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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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Does gravity get stronger when you climb a mountain?

As stated in the question title, what happens to the strength of the gravitational field (or equivalently, your weight) as you climb a hill or mountain? Would a weighing scale show that you were ...
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Schrödinger Equation for a freely falling body near the surface of Earth

Near Earth's surface the Schrödinger equation of a freely falling particle takes the form, $$ \frac {-\hbar^2}{2m} \frac {d^2 \psi (y)}{dy^2} + mgy\psi (y) = E \psi (y). $$ Putting $k=\frac {\sqrt {...
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‘Supersymmetrizing’ an arbitrary quantum-mechanical potential

To my understanding, it is not possible to $``\text{supersymmetrize}"$ an arbitrary quantum-mechanical system unless one knows how to represent the corresponding Hamiltonian in the form $$ H = A^\...
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Determining Electric Potential due to a line of nonuniform charge density [closed]

A rod of length $L$ lies along the x axis with its left end at the origin. It has a non uniform charge density $\lambda = \alpha x$ where $\alpha$ is a positive constant. Calculate the electric ...
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1answer
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Floating potential of a conductor near another conductor with known potential with respect to the earth

Electrostatics textbooks delight at computing the electric field or the potential created by a known distribution of charge, ignoring the fact that this is rather a non practical question. In ...
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Meaning of the term $V(x)$ in the Schrodinger equation [closed]

I'm new to quantum mechanics and I am currently trying to understand finite potential well (although my question is not specific to finite potential well ). In the Schrodinger equation, many texts ...
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Why is Coulomb's force law a $1/r^2$ dependence, while the Coulomb potential has a $1/r$ potential?

My source of confusion comes from reading the following except from my general chemistry textbook, "The energy of interaction between a pair of ions can be calculated using Coulomb's law" $$V = \...
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34 views

Create a square well potential for an electron in practice

If my particle is an electron, how do I create a square well potential (in one dimension) in practice? I would like to know how to actually achieve it. Is it like at both the ends, I need to put some ...
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61 views

Heat produced in movement of charge from inside of shell to outside

The original question is Two concentric metallic shell’s of radius R and 2R, out of which the inner shell is having charge Q and outer shell is uncharged. If they are connected with a conducting ...
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2answers
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Is the potential term in a Lagrangian velocity-dependent?

I know that the Lagrangian of a system has to be dependent on the coordinate (as the type of potential in it is dependent on the coordinate) and on velocity and time (per KE and PE, respectively). ...
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1answer
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Fourier transform of a scatering potential

The Fermi golden rules states $$ \Gamma(\vec{k},\vec{k}') = \frac{2\pi}{\hbar} \left| \left \langle \vec{k}|V|\vec{k}' \right \rangle \right|^2 \delta(E(\vec{k})-E(\vec{k}')) \, .$$ Many places (for ...
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What is the main point in defining electric potential?

What I mean is that as the electric field is a necessity for us to define it because it has practical applications and similarly we need electric potential energy because it is the energy we require ...
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Potential from scattering matrix [duplicate]

Given a scattering matrix, is there a procedure to find the potential from the scattering matrix? I think there should be a way as the scattering matrix holds the information of the boundary ...
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Finding the potential for a given Hamiltonian

Background: So I know from my lecture that if I am given a wave-function, which describes a particle and a potential V(x) in which the particle is in, I can use V(x) in the time-independent ...
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What are wave-functions in QM. corresponding to?

I was learning about a particle trapped in a double well potential $$V(0) = \infty, V(x1)=\infty$$ which can be described by $\psi_n$ for n=0,1,...,$\infty$ with corresponding Energies $E_n$. Just ...
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1answer
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Infinite square well: wall with infinitesimal thickness

Given an infinite square well, it doesn't matter how thick the wall is, the particle is trapped inside the two walls. If we make the wall of arbitrarily small but finite thickness, the particle is ...
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1answer
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Potential energy of a charge in a magnetic quadrupole field

I have a charged particle of charge $q$ that moves with velocity $\vec{V}$ from a position $\vec{r}$, inside a magnetic quadrupole field of the form: $$\vec{B}=B_{0}(x,y, -2z)$$ The Lorentz force acts ...
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Physical meaning of potential in heat equation

I'm working on the mathematical theory of parabolic equations. The prototype of such equations is heat equation given as follows : Let $\Omega$ be a bounded region of the space and $T>0$ a fixed ...
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3answers
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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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1answer
52 views

Misconception about flow of charges

Let's say I have a 5V battery connected in the manner shown in the diagram. I've tried this setup with all sorts of things like pouring brine(salt water) into the soil to decrease its resistance so ...
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1answer
36 views

Why did we take gradient outside the integral sign in Scalar potential derivation?

I tried to understand the reasoning given in it but I couldn't understand it. It says that "as the gradient operation involves x and not the integration variable x', it can be taken outside the ...
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Potential Difference of a battery - What does it mean?

I have studied current electricity for a while now. When I look back at basic concepts, I am quite clear about what current, electron, resistance is. But I cannot imagine about the potential ...
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2answers
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Potential difference of resistors in parallel linked systems

Before the question I want to explain somethings to see if I understand anything wrong please tell me if im wrong: When there is a Potential difference on a system then the electrical charge will move ...
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1answer
70 views

Help me make sense of the spectrum for the quantum wave function of an infinitely hard equilateral triangle

I'm trying to solve the spectrum for a equilateral Tetrahedron with infinitely hard walls. My first guess is to sum up a infinite amount of separable solutions to match the boundary conditions on the ...
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1answer
87 views

Can electric potential be discontinuous?

I am studying the following problem, which is 9.11 of "Modern Electrodynamics" by Zangwill. The idea is that you have a wire attached to a perfectly conducting sphere (radius $a$) buried into the ...
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1answer
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Screening of a coulomb-like potential

Imagine that we have a potential in the form of: $U(r) \propto \frac{1}{r^n}$ in a 2D system, with the high concentration of particles interacting with the above potential. How do you find the ...
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1answer
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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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Electron in free space and Schrodinger's equation

Topic: Quantum Theory of Solids I have come across the following text: Electron in Free Space: Consider the motion of an electron in free space. If there is no force acting on the particle, ...
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Why can't a particle penetrate an infinite potential barrier?

I am studying basic quantum theory. My question is: Why can't a particle penetrate an infinite potential barrier? The reasoning that I have applied is that particles under consideration have finite ...
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1answer
40 views

Is potential instantaneous, unlike fields which take time to alter depending on their mediators?

If there's a Charge distribution 4 Light-years away, static, we have a distinct value of Electric Field and Electric Potential where I'm measuring it through some wack-a-doodle apparatus at my home on ...
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4answers
119 views

How to understand Kirchhoff's Voltage Law?

I'm having a hard time trying to understand why Kirchhoff's Voltage Law is true. I looked for an answer on the forum but I couldn't find a convincing one. So my question is : How to "physically" ...
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1answer
64 views

What is meant when we say “any solution is *the* solution” due to the uniqueness theorem?

I understand the proofs for the uniqueness theorems in electrostatics, but I'm having trouble understanding their application to problem solving. A classic example is a system of concentric shells of ...
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Liénard-Wiechert potential of a charged infinite sheet uniformly translating parallel to itself

This question is motivated by the model used in The Feynman Lectures on Physics Vol II Section 18-4. In the model there are two plane sheets extending infinitely in both their dimensions. Each has a ...
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1answer
180 views

Thermodynamic Stability - Convexity - Concavity of Thermodynamical potential

The thermodynamic stability principle requires convexity of the internal energy upon all of its independent variables. When we pass through the Legendre transforms to build all the other ...
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5answers
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Could someone explain what is a potential?

In many part of physics, me talk about potential (electrical potential, gravitation potential, elastic potential...). All those definition looks very different, and I would like to know how all those ...
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4answers
139 views

Does a particle with infinite energy escape an infinite well?

Currently, my modern physics class is going over particles in finite and infinite wells, general quantum formalism, and tunneling. What happens to a particle as it gains an infinite amount of energy? ...
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How does a piece of wire know there is a voltage potential different?

Imagine water molecules inside a water pipe is moving due to difference in pressure, this pressure can be due to difference in gravitational potential or external force like somebody squeezing at one ...
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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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1answer
30 views

Circumstances that might happen in Hall-effect experiment

In Hall-effect experiment, is it possible that no transverse potential difference will be observed? Under what circumstances might this happen?
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Magnetic vector potential on a semicircle wire

If you're trying to calculate the magnetic vector potential A on a semicircle wire at an arbitrary point P on the other semicircle, is their a difference in method if you are calculating it on a ...
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1answer
29 views

Defining potential of the ground

In electronics, it is customary to define the potential of ground (thinking the Earth as a large conductor) as zero. Is this consistent with the fact that the Earth has a net electric charge that is ...
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1answer
48 views

Grounded parallel plate capacitor

What will be the charge distribution if a parallel plate capacitor, which is not connected to any battery, is given charge on one plate(say Q on the left plate) and is grounded on the outer side of ...
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0answers
59 views

Spring constant and dispersion relation

In order to calculate the dispersion relation (i.e $w(k)$) for the electrons and protons, I used the following relations: $ E = ℏω$, $p = ℏk$, and I substituted them in this formula for energy: $E = ...
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1answer
32 views

How do I determine the accuracy of this two-dimensional potential field?

Let's say I want to solve this problem. I know the values on the boundaries and I guess an initial solution on the rectangular grid inside these boundaries, see figure below. Potential=10 on ...
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0answers
62 views

Taylor expansion for a double well/perturbed infinite square well

I'm trying to estimate the ground state energy for a perturbed infinite square well directly. The potential is piecewise constant $$V(x)=\begin{cases}&\infty, \qquad x<-a/2\\ &0 \qquad -a/2&...
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60 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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1answer
40 views

How a battery maintains the current in the circuit? [duplicate]

How a battery maintains the current in the citcuit? Iwant to know each and every step of this process mathematically and theoretically also.
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1answer
39 views

Grounding and equipotential lines

In my textbook it says: One of the rules for static electric fields and conductors is that the electric field must be perpendicular to the surface of any conductor. This implies that a conductor is ...
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Field between 2 electrodes experiment

We were asked to conduct an experiment that is as follows: Connect 4.5V constant voltage across 2 electrodes of thin Cu wire, dipped in a tub of copper sulfate solution. A needle is connected to a ...
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impossible Poisson's ratio of Lennard-Jones potential type solid (cubic cristal for example), or any potential depending on $r$

We know (for instance : https://en.wikipedia.org/wiki/Poisson%27s_ratio ) that the Poisson ratio is $\nu=1/2-Y/(6B)$, with $Y$ the Young modulus and $B$ the bulk modulus. Let's assume we have a ...