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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How does electricity flow in conductor when potential difference is applied?

Electrons move from higher potential to lower potential. When a conductor is connected to battery, electron move from negative terminal to positive terminal. But the battery itself forms a Electric ...
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984 views

Is there any potential associated with magnetism

Can anybody please tell me if magnetism is a conservative force or if there is a field associated with it? How to reason? One thing I know is that the work done by a magnetic force is equal to $0$.
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A false proof of drag force being conservative

Consider a particle moving along some trajectory in the $x$-$y$ plane, in a viscous medium. Then its equation of motion is given by: $$\mathbf{F}_d = - b \mathbf{v} .$$ it's well-known from the ...
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Anharmonic oscillators: why is $F=-k x-k' x^3$, with no quadratic terms?

The equation of motion of a general anharmonic oscillator includes a position-dependent force that can be expanded in a Taylor series as $$m\ddot{x}+2\mu\dot{x}+k_0+k_1x+k_2x^2+k_3x^3\ldots=F.$$ I ...
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Apparent contradiction between quantum calculations and intuition for reflection at step potential?

I am rather confused because it would seem that mathematical conclusions I have drawn here goes against my physical intuition, though both aren't too reliable to begin with. We have a potential step ...
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1answer
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Child-Langmuir space charge law for non-zero cathode potential (non-zero initial electron velocity)

I'm trying to reconcile some conflicting results that I've found in publications that address the idea of the current in a vacuum diode in the case where the cathode has a non-zero potential, in other ...
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Why doesn't a quantum particle in an attractive 1D potential accumulate at the center?

I have two questions regarding (possibly counter intuitive results) Schrodinger equation and its application to two (strictly hypothetical) scenarios. Consider the 1D potential $V(x) = - \frac{\alpha}...
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Shape of water in rotating bucket

I need to show that the surface of water in a bucket rotating with constant angular velocity will have parabolic shape. I'm quite confused by this problem, but here's what I did: $$\vec{F}_{cf} + \...
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Infinite Wells and Delta Functions

In considering a delta potential barrier in an infinite well, I can just enforce continuity at the potential barrier-it doesn't have to go to zero. Why then does it need to go to zero at the walls of ...
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How can you have a negative voltage?

How can you have a negative voltage? I don't really understand the concept of negative voltage, how can it exist?
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631 views

Voltage as electromotive “force”

Considering the "water analogy" for electricity, it seems voltage is sort of like gravity: (image source: http://learn.olympiacircuits.com/electricity-flows-like-water.html) Now when water actually ...
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Reflectionless potentials in quantum mechanics

Scattering on potential $$V(x) = -\frac{(\hbar a)^2}{m}\text{sech}^2(ax)$$ with 1D equation of Schrodinger is famous problem. It is dealt with in Problem 2.48 of Griffiths book or online here. It is ...
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Finite Square Well Inside an Infinite Square Well

Ok here's a potential I invented and am trying to solve: $$ V(x) = \begin{cases} -V_0&0<x<b \\ 0&b<x<a \\ \infty&x>a \\ \end{cases}$$ and $V(-x) = V(x)$ (Even ...
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Origins of many-particle interactions

The internal potential energy of an $N$ particle system is a general function of the coordinates of the particles: $U(r_1,...,r_N)$. In some approximations and expansions - e.g. virial expansion - it ...
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What is the physical reason for why gravitational potential (or electrical potential) due to two masses at a point can simply be added algebraically?

The simple explanation that textbooks and the internet say is that "gravitional potential is a scalar quantity hence can be added algebraically". However, I'm not sure if it is that simple. Take for ...
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What does a voltmeter actually measure?

For time varying fields (even quasistatic ones) the electric field is given by $${\bf E} = - \nabla \Phi - \frac{\partial {\bf A}}{\partial t}$$ So what does a voltmeter measure? Does it measure a ...
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Properties of the field lines of an irrotational vector field

What are the properties of the field lines of an irrotational vector field like electrostatic field $\bf{E}$? Zero divergence fields like $\bf{B}$ have the property to be always closed field lines. ...
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How to find points with same potential while solving an equivalent resistance problem?

Lately, I've been reading about techniques to reduce networks and find their equivalent resistance/capacitance. While doing this, I came across the cube resistance problem and many other problems (eg. ...
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How electron movement produces current,instead of having a slow drift speed

Just need a clarification here, how the current is produced due to the movement of electrons, in an external circuit,having a very slow drift speed. Normally in a battery there is high potential ...
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Can I determine the potential term in the Schrödinger equation based on the eigenvalues? [duplicate]

Let's imagine I knew a certain system could be described by a one-dimensional Schroedinger equation. I know the mass/momentum term, but not the shape of the potential. Further for some reason I know ...
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A way to derive the Yukawa potential without cheating?

Let's say we have a simple Lagrangian that couples together two real scalar fields with a Yukawa $\phi \psi^2$ coupling. $$\mathcal{L} = \frac{1}{2}(\partial \phi)^2 - \frac{m^2_1}{2} \phi^2 + i\bar{...
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Is there an equivalent of a scalar potential for torques?

For a given scalar potential $V$, it is known that the corresponding force field $\mathbf{F}$ can be computed from $$ \mathbf{F} = -\nabla V $$ Suppose a rigid body is placed inside this potential....
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Is there a time delay during tunnelling?

A particle hitting a square potential barrier can tunnel through it to get to the other side and carry on. Is there a time delay in this process?
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Can we solve the particle in an infinite well in QM using creation and annihilation operators?

The particle in an infinite potential well in QM is usually solved by easily solving Schrodinger differential equation. On the other hand particle in the harmonic oscillator oscillator potential can ...
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What is $R$ in the formula for escape velocity?

From the escape velocity formula $$v_e = \sqrt \frac {2GM}R.$$ Some sources say it is the distance between two objects with mass $M$ and $m$. Some examples I have read, only used radius of the $M$. ...
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When Eigenfunctions/Wavefunctions are real?

When the Hamiltonian is Hermitian(i,e. beyond the effective mass approximation), generally under which conditions the eigenfunctions/wavefunctions are real? What happens in 1D case like the finite ...
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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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How to find a particle's dynamics in general relativity?

About a year ago, I took a course on general relativity. It isn't until now that I realize that, given a metric, I am unsure how to find a particle's dynamics. What I mean by that is, normally I ...
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Potential function - numerical simulation

Using MATLAB, I fixed the potential in a region inside a rectangular plate (100 V) and in the border (50 V). I got the following result of the potential along the plate: I can't find an intuitive ...
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Gravitational Potential of a Sphere vs Gravitational Binding Energy of a Sphere

My question is about two equations regarding uniform spheres that I've run into: $\quad V=\frac{GM}{r},$ and $\quad U = \frac{3}{5}\frac{GM^2}{r}.$ 1) On one hand, $V$ is unknown to me, and is ...
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Infinitely charged wire and Differential form of Gauss' Law

I have tried calculating the potential of a charged wire the direct way. If lambda is the charge density of the wire, then I get $$\phi(r) = \frac{\lambda}{4 \pi \epsilon_0 r} \int_{-\infty}^\infty \...
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Curvature of electrostatic potential is zero

Could you please expound upon this claim? I found such claim on Zangwill's Classical Electrodynamics, which states that constraint coming from Laplacian equation implies electrostatic potential has ...
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Electron travelling through a step potential from $V_0$ to 0

Most of the time you discuss the step potential case when $E>V_0$, you consider an electron (or a beam of electrons) travelling from a region of space $x<0$ in which $V=0$, to a region $x>0$ ...
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Find electric potential due to line charge distribution?

I need help how to set up this integral $$V(\mathbf r)=\frac{1}{4\pi\epsilon_0} \int_L \frac{\rho'_l}{\lvert \mathbf r - \mathbf{r'} \rvert}\mathrm{d}l'. $$ I have a uniform line charge along the $z$...
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Multipole Expansion: Electrostatics

Why in multipole expansion (or the terms therein) goes as mono-, di-, quadru-, octu-, or more specifically why are they in powers of 2? Why can't we have hexapole for instance?
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Kirchoff's rules and inductance

Can Kirchoff's loop rule be applied in a scenario involving an inductor? Kirchoff's loop rule states that the closed loop integral of E dot dl is equal to zero. But, in a situation with an inductor, a ...
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Kaluza-Klein Christoffel Symbols

I have a question regarding the connection coefficients as they pertain to the following paper: http://www.weylmann.com/kaluza.pdf . When I try to calculate the 4D Christoffel symbols from the 4D part ...
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How do aspherical gravitational monopoles look like?

I was recently pointed by laboussoleestmonpays to a beautiful paper from some time ago, Aspherical gravitational monopoles. Alain Connes, Thibault Damour and Pierre Fayet. Nucl. Phys. B 490 no. 1-2 ...
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Demonstration of the existence of a scalar potential for a conservatice force

Mathematically a vector field, $\vec{F}$, is conservative if: $$\oint_{\gamma} (\vec{F}.d\vec{l})=0$$ Physically, the integral is the same as the work done by a force $\vec{F}$ on a body in a closed ...
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Grounding system of conducting plates

So, I always make mistakes on problems such as this (the grounding part), so I'm hoping someone could really explain to me how the process works. There are $n$ large parallel plate conductors ...
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Do potentials make sense in relativistic quantum theory?

In Peskin & Schröder QFT, just before equation 7.93, he writes in passing, Next let us examine how $\Pi _2 (q^2)$ modifies the electromagnetic interaction, as determined by Eq. (7.77). In the ...
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Perturbation theory for a particle in a weak potential

I have a basic question about quantum mechanics, maybe it has a basic answer. Take a free particle in a quartic potential, $L=\frac{1}{2}\dot{x}^2-\lambda x^4$ This is massless $\phi^4$ theory in 0+...
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How to formulate variational principles (Lagrangian/Hamiltonian) for nonlinear, dissipative or initial value problems?

Although this questions is very much math related, I posted it in Physics since it is related to variational (Lagrangian/Hamiltonian) principles for dynamical systems. If I should migrate this ...
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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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Inconsistency between two formulas for Gravitational Potential Energy that don't yield the same result

According to this site the general form of the Gravitational Potential Energy of mass $m$ is $$U=-\frac{GMm}{r}\tag{1}$$ where $G$ is the gravitation constant, $M$ is the mass of the attracting body, ...
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How does one prove that Energy = Voltage x Charge?

We know $$E = q V$$ where $E$ is the energy (in Joules), $V$ is the potential difference (in Volts), and $q$ is the charge. Why is this equation true and how we prove it?
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Facing a paradox: Earnshaw's theorem in one dimension

Consider a one-dimensional situation on a straight line (say, $x$-axis). Let a charge of magnitude $q$ be located at $x=x_0$, the potential satisfies the Poisson's equation $$\frac{d^2V}{dx^2}=-\frac{\...
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What is the equation of the gravitational potential in general relativity?

How is the gravitational potential replaced by the metric tensor in general relativity? $$U_G=\frac {GMm}{r}$$ What is its equation?
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What is the state of the equilibrium for a second derivative equal to zero?

Considering a potential energy of $U$, and a displacement of $x$, the force is given by $F=-\frac{\partial U}{\partial x}$. Since equilibrium is defined as the point at which $F=0$, we can express ...
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Strong Newton's third law of action and reaction: Mathematical Interpretation

According to the strong law of action and reaction for internal forces (Goldstein): $\mathbf F_\mathrm {ij}=-\mathbf F_\mathrm{ji}$ and the forces lie along the direction joining the particles. ...