The potential tag has no wiki summary.
2
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1answer
424 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 ...
0
votes
1answer
55 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
votes
2answers
140 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
votes
2answers
138 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
712 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
116 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, ...
0
votes
1answer
80 views
How to calculate the potential of the ball? [closed]
Consider 2 metals ,the smaller sphere has a radius of a carry +Q charges,what is the potential at the surface of the smaller sphere?
1
vote
1answer
144 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
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2answers
654 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
316 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
votes
1answer
130 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
votes
1answer
762 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
vote
1answer
240 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
358 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
2k 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 ...
1
vote
2answers
123 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
2k 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
212 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
vote
2answers
586 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
699 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
216 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 ...
8
votes
8answers
3k views
What is the difference between electric potential, voltage and electromotive force?
This is a confused part ever since I started learning electricity. What is the difference between voltage and electromotive force (emf)? Both of them have the same SI unit, right? I would appreciate ...
20
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4answers
756 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 ...
14
votes
6answers
950 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 ...
