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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Is the Schrodinger equation ever unsolvable?

In quantum physics, I am aware that the Schrodinger equation $$i\hbar\frac{\partial\Psi}{\partial t}=\hat{H}\Psi$$ dictates how a system evolves over time based on its Hamiltonian, and I also know ...
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DFT Hartree Potential with Periodic Boundary Conditions

Suppose we have a periodic crystal. Let $\rho(r)$ be the electronic density, and let $a$ be the lattice vectors. Due to the periodicity, the Hartree potential can be written as \begin{align} V_H(r)&...
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How to solve the electric potential due to a charge distribution using fast Fourier transforms

I'm writing a toy program to simulate 2D wave functions. I'm using a split-operator method to solve the Schrödinger equation and have no problems with arbitrary potentials. However, I'd now like to ...
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Boundedness of a Hamiltonian and when does a Hamiltonian have a spectrum?

In the context of Quantum Field Theory we put restrictions on the potentials we can use. One argument is boundedness. If the potential is unbounded, for example $V(\phi) = \phi^3$, then `the field can ...
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Estimates of voltage drop with distance in weak electric field

I have an underwater dipole (interpole distance is small, probably $1 ~ cm$, but cannot be estimated easily so this can only be an approximated measure) generating an electric field which voltage can ...
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Are multipoles the coefficients of the charge distribution for a basis of functions?

If I calculate the poles (monopole, dipole, quadrupol ...) for a charge distribution, then I will get something of the form: \begin{align} Q \text{ or } \vec{Q} \text{ or } Q_{ij} \text{ or ....} = \...
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Potential difference in a electric field

I understand that the line integral of the electric field is path-independent. If the source is a point charge of $q$, line integral $\int_{P_1}^{P_2} E\cdot ds$; the integral from $P_1$, $P_2$ which ...
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Conducting Shell and a Metal Sphere

I am have a doubt regarding the topic Conductor in Griffith's text book of Electrodynamics. Griffiths states that, a perfect conductor contains infinite amount of charges, and a metal resembles that ...
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Why is the Bohm quantum potential considered a potential?

In Bohmian mechanics, the term $$\begin{equation} Q = -\frac{\hbar^2}{2m}\frac{\nabla^2 R}{R} \end{equation}$$ is regarded as the quantum potential term. However this is merely a term from the real ...
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What is the electric potential inside a finite box with a charge density?

In order to find the potential inside a box, we use the Laplace equation if there is no charge. For example, for an infinitely long rectangular box along $z$-axis with sides at $x=0, \;x=a, \;y=0, \;y=...
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Variational Method for A Symmetric double well Potential

I am given a set of trial wave functions of the form $$ Φ_n^{\pm}(x)=Ψ_{n}(x-α)\pm Ψ_{n}(x+a) $$ Where $Ψ_n$ are the $n$th Harmonic oscillator wavefunctions. in order to approximate the energy levels ...
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What is the correct gravitational potential energy of a single particle in an $N$-body system?

I am aware that the total gravitational potential energy of a system of $N$ particles is given by pairwise interactions, i.e., you start with a single particle in the system, and then calculate the ...
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Can potentials be used to transmit energy and information?

The famous Aharonov-Bohm effect displays the potential of the physical implications of different potential gauges in em theory. I saw very few experimental and theoretical investigations into this ...
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Why can we talk of electric potential under AC?

An electric potential $V$ is defined by the relation $E = - \nabla{V}$. The existence of such a potential is true in electrostatic (constant electro-magnetic field) because of the Maxwell-Faraday ...
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Vector potential of magnetic dipole [migrated]

When one calculates the vector potential of a magnetic dipole (current circuit), one can arrive at an integral of the form: \begin{equation*} \vec{A} = \frac{I}{cR^3} \oint\limits_L {\vec{dl}} ( ...
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Solving Wheatstone Bridge Using Combination Of Resistors

Is there a way of solving Wheatstone Bridge using a combination of resistors (parallel or series) by changing the structure of the circuit, or some other way, instead of making the potential across ...
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Kinetic term of the Hamiltonian constructed from the action of perturbative string motion is not positive definite

I am trying to reproduce the results from this paper. On page 10 of the paper, they have an equation: $$\frac{S}{T}=\int dt\sum _{n=0,1} (\dot{c_n}{}^2-c_n^2 \omega _n^2)+11.3 c_0^3+21.5 c_0 c_1^2+10....
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Multipole Expansion: Why is my Taylor Series Wrong?

Let's start by a formula. The scalar electrostatic Potential is given by: $$\phi(\mathbf{r}) = \dfrac{1}{4\,\pi\varepsilon_0}\,\int \dfrac{\rho(\mathbf{r'})}{|\mathbf{r}-\mathbf{r'}|}\,\mathrm{d^3 r'}$...
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Is reasonable to have a potential satisfying these two properties?

Let $F\in C^1(\mathbb{R}^3\setminus\{0\}, \mathbb{R})$ satisfying the following properties: a) there exists a constant $c>0$ such that $$\limsup_{x\to 0} F(x) |x|\le -c<0;$$ b) $F(x)\stackrel{|x|...
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How does the scale become horizontal when each side gets same weight?

I am a newbie in physics. now I am reading 'Six Easy Pieces' by Richard Feynman. and I was reading the part of gravitational potential energy. while I was reading Feynman took an example of scale(...
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Does there exist a Coriolis potential, just like there is a Centrifugal potential? [duplicate]

While dealing with central force there is a known result: $$U_\text{eff}(r)=\frac{L^2}{2m r^2}+ U(r) \, $$ If I understand correctly the centrifugal potential term $l^2/(2\mu r^2)$ arises when you ...
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Why is the electric potential formula like this and how is it derived?

So from what I could understand from my Electrical Engineering lectures the electric potential at a particular point charge $A$ is: $$u_A=-\int_{\infty}^{r_A}\vec E\cdot d\vec r$$ The minus here might ...
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How does gravitational potential relate to gravitational acceleration?

I've been wondering about what the gravitational potential V actually tells us, and how it relates to gravitational force and/or acceleration. The formula is $V = -\frac{GM}{r}$. I did some ...
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Is there anything fundamentally different between these two representations of an infinite square well?

The first representation is what I would say the more typical one: $$V(x) = \cases{0 & 0<x<a \\ \infty &else} $$ But it could also be: $$V(x) =\cases{-\infty & 0<x<a \\ 0 &...
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Is gravitational energy belongs to a single object or system "object-Earth"?

I'm new to physics and i just started studying energy and i have a question: Consider an object (mass m=2kg) dropped freely from a height h = 2m (there is no friction between object and air). If ...
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Potential Difference across two cells in series

I studied yesterday that total potential difference across two cells in series is simply the algebraic sum of potential difference of those two cells. And by which logic it has been proved, I am ...
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Electric Potential vs Electric Field

I am really missing conceptual concept between Electrostatic Field and Electric Potential. Say I have a 5 charges and wanted to place them in vertices of a regular hexagon, and one asks me to find ...
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About electric field and electric potential

We know that electric potential is the negative of work done by electric field in moving a unit charge from infinity to that place. This statement shows that electric field causes a potential ...
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Is the concept of motional EMF consistent with Faraday's Law?

Consider a circular homogeneous metallic coil sliding on a smooth horizontal surface in a region of uniform magnetic field $B$ which is perpendicular to the face of the coil. By Faraday's law, the net ...
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Infinity potential well [closed]

For infinity potential well we take the analogy with nucleus. Inside which proton and neutron are bound in principle, if it is an infinite potential well, so particle should not come outside the ...
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Are the $V$ in electronics and the $\phi$ in physics the same?

Is the electric scalar potential $\phi$ in physics the same thing as 'voltage', $V$, in electronics?
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It is possible to create a relativistic theory of gravity more simple than General Relativity via Jefimenko's equations? [closed]

I've came across the Jefimenko's equations, which are the general solutions of Maxwell's Equations and are compatible with Special Relativity. They are formulated in terms of the retarded potential: $$...
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Derivation of the one-form potential in Kerr-Newman spacetime--Sean Carroll GR

In Sean Carroll's GR book, he gives the non-vanishing components of the one-form potential of a Kerr-Newman blackhole, I am not sure how to derive this just from the metric itself. I looked at some ...
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The proof of KVL

Kirchhoff voltage law indicates that :the sum of the potential diffrence across any closed loop will be equal to zero which can be written as $\sum_{i=1}^{n}V_{i}=0$ but what is the proof of this law ?...
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Can the value of potentials be an irrational number? [closed]

I was looking at the boundary conditions of Laplaces equation and I wondered if it is possible, given that the boundary conditions allows for a finite potential, that the potential can be an ...
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Definition of voltage confusion

How come the definition of voltage can be defined as the work required to push a positive charge from a location of lower potential to a location of higher potential (closer to source of electric ...
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Green Theorem in Jackson's Electrodynamics

On Jackson's Classical Electrodynamics page 36, on eq.(1.36), the book derived the Green's theorem: $$\Phi(\mathbf{x})=\frac{1}{4 \pi \epsilon_0} \int_V \frac{\rho\left(\mathbf{x}^{\prime}\right)}{R} ...
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Why there is a reflection coefficient in case of $E>V_o$ (Potential at $x=0$) in a Potential Step? If $E>V_o$ it means all particles transmit

If all the particles transmit through potential, then there should have been zero reflection. So why we are calculating reflection coefficient in case of E>Vo?
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Expectation value of potential operator [closed]

A book says $$\langle r|V|r\rangle$$=$$\sum_{a,a'}\int \psi^*_a(r)V_{aa'}\psi_{a'}(r) $$ define $$\langle r|\psi\rangle=\psi(r)$$ my derivation is $$\langle r|V|r\rangle=\langle r|\psi_a\rangle\...
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Do other methods exist than the method of image charges for computing equipotential field at surface around charged objects?

I am trying to find another method for robotics based on "attractive-repulsive" forces s.t. first object forms the target to reach and the second one (and others) forms the obstacle to avoid....
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Potential Energy for Sum of two opposite forces

Suppose I have the superpostion of a repulsive force pointing in the positive x-direction $$ \frac{B}{x^2}\hat i $$ And the constant force along x-axis pointing towards the origin $$ -A \hat i$$ The ...
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Why electric potential is separable?

In Electrostatics, if we consider a region without charges the electrostatic potential $V$ obeys Laplace's Equation $\nabla^2 V = 0$. We can tackle this with separation of variables. In cartesian ...
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Can a static electric charge stably levitate using the superposition of electric potentials?

According to Earnshaw's theorem for electrostatic fields a charge cannot be kept in stable equilibrium by purely electrostatic fields. The mathematical proof for this is usually as follows: if the ...
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Does the orientation of an anistropic potential impact the Scattering-Matrix?

I was curious if an anistropic potential's orintation depended on a scattering matrix. Is it feasible to create a dependence if not?
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Rotating the Laplacian and relating it to a gauge potential

Suppose we have the free-space Hamiltonian $H=-\frac{\hbar^2}{2m}\nabla^2$ and we introduce a given $2\times2$ rotation matrix $T(\mathbf{r})$ so that $$ \tilde{H}=T^{\dagger}(\mathbf{r})HT(\mathbf{r})...
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Energy transfer in resistors

The change in electric potential energy $\Delta U$ of a charge $Q$ as it moves from $r_1$ to $r_2$ is given by $$\Delta U=Q\Delta V,$$ where $\Delta V$ is the potential difference between the two ...
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A charged conductor NOT in electrostatic equilibrium -- still an equipotential surface?

It is well known that "the surface of any charged conductor in electrostatic equilibrium is an equipotential surface" (Serway/Jewett; emphasis mine). I haven't found a good answer online for ...
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Can shell theorem be applied to electric potential for a point outside of a spherical shell with uniform charge distribution?

Can shell theorem be applied to electric potential for a point outside of a spherical shell with uniform charge distribution? If you are calculating the electric potential difference from a point ...
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Exact Differentials and thermodynamics [duplicate]

Im confused on what the significance of exact differentials are in physics, specifically in thermodynamics. In my book posted here it talks about how by requiring that $dU$ be exact it leads to ...
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Laplace equation with specific boundary conditions

How we can solve Laplace equation in the empty space $z\ge0$ for $V(\vec{r})$ with the given boundary conditions: it goes to zero at infinity and it is zero on the plane $z=0$ except inside a square ...

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