# 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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### 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 ...
221 views

### Does the Schrodinger Equation yield a unique wave function and density?

I am learning DFT and the Hohenberg Kohn Theorem of Existence. And it says that there is a one-to-one correspondence between the external potential and the density. However the proofs that I have seen ...
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### Understanding conformal mapping in electrostatics

I'm trying to understand the use of conformal mapping to solve problems in electrostatics. To better understand the idea, I'm trying to learn how to solve this example (but you can propose any other ...
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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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### What does the term 'high voltage' really mean?

This might be a dumb question but i am not so familiar with the word voltage: What does the textbooks really mean when they say high voltage?. Does that mean: There are more charges so more voltage, ...
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### Why is the spin-orbit interaction for a nucleus so much more important than the spin-orbit interaction in atomic physics?

In atomic physics, the spin-orbit is a small correction between 1/1000 and 10ppm, so fairly small. In contrast, in nuclear physics the inclusion of the spin-orbit interaction is necessary to reproduce ...
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### 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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### Dilemma in Theory of Superposition of Electric potential

Electric potential is the amount of work done in bringing a unit charge from infinity to a point. Here we take infinity as a reference point. The unit charge might have higher or lower potential ...
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### What are many-body potentials? Why are they important?

I have been studying molecular dynamics and statistical mechanics, and I have been running into this term called "many-body" forces. I have been reading this paper: https://doi.org/10.1080/...
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### How do you normalize this wave function?

I have a basic question in elementary quantum mechanics: Consider the Hamiltonian $$H = -\frac{\hbar^2}{2m}\partial^2_x - V_0 \delta(x),$$ where $\delta(x)$ is the Dirac function. The eigen wave ...
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Considering the potential $\psi(r)$ of a sphere of mass $M$ with density $\rho(\mathbf r')$, connected by a small volume positioned in the $P'$ point as shown in the figure: The $\psi(r)$ is: $$\... 0answers 227 views ### What is a good analogy for electric potential? When the electrical field was defined I could totally relate to \vec{E} being like \vec{g} in mechanics. But for the electric potential I don't know what would be equivalent analogy. Any ... 0answers 122 views ### How to derive the simplest 1D Superpotential Hamiltonian? In the superpotential wiki article there are definitions of two supersymmetric operators:$$Q_1=\frac{1}{2}\left[(p-iW)b+(p+iW)b^\dagger\right] \\ Q_2=\frac{i}{2}\left[(p-iW)b-(p+iW)b^\dagger\right] $$... 0answers 320 views ### Accelerated ion beam current If an electron gun creates a 10\space mA electron beam and each electron collides with a gas atom and creates an ion through impact ionization, can the ions then be accelerated with a separate ... 0answers 108 views ### Conservation of momentum in statistical physics in presence of a potential Imagine a number of particles, all confined in a parabolic potential. The particles initially have a random velocity and are let free to bounce off each other (say, it's rigid spheres). Does ... 1answer 446 views ### Misbehaving singular isothermal sphere potential The singular isothermal sphere (SIS) is a useful simple model often used in astrophysics. It has density profile:$$\rho(r) = \frac{\rho_0 r_0^2}{r^2}$$This is well known to have some quirks (... 1answer 62 views ### Meaning of potential in a discharging capacitor I am dealing with this thing I cannot figure out. When a capacitor is discharging, the electric field inside it varies with time so we cannot perform the line integral to determine the potential ... 0answers 131 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 ... 0answers 87 views ### Charge distribution and potential in a 1-dimensional quasistatic system Suppose you have an 1-dimensional system with a charge distribution \rho(x) (not given) moving with an speed v(x) (not given), calculate the potential \phi(x) and the charge distribution \rho(... 0answers 420 views ### Symmetries of separable potential For separable potential, say x^4+y^4, its symmetry are degenerate. Is that a generic case to every separable potential? I will explain my question: The potential x^4+y^4 has A_1, B_1, A_2, B_2, ... 1answer 163 views ### Is there something wrong in my book's derivation of work done on charge? For finding potential at a point due to a +ve charge (q), we find work done to move a unit +ve charge (q_o) from infinity to that point in the presence of +ve charge (q) Since both charges ... 1answer 193 views ### At what distance is lightning dangerous for someone lying down? My 8 yo child told me that they learned at school that they should lay down flat on the ground in case of lightning. I told him that the more correct position is crouching down with feet together, but ... 2answers 3k views ### Charge flow between a sphere (inside) a spherical shell irrespective of the charge of the shell A small sphere of radius r_1 and charge q_1 is enclosed by a spherical shell of radius r_2 and charge q_2. If q_1 is non-zero and the two spheres are connected by a wire, then, charges will ... 1answer 32 views ### Difference between grounding the inner and outer side of a thick spherical shell I have a conducting sphere with radius R_1 and charge Q_1 inside a conducting thick spherical shell with inner radius R_2>R_1 and outer radius R_3>R_2. Both the spheres have the same ... 2answers 28 views ### Potential on an Uncharged Conducting Sphere Due to a Point Charge I'm working on a problem where I need to find the change in potential of a point on a conducting sphere ("A") a distance 3R from a point charge "q" (R=radius of the sphere). My ... 0answers 26 views ### How is \nabla\cdot \mathbf P sufficient to describe the volume polarization \mathbf P I'm self-studying Panofsky and Philips' Classical Electricity and Magnetism. In Section 1-10, they talk about the potential due to a volume polarization \mathbf P being effectively divorcing into ... 0answers 63 views ### Magnetic monopole, vector-potential and differential forms When written in the language of exterior algebra, Maxwell-Thomson equation writes as dB=0 where d is the exterior derivative and B is the magnetic flux 2-form. From Poincaré's lemma, it follows ... 1answer 136 views ### Why does potential of a conductor decreases if a negatively charged conductor is brought near a positively charged conductor? Also, how should I imagine potential in my mind? How should I picture it? 0answers 72 views ### Reference needed for effective gravitational potential in General Relativity In Wikipedia ( https://en.wikipedia.org/wiki/Two-body_problem_in_general_relativity ) one can find the following expression for the effective gravitational potential in the Schwarzschild approximation ... 0answers 132 views ### Can the WKB approximation be used for this double well potential? For a positive constant C, the double well potential V(x) = -C|x|  exists between two infinitely high potential walls at x=a and x=-a. I wish to use the WKB approximation to obtain an equation ... 0answers 64 views ### How does the delta prime boundary conditions behave when the jump factor approaches infinity? I recently came across the concept of a \delta'(x) (delta prime) potential, which is basically a potential which imposes the boundary condition: \frac{\partial\psi}{\partial x} is 'continuous' at ... 0answers 43 views ### Origin of the definition of the electric potential of a black hole All the papers I’ve seen in black hole thermodynamics (e.g. arXiv:hep-th/9908022) define the electrostatic potential of a black hole with horizon Killing vector \xi^a as$$\Phi := \xi^a A_a \big|_{...
I have been struggling with this problem for some time by now. An insulated metal sphere of radius $a$ with total charge $q$ is placed inside a hollow grounded metal sphere of radius $b$. The centre ...