# 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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323 views

### 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 ...
417 views

### 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 ...
186 views

### $D$-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 ...
84 views

### Why does field strength follow the inverse square law but potential does not?

Either in a gravitational or electrical field, let's say an electrical field, the electrical field strength follows the inverse square law. This is fairly intuitive just due to the geometry of the ...
29 views

### 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 ...
77 views

### 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 \...
152 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 ...
113 views

### How to derive the simplest 1D Superpotential Hamiltonian?

In the superpotential wiki article there are definitions of two supersymmetric operators: $$Q_1=\frac{1}{2}\left[(p-iW)b+(p+iW)b^\dagger\right] \\ Q_2=\frac{i}{2}\left[(p-iW)b-(p+iW)b^\dagger\right]$$...
1k views

### Method of image charges for a point charge and a non-grounded conducting plane

I know how to solve Laplace's equation for a point charge in front of a grounded conducting infinite plane. But I want to know what happens (both physics and math) when the infinite conducting plane ...
311 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 ...
103 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 ...
226 views

### Does a Static $E$-field Increase the Gauge Invariant Vector Potential Without Bound?

The gauge invariant formulation of Maxwell's Laws (7.13): Indicates that the transverse electric field is the time derivative of the transverse vector potential. This gauge invariant vector ...
61 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 ...
128 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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### 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 ...
146 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 ...
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### Do 2 conductors (1 grounded via resistor) reach equipotential, before surplus electrons drain to earth?

Case I: a negative conductor makes contact with a neutral conductor. Negative donates some electrons to neutral, until there is 0 potential difference. Then they both are slightly negative. This ...
74 views

### What if in potentiometer, the loops are not balanced to cancel the potential and current flows?

As described in the book (image) that loops should be balanced with equal potential with help of the galvanometer. What if the we do not balance it to zero and have some current flowing? Can we still ...
193 views

### Derivation of Feynman Rules for a $\frac{1}{\phi}$ potential

The question is more mathematical in nature. If one had a potential $V(\phi) = \frac{\lambda}{\phi}$, where $\lambda$ is a constant, then how does one derive the Feynman rules for this scalar field's ...
1k views

### Physical interpretation of a complex potential for a particle in quantum mechanics

In Griffiths' Quantum Mechanics, it is mentioned in a problem that For an unstable particle that spontaneously disintegrates with a lifetime $\tau$, the total probability of finding the particle ...
491 views

### Dirac Delta potential and perturbation

I have a Dirac Delta potential as follows : $$V(x)= - \alpha \delta (x)$$ I know how to solve that problem. There is exactly one bound state. Now let's say I have an initial wave function in this ...
517 views

### Guess the wave function in a given potential

Are there any techniques in guessing the ground state wave function in any given potential? For example, for a given potential like $$\frac{1}{1-x^2}$$ or $$\frac{1}{1-x^3}~?$$ I know wave ...
43 views

### Gauge Permitting c Magnetic Vector and Instant Electric Scalar Potentials?

The Lorenz gauge requires c propagation of both scalar and vector potentials. The Coulomb gauge requires instant "propagation" of these potentials but is stated in such a way as to permit c ...
162 views

### Significance of imaginary mass

Can real mass be thought of as producing a deformation in spacetime leading to a stable equilibrium (valley curve in gravitational potential energy) of the massive body, and imaginary mass as similar, ...
391 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 (...
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### Is it possible for two polarizable bodies to induce dipoles in each other in the absence of an external electric field?

If there exist two initially neutral bodies (say atoms) some distance apart, with no external electric field applied, can they induce dipoles within each other?
518 views

### Is hydrogen atom in a box solvable analytically?

Schrödinger's equation for hydrogen atom in free space can be easily solved by switching to center of mass frame, introducing reduced mass and separating variables in the resulting 3D problem. But ...
Usually in physics textbooks, if the effective potential of the radial schroedinger equation $$-\frac{d^2}{dr^2}u(r) + \frac{\ell(\ell+1)}{r^2}u(r) + V(r)u(r) = E u(r)$$ falls below zero in some ...
Suppose we have a 1D potential $V(x)$ of finite range, i.e., $$V(x) ~=~0$$ for $|x| > b$. The potential is assume to support at least two bound states, but might have more, say $n\geq 2$. ...