sqrt{2/L}\:e^{-iE_nt/\...
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Factors affecting Battery Voltage

How do batteries produce a certain voltage, such as 1.5V or 9 V? From what I understand, battery EMF comes from oxidation of the anode, which releases electrons that can flow through a circuit. But ...
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Why do we talk more about electric potential in electrostatics and not electric potential energy?

There is a concept in electrostatics called electric potential, which is defined as the amount of electric potential energy (which is a clear translation of gravitational potential energy except for ...
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$\sin$ and $\cos$ components in symmetric infinite potential well problem

Consider an infinite potential well in one dimension with boundaries at $\pm a/2$. Can $\psi(x) = A \sin(kx) + B \cos(kx)$ for this system? The way it was answered was "mathematically acceptable but ...
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Quasi-classical energies for neutron in gravitational potential [closed]

Lets consider a ultra cold neutron gas in a gravitational potential. The known quasi-classical energy up to the classical turning point is $$ E_n =\sqrt[3]{\frac{9m}{8}(\pi\hbar g (n-\frac{1}{4}))^2} ...
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Predicting the value of $n$ for the energy of a wavefunction in the infinite square well by inspection

$$E=\frac{n^2 \pi ^2 \hbar^2}{2ma^2}$$ Is it always possible to tell the value of $n$ by inspecting the shape of the wavefunction in the infinite square well no matter what the value of $a$ is? ...