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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What is the origin of the Dirac delta term in the dipole electric field?

I am a bit lost how one has deduced the formula for electric field with electric dipole because of some inconsistency between different sources. The Wikipedia article contains a delta function in the ...
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Potential functions

Can someone please explain what a potential is? Example. velocity potential in ideal flows, acoustic potential (gradient of which gives the particle velocity in a sound wave). Whenever I see potential ...
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Physical interpretation of circuit with battery charging capacitor

In the picture below, we are charging up the capacitor, by connecting it (and the resistor to a battery of voltage $V_0$, at time $t = 0$). In terms of what is happening physicially, how would you ...
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Potential energy of a dipole in a uniform electric field convention?

When finding the potential energy of a dipole in a uniform electric field, I was told by my lecturer that the convention is that the potential energy is 0 when the dipole moment and electric field ...
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Can we have discontinuous wavefunctions in the Infinite Square well?

The energy eigenstates of the infinite square well problem look like the Fourier basis of L2 on the interval of the well. So then we should be able to for example make square waves that are an ...
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Why doesn't the potential difference across an inductor increase over time?

For school, I was trying to solve a question that features a circuit with a resistor, an inductor, and a battery all connected in series. It then shows an increasing concave down graph of something vs....
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Wave function with a delta potential

I have a particle and a potential $V(x)=\frac{\hbar^2}{2m}k\delta(x)$. Where $\delta (x)$ is the Delta function, and I am interested in the solutions of the stationary Schroedinger equation. If $\...
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What is the physical meaning of electric potential, potential difference, and voltage?

When resembling the electricity flow through a wire to people walking through a street: electrons are people, current is the number of people, resistance is the barriers on the way. But what is the ...
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Relation between Electric field and potential

I am unable to understand from this - sign comes. Which step I have done wrong?
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Why does a capacitor discharge?

Suppose a charged capacitor (parallel plates), the negative and positive charges on two plates attract each other. Which force cause the negative charge carriers (electrons) move through the circuit ...
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How can a generic potential transform under Lorentz transformations?

The standard relativistic particle Lagrangian is $$L = - \sum m_i \sqrt{1-v_i^2} - V(x_i).$$ The first term contributes a scalar to the action, as it should, but the second term is not clearly a ...
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Is there a potential which is “bad” in classical mechanics and “good” in QM or conversely?

I am asking for a counterexample or a proof for the following statement: Let $V$ be some (time-independent) potential in $\mathbb{R}^n$, then the following statements are equivalent (under some mild ...
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What is the difference between electric potential, potential difference, and voltage?

I see both terms being used from time to time. Are they interchangeable?
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What is a potential well?

What exactly is a potential well physically? [I've read the linked Wiki article, but it doesn't answer my questions, such as, what does it mean for a particle to "move along a potential" and "roll ...
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What is physical meaning of $|\phi|^2$ in quantum field theory and pedagogical spontaneous symmetry breaking?

If wavefunction is $\phi$, we know that $|\phi (x)|^2$ represents probability of finding a particle at $x$. Now let us talk about some pedagogical example in spontaneous symmetry breaking in QFT, ...
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Is there any good reason/argument/heuristic why one can approximate forces by approximating the potentials?

My question Is there any good reason/argument/heuristic why one can approximate forces by approximating the potentials? (As a concrete example, in Electrostatics.) Motivation for the question I am ...
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What is the meaning of $U''(x)=0$?

Most potentials with a minimum can be described approximately as a harmonic oscillator. So the procedure is to Taylor expand $U(x)$: $$U(x)=U(0)+U'(0)x+\frac{1}{2}U''(0)x^2 +...$$ If we suppose ...
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Conditions of applicability of potential flow about an airfoil

In many cases the flow about an airfoil is calculated by solving the Laplace equation, (for example in the Hess-Smith panel method). If the velocity field is irrotational and its divergence its zero, ...
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Physical Significance of $U$ (Internal Energy ) , $H$ (Enthalpy) , $F$ (Free Energy) and $G$ (Gibbs Free Energy)? [closed]

I know their mathematical definitions and how these terms are interrelated (mathematically) but I fail to understand the physical meaning of none but one which is INTERNAL ENERGY . It seems ...
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Calculate the charge distribution given the potential $\Phi(x,y) = 2(\tan^{-1}(\frac{1+x}{y}) + \tan^{-1}(\frac{1-x}{y}))$ [closed]

So this problem actually comes from The Classical Electromagnetic Field by Leonard Eyges and says: Find the distribution of charge giving rise to an electric field whose potential is $\Phi(x,y) = 2(...
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What potentials have infinitely many bound states? [closed]

Some potentials have only finitely many bound states (the finite square and delta function are two good examples) Others have infinitely many bound states (for example the infinite square well and $1/...
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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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1D Finite potential well: solutions with $\sinh$ and $\cosh$?

So I am studying the (one dimensional) quantum mechanical finite potential well defined by: $$ V(x) = \cases{0, &|x|>a\cr -V_0, &|x|<a} $$ where $V_0>0$ is a real number. I know ...
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Potential generated by a hollow sphere with a hole

The sphere has radius $R$ and is missing its "pole" - meaning that in the area $\theta\leq\alpha$ there is nothing. The object has a homogenous charge density $\sigma=\frac{Q}{\pi R^2}$ I'm trying to ...
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Where does the Pauli Repulsive Force come from that counteracts the attraction between atoms and ions? [duplicate]

I'm learning about such things as ionic and covalent bonds, and the reason given for the ionic bonds is electrostatic attraction. However, if that were true, then the two ions would accelerate toward ...
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Is it possible to tell whether a potential is unbounded using only perturbation theory?

A very common inverse problem in mathematical physics is trying to understand the potential of a quantum mechanical system given its scattering data. Such problems, although very interesting, are very ...
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Method of images for intersection of two planes

Vanderlinde's Classical Electromagnetic Theory discusses the method of images, with examples given for intersecting infinite conducting (half) planes. In particular, the "kaleidoscope" effect of ...
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Can conductor be charged?

I have a copper conductor. For a while, I apply a voltage of $12kV$ DC from a source. After removing the source, will the conductor stay charged from the source if is not earthed? Will it discharge ...
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Is the superposition principle a postulate in electrostatics?

Consider two electrical point charges $q_1$ and $q_2$ described by the total charge distribution $\rho = \rho_1 + \rho_2 = q_1 \delta(\vec{r} - \vec{r_1}) + q_2 \delta(\vec{r} - \vec{r_2})$. The total ...
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Why does the potential difference between two charged plates increase as they move further apart?

Suppose a uniform electric field $E$ exists between to oppositely charged metal plates (one is positively charged and one is negatively charged). If the plates move apart, and the charges on each ...
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Why do we not require higher derivatives to match at boundary when solving the Schrödinger equation in a given potential?

When solving the time independent Schrödinger equation for a given potential in 1D, the main part of the solving involves matching boundary conditions. Usually, we require the value and the first ...
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Argument for symmetry of potential

Consider the following electrostatic charge configuration of a spherically symmetric, perfect conductor with total charge $Q = 2q$, where $q > 0$. A point charge $q$ is placed at the position shown....
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Why is chemical potential equivalent to a true potential?

My K&K thermal physics testbook says chemical potential is equivalent to a true potential: the chemical potential is equivalent to a true potential energy: the difference in chemical potential ...
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How should I think of a liquid in terms of interatomic potential and molecular speed?

A rather simple question for liquids specialists I guess but I have hard time finding information about this. Here is my problem. I understand the ideal gas theory and the Maxwell's speed ...
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Kinetic energy and Potential of a photon

How does the potential and kinetic energy of a photon relate? Do they mean the same thing? Also how does De broglie wavelength and Potential relate?
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Potential difference between Earth's surface and 2 meters above

Assuming Earth is a charged sphere of radius $R = 6400\times10^3$ m with uniform surface charge density $\sigma = -10^{-9}$ C/m2 and with $\epsilon_0 = 8.85\times10^{-12}$ F/m I find that $$V(R+2)-...
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How does current flow in a irregularly shaped heterogeneous resistor?

The motivation for my question is understanding how electricity gets through your skin as opposed to running along it, and how the presence of things like water on the skin affect the relative ...
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$D$-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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Classification of equipotential curves between two equal point charges

The equipotential curves of two parallel equal-density line charges (in a plane perpendicular to the line charges) are known to be Cassini ovals. This is because the potential at a point a distance $...
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Particle in infinite potential well which is doubled in size at $t_0$

I am currently studying for an exam in Quantum Mechanics and came across a solution to a problem I have trouble with understanding. The Problem: A Particle sits in an infinite potential well ...
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How do we recover units of force from units of gravitational potential?

The gravitational potential $G_\text{pot}$ has units of energy per unit mass: $$ \bigg[\rm\frac{J}{kg}\bigg] = \bigg[\rm\frac{kg\cdot m^2}{s^2\cdot kg}\bigg] = \bigg[\rm\frac{m^2 }{s^2}\bigg]. $$ ...
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Why does a delta-function well have only 1 bound state?

From Griffiths, Introduction to Quantum Mechanics, pg. 73: Evidently, the delta-function well, regardless of its "strength" $\alpha$, has exactly one bound state $$\psi(x) = \frac{\sqrt{m \...
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Gravitational potential in GR

Why in GR does the $g_{\mu\nu}$ describe potential?
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Plotting $\psi$ for finite square well potential

Lets say we have a finite square potential well like below: This well has a $\psi$ which we can combine with $\psi_I$, $\psi_{II}$ and $\psi_{III}$. I have been playing around and got expressions ...
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Why is choosing a suitable thermodynamic potential important?

Say we are undergoing an isothermal process that eventually settles at equilibrium. $F$ will minimize at equilibrium, and if the entropy of the system is not held constant $U$ will not. Why do we care ...
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Capacitance of a single charged plate?

Lets say we have a single plate that has a charge of $+Q$ on it. A plate with charge $-Q$ is infinite distance away. Will the plate with $+Q$ have a capacitance associated with it? Why or why not? I ...
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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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Higher order derivatives - Equation of motion

One possible starting point to create a physical theory is the Lagrangian $L$. There we assume that the variation of the action $\delta S = \delta \int_{-\infty}^\infty dt \ L = 0$. In classical ...
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Force on a point charge $q$ inside a cavity in an uncharged conductor

This is problem 2.40 from Introduction to Electrodynamics by D. J. Griffiths: A point charge $q$ is inside a cavity (not necessarily spherical or anything similarly regular) in an uncharged ...
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Is the electric field strength along an equipotential surface constant?

I'm trying to determine whether or not the electric field strength $|\vec{\mathcal{E}}|$ is constant everywhere on an equipotential surface. I know an equipotential surface is defined as $$ S = \{\...