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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Electrohydrodynamics: How will electric potential develop in a fluid when potential is applied from ends

Lets say, I have a fluid in a rectangular enclosure (2D). I apply electric potential $U=U_1$ at left boundary and $U_2$ at right boundary. In the lower and upper boundaries, the potential varies ...
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103 views

Definite energy states for a single non-relativistic particle with a time dependent potential

Do definite energy states exist for a single particle when its potential itself changes with time? I tried solving it and the equations seem to show that they do not exist. But then i am confused as ...
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78 views

How is electric field strength related to potential difference?

I was looking at the derivation of drift velocity of free electrons in a conductor in terms of relaxation time of electrons. Here a metallic conductor XY of length $\ell$ is considered and having ...
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53 views

What is the physical meaning of the norm of the electromagnetic four-potential?

In SI units this would be $\frac{1}{c^2}\phi^2 - A_x^2 - A_y^2 - A_z^2$. Is this just not a physically meaningful quantity at all because it's not gauge invariant?
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51 views

Mass of small fluctuation around vacuum

For a potential $V$, how do we define the mass of a small fluctuation around its vacuum? For example I have the potential $$ V_\mathrm{eff}(\phi) = \frac{1}{2} \left(\frac{\rho}{M^2} - \mu^2\right) ...
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Bound states in 1D & 2D [duplicate]

Why does Mother Nature allow bound states in arbitrarily weak attractive potential in 2D but not in 3D? See, for example, this article, arXiv:math-ph/0208011.
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200 views

What does raising voltage do?

If I raise the voltage of a wire from 0V to 1000V and then to 5000V, am I merely packing it with more and more electrons (with those electrons being trapped there until they find a path off the wire)? ...
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Potential difference between point on surface and point on axis of uniformly charged cylinder

Question: Charge is uniformly distributed with charge density $ρ$ inside a very long cylinder of radius $R$. Find the potential difference between the surface and the axis of the cylinder. Express ...
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Nonlocal interaction effects on bose-einstein condensates

I'm studying an interacting bose-einstein condensate using the energy functional proposed in this paper K. Huang, C.N. Yang, Phys. Rev. 105 $$ E\left[\phi\right] = \int d^3\vec{r} ...
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168 views

The Effect of Tortoise Coordinates

Referring particularly to http://arxiv.org/abs/hep-th/9909056 in regard to the wave equation for Schwarzschild-AdS black holes (p.4), I'm trying to understand tortoise coordinates. So starting ...
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123 views

Special case of work done by two opposing forces of equal magnitude on a body possesing inertial motion

Consider an elevator moving upward with constant velocity. The constant velocity is maintained by an upward tensional force equal to weight. If we add the total work done on the elevator it will be ...
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67 views

Why is electric potential positive?

If there is a positive charge $q$ at the origin of a coordinate system, the electric potential $\phi$ at a distance $r$ from $q$ is (by definition, if we take the point of zero potential at infinity): ...
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137 views

Name of battery voltage when load connected/disconnected

If I had a 3V battery, and when no load connected it reads 3.2V, and with a load 2.8V (just a hypothetical example), what is the name for these two terms, with a load or no load? I know the voltage ...
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388 views

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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2answers
122 views

Modeling a potential well

I attempted to simulate the interaction of a moving particle and a potential well in Mathematica. The particle should experience a force of -$1/r^2$, if the equation for the potential well is -$1/r$. ...
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86 views

Is the “Force” of Gravity Simply Hamilton's Principle on a Curved Spacetime?

It's my understanding that General Relativity abstracts away the concept of gravity as a force, and instead describes it as a feature of spacetime by which massive objects cause curvature. Then it ...
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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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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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Basics of Current Electricity

I have certain questions which confuse me a great deal. I want to have a very basic and clear idea about some concepts. Here it goes: 1) I am really confused on how a battery actually works. The very ...
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69 views

If batteries are a source of energy, would not lower-valued resistors cause a violation of the conservation of energy?

Here's the conundrum I have been facing. Yesterday I asked the question: how can batteries constantly motivate electrons to complete a circuit? (What maintains constant voltage in a battery?) After ...
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290 views

How to solve the Laplace Equation in the hollow square region?

Suppose the values of $a$, $b$, $V_1$ and $V_2$ is given. I want to find the solution of the Laplace equation, $$\frac{\partial^2 \phi}{\partial x^2}+\frac{\partial^2 \phi}{\partial y^2}=0$$ in the ...
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122 views

Argument for symmetry of potential of a spherical capacitor filled with dielectric

A spherical capacitor with inner radius $r_1$ and outer radius $r_2$ is filled with dielectric material with permittivity $\epsilon=\epsilon_0+\epsilon_1\cos^2\theta $. $\theta$ is the polar angle. ...
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208 views

What maintains constant voltage in a battery?

I know there's lots of questions that address similar situations, (Batteries connected in Parallel, Batteries and fields?, Naive Question About Batteries, and the oft-viewed I don't understand ...
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82 views

Justification of discrete spectrum for V(x) unbounded at $\pm \infty$ in Pauling and Wilson

In Pauling and Wilson, Introduction to Quantum Mechanics, they offer the following intuitive reason for the discrete spectrum of a potential which is unbounded at $\pm \infty$: This is ...
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Units and missing constants in quintessence expressions?

In cosmology, quintessence is an alternative to the cosmological constant. In this approach (described here), we consider a scalar field $\phi$ and its self-interacting potential $V\left(\phi\right)$ ...
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Surface potential resulting from the charge transfer between insulator and conductor

Common non-contact electrostatic voltmeters are used to measure the surface potential. Imagine we place a charged insulator on top of the conducting plate (insulated from the surrounding) and measure ...
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172 views

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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Is there some quantum potential producing exponential eigenvalues?

Usual central potentials produce quantum spectra with energy levels going as $n$, $n^2$, $n^3$ and so on, being $n$ the quantum number of the orbit. In the other extreme we have "dirac-delta" ...
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76 views

Variation of Electrostatic Potential with Distance in a Uniform Field

I came across this question in a problem book: If a proton is released from rest in a uniform electric field, does the electric potential at those points where the electron moves increase or decrease. ...
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83 views

WKB approximation in two dimensions

Does anybody know how to implement the WKB approximation for the two-dimensional Schrodinger equation with a harmonic oscillator potential: $\frac{1}{2}\Biggl[-\biggl(\frac{\partial^2}{\partial ...
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1answer
457 views

Initial condition for Fourier transformed Schrödinger equation

I asked in this thread Time-dependet Schrödinger equation how to solve the Time-dependent Schrödinger equation. One of JamalS' recommendations was the Fourier transform, which is why I want to quote ...
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213 views

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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528 views

What is an “Interaction Hamiltonian”

I'm an undergraduate reading up on some quantum physics so that I can help out more in the lab that I'm working in this summer. In the book I'm reading (Shankar's "Principles of Quantum Mechanics") I ...
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94 views

Infinite Round Square-Well zeroes of Spherical Bessel function

Consider a potential well where the potential is zero within a spherical well of radius a centered on the origin. Taking $a$ as our length scale and $\hslash^2/(2ma^2)$ as our energy scale, we gain ...
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32 views

Particle in a box under harmonic driving

Is the particle in a box under harmonic driving electric field solvable analytically? Here is the Schrodinger equation: $$ i\frac{\partial \psi(x,t)}{\partial t}=\left[-\frac{1}{2} ...
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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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249 views

Storing kinetic energy instead of potential energy - practically possible?

One of the big problems today considering energy is its storage (e.g. batteries are not that efficient, very expensive and polluting). Energy is classically mostly stored as some kind of potential (in ...
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Potential at Center of Earth

If using the surface of the earth as a reference point how much work is needed for gravity to pull me to the center. Is it negative infinity or am I wrong? Also is a single value of potential ...
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142 views

Meaning of “Grounded”

In my opinion, "grounded" means having the same potential as the potential at infinity, which is usually set to zero. Now if we consider a conductor inside a uniform electric field, what is the ...
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282 views

Grounded conductor inside a uniform electric field [duplicate]

I am working on a textbook problem of a grounded conductor inside a uniform electric field. The textbook states that "grounded" means potential = 0. In my opinion, "grounded" should mean "same ...
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1answer
168 views

Derive force from the pair-wise potential equation [closed]

How can we calculate the force exerted on particle $i$ by particle $j$ given a general potential function $V(d)$? Let's discuss this genenal question with a concrete example below. To simulate the ...
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Electric field between electrodes of different shapes [duplicate]

How to calculate electric field between two electrodes - square and circular?
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93 views

Quick question on sketching wavefunction in well

Usually for an infinite well, the sketch for n=3 level is this: Now I think if one side of the potential barrier is higher, the particle will be more likely to spend time on the left side than ...
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82 views

Integration over $S^2$ in electrostatics

I'm studying for a test in electrostatics and I'm always failing on putting up the correct integrals. In one problem I have the surface of a sphere with radius $a$ and an opening angle of $2\theta$. ...
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186 views

How to measure vector potential such as that of magnetic field?

If we want to measure gravitational potential energy of a body-earth system, we can simply do it by measuring the body's height from ground. How could we can measure vector potential such as that of ...
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1answer
131 views

How the electric potential of a charged body depends on the surface area of the body?

I have studied in the book that electric potential of a body depend on the surface area of the body, that is as the surface area increases potential decreases keeping the charge as constant and vice ...
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172 views

Is there a surface charge density?

Consider a dielectric sphere placed within a dielctric medium. There is a uniform electric field $E_0$ present throughout in the medium. Would there be surface charge on the sphere?
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226 views

Find the points where potential is null

Let's say we have two charges called $q_1$ and $q_2$, respectively $20 \, C$ and $-40\,C$, at a distance $d=1\,m$ We want to find all the points where electric potential is null. I solved the ...
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470 views

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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877 views

Why do electrons move towards regions of lower potential?

Can someone explain why electrons move from high to low potential regions in quantum mechanics? By the way, what is the very definition of this potential? Moreover, how does this generalize to other ...