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2
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2answers
1k views

How is capacitance defined for three concentric spheres?

If we have a configuration of metal concentric spheres (each of negligible thickness) of radii $r_1,r_2,r_3$ respectively and $r_1<r_2<r_3$, and we are given the potentials of the spheres to be ...
1
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1answer
70 views

Potential at a point

What is the electric dipole moment of the charge distribution with $q$ at $(0,0,1)$, $q$ at $(0,0,-1)$ and $-2q$ at $(0,0,0)$? I would think that it is $\vec{0}$ by the definition ...
-1
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2answers
185 views

Show that the energy levels of a particle in a specific potential are $E_n=(n+\frac{1}{2})h\omega-\frac{1}{2}\frac{F^2}{m\omega^2}$ [closed]

A particle of mass m moves on the x-axis under the influence of the potential $$V(x)=\frac{1}{2}m\omega^2x^2+Fx$$ Can anyone help me, using Schrödinger's equation in one dimension that the energy ...
2
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2answers
186 views

Differences In Potential Equations

Could someone please describe the differences between the uses each of these potential equations: Potential due to a point charge: $V = \frac{k \cdot q}{r} - \frac{k \cdot ...
2
votes
4answers
1k views

How does instant charging of one plate affect the potential of the other plate of a floating capacitor?

If I have an uncharged floating capacitor and I instantaneously connect one plate to some potential, then that plate will acquire some charge. In practice, the other floating plate will ...
3
votes
0answers
194 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, ...
2
votes
1answer
243 views

Complex Potentials, Potentials and Fields

Suppose an electric field $E=-\nabla \psi$ where $\psi=-Q\ln r$ where $Q$ is just some constant and I have found its harmonic conjugate to be $-Q\theta+c$ where $c$ is some constant. What does it say ...
0
votes
2answers
971 views

How to calculate the electric field at a point in space

Let's say I have a uniformly-charged wire bent into a semi-circle around the origin. How can I find the electric field (magnitude and direction) I'm not even sure if I should use Coulomb's or Gauss' ...
3
votes
3answers
470 views

About constructing potential energy functions

There are many classical systems with different potential functions. My problem is that I do not understand how one can construct a certain potential function for a certain system. Are there any ...
2
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1answer
216 views

Infinite quantum well width $L$ to $2L$ adiabatic process

If we change width of the infinite quantum well $L$ to $2L$ slowly enough, how it does change energy levels.
2
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1answer
1k views

How to calculate time evolution of a wave function in an 1D infinite square well potential?

A particle in an infinite square well has an initial wavefunction $$\psi (x,0) ~=~ Ax(a-x) \qquad \mathrm{for}\qquad 0\leq x\leq a.$$ Now the question is to calculate $\psi (x,t)$. I have ...
1
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1answer
315 views

A quantum particle in a box (with a catch)

I am reading Shankar's Quantum Mechanics and I am looking at the case where there is one particle inside a box, where the potential is zero inside the wall and abruptly goes to infinity outside the ...
2
votes
2answers
545 views

Why do two ends of a long conducting wire have the same electric potential?

I am not seeing the "big picture" here. If I have two conducting spheres separated by a long conducting wire, why would the spheres share the same electric potential? I think of the spheres as point ...
1
vote
1answer
4k views

Current against the inverse of resistance graph, $I = V/R +c$

If I have a plot of current ($y$ axis) against 1/Resistance ($x$ axis). The circuit it is measured from is a simply 2 resistors connected in parallel to battery, where the potential across the ...
3
votes
1answer
666 views

Time-Dependent Potentials in Quantum Mechanics

A potential that depends on time is usually solved using the time dependent perturbation theory in standard undergraduate textbooks in quantum mechanics. The reason usually mentioned is that time ...
1
vote
2answers
134 views

Equivalence between Differential Geometry and Mechanics?

Given a metric $$ ds^{2}~=~ g_{a,b}dx^{a}dx^{b}. $$ Here Einstein's summation convention is assumed for $a$ and $b$. Then given the Laplacian over that metric, can then we find a metric $ ...
4
votes
3answers
4k views

Force as gradient of scalar potential energy

My text book reads If a particle is acted upon by the forces which are conservative; that is, if the forces are derivable from a scalar potential energy function in manner $ F=-\nabla V $. I ...
3
votes
2answers
234 views

Alternative definitions of potential?

I hope this question is simple and can be quickly cleared up. In a 1D conservative dynamical system, I've always been taught that the potential function is the function $V(x)$ such that: ...
1
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2answers
1k views

If electric charges accelerate towards lower potential energies, why do opposite charges attract?

I know my logic must be wrong but I can't figure out why. I know that charges must accelerate towards lower potential energies simply because that's a general rule of nature. However, when you release ...
2
votes
2answers
1k views

What is the potential difference between point X and point Y?

Here is the problem: In the above figure I want help on finding the potential difference between X and Y. It is getting quite confusing due to the battery in the middle. I found the current in both ...
9
votes
2answers
343 views

Motivation for Potentials

This is a hypothetical question about "pedagogy". Let's say I am trying to take someone who has just a very small amount of knowledge about Newtonian mechanics and convince them that the Lagrangian ...
11
votes
8answers
9k views

What is the difference between electric potential, potential difference (PD), voltage and electromotive force (EMF)?

This is a confused part ever since I started learning electricity. What is the difference between electric potential, potential difference (PD), voltage and electromotive force (EMF)? All of them have ...
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4answers
4k views

What is the electric potential at a point?

1) What does the electric potential at a point exactly mean? My teacher tells me that current flows from higher potential to lower potential but when I ask him the reason, he fails to give me a ...
23
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4answers
1k views

In quantum mechanics, given certain energy spectrum can one generate the corresponding potential?

A typical problem in quantum mechanics is to calculate the spectrum that corresponds to a given potential. Is there a one to one correspondence between the potential and its spectrum? If the ...
17
votes
6answers
1k views

Why can we treat quantum scattering problems as time-independent?

From what I remember in my undergraduate quantum mechanics class, we treated scattering of non-relativistic particles from a static potential like this: Solve the time-independent Schrodinger ...
3
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2answers
530 views

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 ...