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1answer
79 views

What is the correct way to take out equivalent capacitance here?

So here I have a capacitor with two plates , one positively charged and one negatively, as shown in the figure. Now the material between them is $k_1$ for thickness d/2 and $k_2$ for the other d/2. ...
0
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0answers
30 views

Looking for Solutions to Symmetric Potential

I'm a little confused on the basic method of finding a separable solution to a give potential distribution. If we have a symmetric potential, say it hits zero and $-a$ and $a$, constituting two sides ...
0
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1answer
54 views

Calculating electric potential from a changing electric field

Assuming that I calculated the electric field in a single point between a uniform charged positive sphere and an infinite long wire charged positive uniformly. Now, I want to calculate the velocity of ...
2
votes
1answer
65 views

Sign convention for EMF

When we define the field generate by EMF, why there is not negative sign in $\mathcal{E} = \oint \vec{E} \cdot d\vec{l}$? Usually we talk about potential, there should be a negative sign, right?
2
votes
1answer
88 views

A zero gravitational potential and non zero gravitational field

Give an example of a situation in which there is a non-zero gravitational field and a zero gravitational potential at the same point? $$dV=-\vec E\cdot d\vec r.$$ The above equation implies that ...
1
vote
2answers
121 views

Interaction energy between dipole and potential

It is known that interaction energy = $-\vec{p}.\vec{E}$ where $\vec{p}$ is dipole moment and $\vec{E}$ is the electric field. I have to calculate the interaction energy of a system whose dipole ...
2
votes
2answers
57 views

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 ...
0
votes
1answer
84 views

Calculating the Reflection Coefficient of a Potential Step Explicitly

So I'm using the following definition for the Reflection coefficient : $$\frac{\vec{j}_{reflected}}{\vec{j}_{incident}}$$ Hence, since : $$\psi_{reflected}=Be^{-ikx}$$ and ...
1
vote
1answer
135 views

Clarification of multipole expansion for a point charge

In Griffith's electrodynamic: 3.4.2 He pointed out that the monopole term is the exact potential for a single point charge. However I was under the impression that different configuration of a ...
7
votes
6answers
277 views

Origins of many-particle interactions

The internal potential energy of an $N$ particle system is a general function of the coordinates of the particles: $U(r_1,...,r_N)$. In some approximations and expansions - e.g. virial expansion - it ...
2
votes
1answer
186 views

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 ...
1
vote
3answers
183 views

How can the potential on a cube's surface replicate the potential of a point particle?

If i have a cube (either hollow, or an insulating solid) and i want its surface have a potential such that it looks like a point particle outside of the box does that mean the exact potential on the ...
1
vote
1answer
59 views

Reflection of an evanescent matter wave within a finite barrier?

To my understanding if I have a finite barrier with potential $V(x)>E$, then to the left of the barrier, the wavefunction can be represented as two exponentials: $$\psi= e^{(ik_{left} x)} + ...
4
votes
2answers
137 views

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 ...
1
vote
1answer
46 views

Taylor expansion term equals zero?

I have to Taylor expand an effective potential $U_{eff}$, which is given by: $$U_{eff}(r)=-\frac{Gm_{1}m_{2}}{r}+\frac{l^{2}}{2\mu r^{2}}$$ I then expand it and get: ...
2
votes
3answers
123 views

Calculating the Potential from the E-Field

I find that often times I'll be tripped up by questioning whether or not I can do something mathematically, and be unable to come up with a satisfying answer. This is, unfortunately, one of those ...
1
vote
1answer
332 views

Relating Schrödinger's Wave Equation and Heisenberg Uncertainty Principle

A homework question that I don't conceptually understand: A quantum particle of mass M is trapped inside an infinite, one-dimensional square well of width $L$. If we were to solve Schrodinger's wave ...
0
votes
2answers
432 views

Schrödinger's Equation and the depth of a finite potential well

Before I ask my question, I have to stress: I have absolutely no idea what the math is going on. I've read my textbook, several Wikipedia articles, scoured the internet, and don't feel anymore ...
0
votes
2answers
82 views

Sign of Potential Energy

The mass is released at height $h$ above the spring, how far will the spring move? $E_i=mgh, E_f= kx^2/2+mgx$...why the second equation isn't $ E_f= kx^2/2-mgx$? Since it is below the "zero".
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1answer
69 views

Electric Potential Energy

When work is done on a positive test charge by an external force to move it from one location to another, does the potential energy increases or decreases, and does the electric potential increases or ...
7
votes
2answers
516 views

Infinite and Finite Square Wells

For the infinite square well in the first region, outside the well: $$\frac{-\hbar^2}{2m}\frac{d^2 \psi}{dx^2} + V(x) \psi (x) = E \psi (x),$$ where you set $V = 0$. Rearranging gives $$\frac{d^2 ...
5
votes
4answers
2k views

How electron movement produces current,instead of having a slow drift speed

Just need a clarification here, how the current is produced due to the movement of electrons, in an external circuit,having a very slow drift speed. Normally in a battery there is high potential ...
4
votes
2answers
95 views

Definition of quantum anharmonicity

I have been reading research papers in mathematical physics for some months now, and I've seen the the term "anharmonic oscillator" quite frequently. At first I assumed that given a Schrodinger ...
0
votes
0answers
42 views

Scalar potential in em field task

(Sorry for my English) Task. There is a volume with some arbitrary current or voltage source connected to wires. One wire is buried in the ground. I know values of electric and magnetic fields in ...
0
votes
1answer
104 views

Question related to Equipotential Surface

How will you show that equipotential surface is always directed perpendicular to electric field?
3
votes
1answer
81 views

Intuitive explanation of difference in $r$-dependence between dipole and monopole

For an electric monopole, its potential scales with $\frac{1}{r}$, where $r$ is the distance from the point of interest to the charge. However, for a dipole, its potential scales with $\frac{1}{r^2}$. ...
1
vote
0answers
104 views

Particle in a higher-dimensional box with an attractive delta potential

Suppose you have a particle in the box $[0,L]^d$, with an attractive Dirac delta potential $-\delta_{\vec w}(x)$ at $\vec w$. How do you solve the Schroedinger equation for this system? In the case ...
0
votes
1answer
222 views

Electrical Potential Energy and Electric Force [closed]

Under certain circumstances, potassium ions $(K+)$ move across the $8.0 nm$ thick cell membrane from the inside to the outside. The potential inside the cell is $−70 mV$ and the potential outside is ...
2
votes
0answers
139 views

Understanding the algebra associated with an implicit potential

In the paper here(page 7-8) the authors make a claim that the Natanzon potential (an implicit potential) follows an $SO(2,2)$ algebra. This potential defined as : $$ U(z(r)) = ...
1
vote
4answers
311 views

Electric potential and maximum charge on a conductor

Does increasing the amount of electric charge on a conductor cause an increase in its electric potential to a point at which it becomes maximum; where it can hold no more extra charge? Is it true? ...
0
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0answers
12 views

How are the triangular Lagrange points in a Three body Problem stable, yet having a higher effective potential? [duplicate]

Stability usually favours lower potential. Yet the triangular L -points (lagrange points) L4 and L5 are stable, having higher effective potential than the other collinear L points (L1,L2,L3)
0
votes
1answer
82 views

Increasing potential in a voltage doubler

When I use a sinusoidal input AC-voltage from -1 Volt to +1 V , the potential between the diode and the capacitor is increasing. But why do I reach a value of 2 Volt over the diode? I deliberately ...
3
votes
1answer
158 views

In a positively biased PN junction, where do the injection carriers come from?

I am not quite understand i-v character of PN-junction diode. Here is the model in textbook. The PN junction diode can be divided into three regions. They are One depletion region near the PN ...
2
votes
2answers
440 views

Solving quantum radial equation for infinite potential spherical annulus for $l=0$

There is a mass $m$ in a potential such that $$ V(r) = \left\{ \begin{array}{lr} 0, & a \leq r \leq b\\ \infty, & \text{everywhere else} \end{array} \right. $$ ...
3
votes
1answer
168 views

Transmission + Reflection coefficients >1 For Potencial Barrier with Negative Complex Part Contradicts Paper

I am studying reflection and transmission coefficients for a barrier consisting of a a step potencial defined by: $$V(x):=\begin{cases}0&{\rm if}\,|x|>a/2 \\ V_0+iW_0 & {\rm ...
0
votes
1answer
184 views

Infinite potential square well solutions

My question is about understanding the different solutions of the potential square well. Imagine a square well defined this way: $$ V(x) = \begin{cases} ∞&\,{\rm if} x<0 \\ 0&\,{\rm ...
0
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0answers
43 views

dispersion relation in presence of a potential

Let there be a particle in a step potential: if its energy $E$ is higher than the step $V_0$, then it will have the momentum $\sqrt{2m(E-V_0)}$ and no more $\sqrt{2mE}$. (See ...
3
votes
3answers
200 views

Bound States clarification

Our professor hasn't explained what bound states are. Could you give me an idea of what they mean and their importance in quantum-mechanics problems with potential (e.g. a potential described by a ...
3
votes
2answers
706 views

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 ...
2
votes
1answer
222 views

Energy and time evolution of a particle in a potential well

Hoping this is not a silly and stupid question let me ask for help in this problem. I have a particle in an infinite square well (the box is from 0 to a), in the state described by the function ...
0
votes
0answers
412 views

Vector and scalar potentials of plane wave

Consider a simplest 3D solution of Maxwell's equations: $$\vec B=\vec e_z \cos\left(\frac{2\pi}{\lambda}(ct-x)\right),$$ $$\vec E=\vec e_y\cos\left(\frac{2\pi}{\lambda}(ct-x)\right),$$ and ...
5
votes
1answer
127 views

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 ...
2
votes
2answers
239 views

Wave function for an electron in and around a small charged sphere

I am interested in solutions of the Schroedinger equation. For simplicity I started my studies with the $n=1$ ground state of the hydrogen atom. I was particularly interested in the higher moments of ...
0
votes
2answers
358 views

Detecting the presence of a delta potential

Suppose you have a particle in a box, and there may or may not be a Dirac delta potential somewhere in the box. How could one detect whether or not the potential is present? Furthermore: If there's ...
0
votes
1answer
239 views

Integers, Energy levels, and wavenumbers for a particle in a 2D box

(This question is not about coding) I have built a little code in Python that allows the user to plot the energy vs the wave number of particle in a 2D box, depending on what values for the integers ...
1
vote
0answers
65 views

What is a potential in De-Broglie-Bohm theory?

As I have so far understood, the De-Broglie-Bohm theory is based on two equations: The Schrödinger equation. The Guiding equation of the De-Broglie-Bohm theory. In the Schrödinger equation (as ...
0
votes
1answer
59 views

A question about electric field

I would like to understand why is it the charge density while dealing with currents is $\mathop{\mathrm{div}}(E)/4\pi$, while when dealing with insulators is $-\mathop{\mathrm{div}}(E)/4\pi$? Thank ...
0
votes
1answer
143 views

Electrical potential difference?

What is the electrical potential difference and why we have to talk about a difference and not about the electrical potential itself? What is the electrical potential difference in practical terms ...
0
votes
2answers
134 views

Are $G$, $F$ and $H$ (thermodynamics potentials) extensive quantities?

Internal energy $E$ is an extensive quantity for most systems. But energy extensivity is not valid in systems with long-range interactions, like gravity (e.g. in astrophysical systems). For extensive ...
4
votes
1answer
142 views

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. ...