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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Sphere half-submerged on a dielectric

This is a classic problem in electrostatics with a twist, so I thought it could be useful for others here. I did have a problem with the integration at the end, but on general I think the idea can ...
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1answer
221 views

Does the Schrodinger Equation yield a unique wave function and density?

I am learning DFT and the Hohenberg Kohn Theorem of Existence. And it says that there is a one-to-one correspondence between the external potential and the density. However the proofs that I have seen ...
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734 views

Understanding conformal mapping in electrostatics

I'm trying to understand the use of conformal mapping to solve problems in electrostatics. To better understand the idea, I'm trying to learn how to solve this example (but you can propose any other ...
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271 views

$D$-dimensional Schrodinger's equation with a Dirac delta potential

I know that for $D\geq 2$, there is no bound state for a Dirac potential $V=-\alpha \delta(\textbf{x})$ unless we use an ultraviolet cutoff $k_{max}=1/a$. I showed this by solving the Schrodinger's ...
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1answer
78 views

What does the term 'high voltage' really mean?

This might be a dumb question but i am not so familiar with the word voltage: What does the textbooks really mean when they say high voltage?. Does that mean: There are more charges so more voltage, ...
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1answer
58 views

Why is the spin-orbit interaction for a nucleus so much more important than the spin-orbit interaction in atomic physics?

In atomic physics, the spin-orbit is a small correction between 1/1000 and 10ppm, so fairly small. In contrast, in nuclear physics the inclusion of the spin-orbit interaction is necessary to reproduce ...
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94 views

Maxwell theory : How to justify the potential gauge fields if there are magnetic monopoles?

Without magnetic monopoles, the Maxwell equations are these (I'm dropping vector notations and all constants, for simplicity): \begin{align} \nabla \cdot E &= \rho_{elec}, \tag{1} \\[12pt] \nabla \...
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2answers
96 views

Dilemma in Theory of Superposition of Electric potential

Electric potential is the amount of work done in bringing a unit charge from infinity to a point. Here we take infinity as a reference point. The unit charge might have higher or lower potential ...
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39 views

What are many-body potentials? Why are they important?

I have been studying molecular dynamics and statistical mechanics, and I have been running into this term called "many-body" forces. I have been reading this paper: https://doi.org/10.1080/...
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174 views

How do you normalize this wave function?

I have a basic question in elementary quantum mechanics: Consider the Hamiltonian $$H = -\frac{\hbar^2}{2m}\partial^2_x - V_0 \delta(x),$$ where $\delta(x)$ is the Dirac function. The eigen wave ...
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1answer
94 views

Vacuum polarization or electron with structure?

Is it possible to construct some charge density $ρ(r)$ to get the Uehling-Potential? $${\displaystyle V_{\text{Uehling}}(r)\approx -Z\alpha \hbar c{\frac {1}{r}}\left(1+{\frac {\alpha }{8\pi ^{2}{\...
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How are the equiliberium points of the electric potential characterized?

I am interested in information about the points where the force per charge of a classical electrostatic potential is exactly zero. Loosely speaking, that is to say, if $$ V(\vec{r};\vec{r}_1,\cdots,\...
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Multipole expansions: test on a function $\zeta=\zeta(t)$

Considering the potential $\psi(r)$ of a sphere of mass $M$ with density $\rho(\mathbf r')$, connected by a small volume positioned in the $P'$ point as shown in the figure: The $\psi(r)$ is: $$\...
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227 views

What is a good analogy for electric potential?

When the electrical field was defined I could totally relate to $\vec{E}$ being like $\vec{g}$ in mechanics. But for the electric potential I don't know what would be equivalent analogy. Any ...
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How to derive the simplest 1D Superpotential Hamiltonian?

In the superpotential wiki article there are definitions of two supersymmetric operators: $$Q_1=\frac{1}{2}\left[(p-iW)b+(p+iW)b^\dagger\right] \\ Q_2=\frac{i}{2}\left[(p-iW)b-(p+iW)b^\dagger\right] $$...
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320 views

Accelerated ion beam current

If an electron gun creates a $10\space mA$ electron beam and each electron collides with a gas atom and creates an ion through impact ionization, can the ions then be accelerated with a separate ...
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108 views

Conservation of momentum in statistical physics in presence of a potential

Imagine a number of particles, all confined in a parabolic potential. The particles initially have a random velocity and are let free to bounce off each other (say, it's rigid spheres). Does ...
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1answer
446 views

Misbehaving singular isothermal sphere potential

The singular isothermal sphere (SIS) is a useful simple model often used in astrophysics. It has density profile: $$\rho(r) = \frac{\rho_0 r_0^2}{r^2}$$ This is well known to have some quirks (...
3
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1answer
62 views

Meaning of potential in a discharging capacitor

I am dealing with this thing I cannot figure out. When a capacitor is discharging, the electric field inside it varies with time so we cannot perform the line integral to determine the potential ...
3
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131 views

Is the "Force" of Gravity Simply Hamilton's Principle on a Curved Spacetime?

It's my understanding that General Relativity abstracts away the concept of gravity as a force, and instead describes it as a feature of spacetime by which massive objects cause curvature. Then it ...
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87 views

Charge distribution and potential in a 1-dimensional quasistatic system

Suppose you have an 1-dimensional system with a charge distribution $\rho(x)$ (not given) moving with an speed $v(x)$ (not given), calculate the potential $\phi(x)$ and the charge distribution $\rho(...
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420 views

Symmetries of separable potential

For separable potential, say $x^4+y^4$, its symmetry are degenerate. Is that a generic case to every separable potential? I will explain my question: The potential $x^4+y^4$ has $A_1, B_1, A_2, B_2, ...
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1answer
163 views

Is there something wrong in my book's derivation of work done on charge?

For finding potential at a point due to a +ve charge $(q)$, we find work done to move a unit +ve charge $(q_o)$ from infinity to that point in the presence of +ve charge $(q)$ Since both charges ...
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1answer
193 views

At what distance is lightning dangerous for someone lying down?

My 8 yo child told me that they learned at school that they should lay down flat on the ground in case of lightning. I told him that the more correct position is crouching down with feet together, but ...
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2answers
3k views

Charge flow between a sphere (inside) a spherical shell irrespective of the charge of the shell

A small sphere of radius $r_1$ and charge $q_1$ is enclosed by a spherical shell of radius $r_2$ and charge $q_2$. If $q_1$ is non-zero and the two spheres are connected by a wire, then, charges will ...
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1answer
32 views

Difference between grounding the inner and outer side of a thick spherical shell

I have a conducting sphere with radius $R_1$ and charge $Q_1$ inside a conducting thick spherical shell with inner radius $R_2>R_1$ and outer radius $R_3>R_2$. Both the spheres have the same ...
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2answers
28 views

Potential on an Uncharged Conducting Sphere Due to a Point Charge

I'm working on a problem where I need to find the change in potential of a point on a conducting sphere ("A") a distance 3R from a point charge "q" (R=radius of the sphere). My ...
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26 views

How is $\nabla\cdot \mathbf P$ sufficient to describe the volume polarization $\mathbf P$

I'm self-studying Panofsky and Philips' Classical Electricity and Magnetism. In Section 1-10, they talk about the potential due to a volume polarization $\mathbf P$ being effectively divorcing into ...
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63 views

Magnetic monopole, vector-potential and differential forms

When written in the language of exterior algebra, Maxwell-Thomson equation writes as $dB=0$ where $d$ is the exterior derivative and $B$ is the magnetic flux 2-form. From Poincaré's lemma, it follows ...
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1answer
136 views

Why does potential of a conductor decreases if a negatively charged conductor is brought near a positively charged conductor?

Also, how should I imagine potential in my mind? How should I picture it?
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Reference needed for effective gravitational potential in General Relativity

In Wikipedia ( https://en.wikipedia.org/wiki/Two-body_problem_in_general_relativity ) one can find the following expression for the effective gravitational potential in the Schwarzschild approximation ...
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132 views

Can the WKB approximation be used for this double well potential?

For a positive constant $C$, the double well potential $V(x) = -C|x| $ exists between two infinitely high potential walls at $x=a$ and $x=-a$. I wish to use the WKB approximation to obtain an equation ...
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64 views

How does the delta prime boundary conditions behave when the jump factor approaches infinity?

I recently came across the concept of a $\delta'(x)$ (delta prime) potential, which is basically a potential which imposes the boundary condition: $\frac{\partial\psi}{\partial x}$ is 'continuous' at ...
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Origin of the definition of the electric potential of a black hole

All the papers I’ve seen in black hole thermodynamics (e.g. arXiv:hep-th/9908022) define the electrostatic potential of a black hole with horizon Killing vector $\xi^a$ as $$\Phi := \xi^a A_a \big|_{...
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58 views

Potential between a metal sphere and spherical shell which are not quite concentric

I have been struggling with this problem for some time by now. An insulated metal sphere of radius $a$ with total charge $q$ is placed inside a hollow grounded metal sphere of radius $b$. The centre ...
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29 views

Are dipole interactions considered short range in 2d

Every paper that I read about dipole-dipole interactions always call them long-range interactions. Is dipole-dipole interactions can be considered short-range in 2D? As we know it behaves as $\...
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1answer
54 views

Explicit form of S-matrix on the line

Consider the Hamiltonian $H$ on functions on the line with \begin{eqnarray} H=H_0+V,\\ H_0=-\frac{1}{2m}\frac{d^2}{dx^2} \end{eqnarray} where $V$ is a potential vanishing outside of a bounded interval....
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What exactly do the zero-modes of the instanton mean?

I am studying instantons in quantum mechanics. My question is regarding the the zero mode of the fluctuation determinant that we get because the solution for the instanton breaks time translation ...
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1answer
73 views

Gravitational Potential Derivation

The definition of Gravitational Potential at a point is the work done per unit mass in moving it from infinity to that point. However the work is positive and if you perform the integral you get a ...
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1answer
54 views

Effective potential in a time-dependent spacetime

My question is regarding an arbitrary time-dependent spherically symmetric spacetime with line-element, in co-moving coordinates, to be $$ds^2 = -f(R) dt^2 + a(t)\bigg\lbrace\frac{dR^2}{f(R)} +R^2d\...
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Would the voltmeters give different readings in a circuit with induced current?

$\def\vE{{\vec{E}}}$ $\def\vD{{\vec{D}}}$ $\def\vB{{\vec{B}}}$ $\def\vJ{{\vec{J}}}$ $\def\vr{{\vec{r}}}$ $\def\vA{{\vec{A}}}$ $\def\vH{{\vec{H}}}$ $\def\ddt{\frac{d}{dt}}$ $\def\rot{\operatorname{rot}}...
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1answer
61 views

Difference, in terms of completeness, between the Dirac well and barrier

I was in my undergraduate QM lecture and we just finished with the Dirac barrier. My question is as follows: We know that the Dirac well’s complete set of solutions requires one bound state and an ...
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195 views

What does it mean for a potential not to have a Fourier transform?

Consider an isotropic potential $\phi(r)$ corresponding to the classical force of interaction between two point-particles. The Fourier transform of this potential $$ \Phi(k) = \int \exp(-i\vec k\cdot\...
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175 views

Which test function (under variational method of approximation) should be used for a linear potential?

There is this problem, it is not for evaluation, I mean, it is not homework. There is a 3-dimension potential $V(r)=C . r$, where $r$ is the radial coordinate and $C$ is a real constant (I think it ...
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69 views

Vector potential of a partially-known magnetic field

let's consider a three-dimensional space permeated by a known magnetic field $\vec{B}$. Let's consider in this space a topologically spherical surface $\mathcal{S}$ centred in the origin. I put a ...
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433 views

Magnetic Vector Potential of Hollow Cylinder

I'm modeling a MIT (Magnetic Induction Tomography) apparatus. In order to extract the Jacobian/stiffness matrices for the conductivity distribution, I need to calculate the magnetic vector potentials, ...
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101 views

The formula for the average number of fermions $\langle N \rangle$

In the context of Fermi gases (or fluids in general), one would typically in the grand-canonical formalism use the formula $\langle N \rangle = -\frac{\partial \psi}{\partial \mu}$, where $\psi$ is ...
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1answer
313 views

The Schrodinger equation with strange potential

The particle of mass $m$ moves in potential $$V(x) = \dfrac{\alpha \left( \left( 2 \alpha +1 \right)x^2-a^2 \right)}{m \left( a^2 + x^2\right)^2},$$ and $\alpha > 1/4$. Find the energy and the ...
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1answer
283 views

Energy spectrum for a step potential

Most of the books tend to give this explanation that for a bound physical system, the energy and momentum eigen values have discrete spectrum and otherwise, they have a continuous spectrum, which I ...
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220 views

Standing spherical wave solution

Let's say we have a spherically symmetric light wave $u(r,t,\theta,\phi)= u(r,t)$ that satisfies the following wave equation with spherically symmetric potential $V(r)=2/r^2$ (also set $c= 1$ so $\...

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