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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Why do we use potential for quantizing the electromagnetic field?

For quantizing the electromagnetic field authors go to its potential and then find themselves facing to the problems of degree of freedom from gauge transformation. Why we can't simply quantize ...
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How is the curl of the electric field possible?

Taking the curl of the electric field must be possible, because Faraday's law involves it: $$\nabla \times \mathbf{E} = - \partial \mathbf{B} / \partial t$$ But I've just looked on Wikipedia, where it ...
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Method of image charges — Why is a *grounded* plate needed?

In the classic image charge problem of a charge $q$ above an infinite grounded plane, it is well known that the field lines essentially behave as though there were a negative charge behind it, and the ...
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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 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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Can two different Schrödinger equations have the same wavefunction?

Is it possible for two Schrödinger equations describing different systems to have the same wavefunction? And if that is the case, why or why not?
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1answer
997 views

Concrete example of the application of complex analysis in electrostatics [closed]

I've heard complex analysis can be useful in solving electrostatics problems, but despite doing some research I was unable to find any concrete examples. Would anyone be able to provide a simple ...
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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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1answer
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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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Why electron can not be found at some node locations in the infinite potential well? [duplicate]

Consider electron in an infinite potential well, studied in quantum mechanics. Position probability density of the electron is $$ P_n(x)=\left(\frac{2}{L}\right)\sin^2\left(\frac{n\pi x}{L}\right)$$ ...
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Semiclassical quantization of bouncing ball

Consider an elastically bouncing ball of mass $m$ and energy $E$. This has a triangular potential $$ V(x)~=~\left\{\begin{array}{ll} mgx & \text{if } x>0, \\ \infty & \text{if } x<0, \...
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General question about the potential barrier problem: Why does $\exp( kx)$ diverge when $x>0$ in the case when $E < V(x)$?

For the two images below, the first potential barrier has particles approaching it where $E > V_o$ & the second has a particle that has $E < V_o$, where $E$ is the energy of the particles ...
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An Electric Potential Glued to a Cube-Shaped Insulator to Replicate a Point Charge: Charge Distribution

I have been going back over this problem with a friend for the better part of a day: A potential is glued to a cube-shaped insulator so that outside of the insulator the field is the same as a point ...
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Why does the electric potential for an infinite line charge seem to have to be worked out from negative infinity rather than positive infinity?

The electric field of an infinite line charge in the plane perpendicular to the line charge can be given as: $$E=\frac{1}{2\pi \epsilon r}$$ Where $r$ is the perpendicular distance from the line. ...
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Electrostatics and potential of points around charged plates

For an infinite plane charged surface electric field is constant above it no matter how far we go from the surface. So if the electric field remains constant in magnitude, how can the potential ...
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Potential difference between two assymetrically charged plates

What is the potential diff between two plates of charges $q_1$ and $q_2$ ($q_1$ $>$ $q_2$)? I know the equation is $V = \frac{q_1-q_2}{2C}$ where $C$ is the capacitance of the system but how has ...
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Velocity-Dependent Potential and Helmholtz Identities

I'm currently working through the book Heisenberg's Quantum Mechanics (Razavy, 2010), and am reading the chapter on classical mechanics. I'm interested in part of their derivative of a generalized ...
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1answer
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Power series solution for a shifted spherical harmonic oscillator

I'm trying to solve the Schrodinger equation for a radial Harmonic oscillator whos equilibrium point has been shifted away from the origin, i.e. $V(r) = V_0(r-1)^2$. The standard approach is to make ...
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How will a particle with energy less than $V_{\rm min}$ behave?

Consider e.g. the finite square well: $V = -V_o$ between $x=-a$ and $x=a$, $V=0$ elsewhere Now for scattering states, $E$ must be $> 0$. For normalizable bound states, $E$ must be $< 0$ and $&...
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General potential of rotating system

I'm new here at the physics site, and not really that deep into the area of which i'm going to ask a question about now. Therefore please feel free to ask clarifying questions. I'm trying to deal ...
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Electric potential due to a point charge in Gaussian/CGS units

I learned electrostatics in SI units. In SI, the electrostatic potential due to a point charge $q$ located at $\textbf{r}$ is given by $\Phi(\textbf{r}) = \frac{q}{4 \pi \epsilon_0 |\textbf{r}|}$. ...
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Meaning of a battery being 2.5 V

So this is a question with which I have been stuck for a while and it all revolves around the concept of volt. I have posted a LOT of questions on physics forums while trying to understand the ...
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Why does the superposition principle work in method of images?

Okay, let there be a conducting sphere having radius $a$ initially charged with $Q$ & insulated. Now, $q$ is brought in front of the conductor at $y$ from the center. Now, Jackson in his book ...
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1answer
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Relation between potential difference and electric field

I was reading an article about resistivity when I faced this equation: $$V_P-V_O=\int_P^O E.dr$$ The equation is in one dimension and $P$ and $O$ are points on the $x$ axis. The Electric field is ...
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How can current flow in an ideal wire if all of its points are at the same potential? [duplicate]

If I have an ideal wire and I connect a battery to it, then the potential drop is zero along the wire, right? So, all its points must be at the same potential. Well, that means charges ( which are ...
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Work done in moving a charge

So, recently while I was studying electric fields and charges for a test, I came across the definition of electric potential as - The amount of work done in moving a unit positive test charge from ...
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Electric Field Topology in a Wire - Exact Duplicate [closed]

1. How is the electric field set up in a wire by a battery so that we can assume that potential at a node is constant? 2. What happens to the electric field across a resistance which makes voltage '...
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Particle in a 1D Box with Symmetric potential: How find solutions?

I am working on a problem in which I shall find the normalised solution to the 1D particle in a box. Solving for the particle in an asymmetric potential is quite straight forward, but I run into ...
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When to use method of images in Electrostatics?

I am a bit confused about when to use the method of images in E&M? For example, in Griffith's Electrodynamics Example 3.2, the problem reads: A point charge $q$ is situated a distance $a$ from ...
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Stationary states of a triangular prism

I need to find the wavefunctions of the stationary states of a 3d square potential well with its boundaries defined by a triangular prism - like the one illustrated on the wikipedia page: https://en....
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Bound states of the $V(x)=\pm \delta'^{(n)}(x)$ potential?

The $\delta(x)$ Dirac delta is not the only "point-supported" potential that we can integrate; in principle all their derivatives $\delta', \delta'', ...$ exist also, do they? If yes, can we look for ...
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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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In the Lennard-Jones potential, why does the attractive part (dispersion) have an $r^{-6}$ dependence?

The Lennard-Jones potential has the form: $$U(r) = 4\epsilon\left[ \left(\frac{\sigma}{r}\right)^{12} - \left(\frac{\sigma}{r}\right)^{6} \right]$$ The (attractive) $r^{-6}$ term describes the ...
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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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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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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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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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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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Electric potential vs potential difference

What is the difference between electric potential and potential difference? In our course book, they are given as separate topics but their definition is given the same.
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Electrostatic Potential Energy Derivation

How is the boxed step , physically as well as mathematically justified and correct ? Source:Wiki http://en.wikipedia.org/wiki/Electric_potential_energy As work done = $- \Delta U $. for Conservative ...
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From Liénard-Wiechert to Feynman potential expression

When studying the potential of an uniformly moving charge in vacuum, Feynman proposes to apply a Lorentz transformation on the Coulomb potential, which reads in the rest frame $ \phi'(\mathbf r',t') =...
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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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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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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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How do we find the number of bounded states in this potential?

for the potential $$V(x)=-\frac{1}{1+\frac{x^2}{m^2}}$$ we can approximate the wave function and bounded state accurately for $x << m$ as simple harmonic oscillator, so what are we gonna do if ...
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Locally every force admits a potential?

I have a little doubt about a force being or not conservative. Well, as I understood, some forces cannot be expressed as exterior derivative of some scalar potential because the work done by the force ...
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A simple demonstration that the electrostatic potential has no extrema in free space

The electrostatic potential $V$ cannot attain a local maximum or minimum in free space (a region of space where there are no charges). The claim makes sense intuitively: if $V$ had a local maximum ...
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1answer
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Resistance and potential difference across it

I have this question that has baffled me for hours now. My question is what really happens when charge passes from one point to another in a circuit for eg what happens when it passes over a resistor....
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Why does a electric Potential have to be real, but not a Potential in quantum mechanics?

So I had this Problem when I had to learn about classical electromagnetism: Why is it, that we use complex numbers when calculating stuff, but in the end only the real part is important (for example ...
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Bound states for sech-squared potential

I'm working on an introductory qm project, hope somebody has the time to help me (despite the length of this post), it will be highly appreciated. My goal is to determine the bound states and their ...