Scalar and vector potentials in electromagnetism. The scalar potential is potential energy per unit charge. For potential energy, use the potential-energy tag.

learn more… | top users | synonyms

1
vote
0answers
30 views

Condition on $U_{eff}$ for a mass to get trapped in orbit around a heavier mass

this question is now solved, and I have already edited the wikipedia page The wikipedia page on Effective Gravitational Potential states that $$U_{eff} \leq E$$ is a condition for a free mass getting ...
0
votes
3answers
48 views

Can we have negative Electrostatic potential

What does it mean to have a negative electric potential? not talking about potential difference or voltage.
0
votes
1answer
37 views

What's my $dM$? Gravitational Potential inside a circle of mass

I'm trying to find the gravitational potential for an arbitrary point within a ring of uniform mass density. The point is constrained to be in the same plane as the ring. So we start with: ...
2
votes
1answer
38 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 ...
0
votes
0answers
21 views

Deriving the Force on an ion in the Classical Harmonic Crystal

I was following Solid State Physics by Ashcroft and Memrmin and their introduction to the Classical Theory of the Harmonic Crystal. (Chapter 22) If there are a large number of ions in a straight ...
0
votes
1answer
29 views

Does the electric field inside a circuit cause a potential drop with distance?

We know that when the system reaches steady-state(current does not change with time),the electric filed inside the circuit is constant. In many textbooks and lectures,professors make a graph like this ...
0
votes
1answer
49 views

Why do resistors always cause a voltage drop equal to the voltage of the battery

Consider a wire connected to a battery. Now,potential is analogous to the energy of the particles.And potential in a resistor drops because of the friction inside the resistor(considering there is no ...
2
votes
1answer
55 views

Why doesn't the potential drop as a $E=\nabla V$ inside a circuit when there is no resistor?

Considering that an electric field exists outside a battery and inside a circuit, shouldn't the potential drop while we move along the wire even if there is no resistor ($E=\nabla V$)? I am asking ...
2
votes
2answers
61 views

Classical Hall effect when current has neutral charge

Suppose I have a current of both negative and positive charges(I know that there is also current from only negative and only positive charges,I'm not confused) along an infinite wire of square ...
3
votes
6answers
654 views

Is electromagnetic vector field a sum of E and B?

I have a hard time to fully understand (classical) electromagnetic field theory with respect to Helmholtz's decomposition. Let me start from Helmholtz's theorem: Any vector field of class ...
1
vote
1answer
112 views
+50

Eigenvalues of the radial Schrödinger equation on a finite integration interval

There are numerous ways to estimate the eigenvalues of a radial Schrödinger equation, see http://arxiv.org/abs/math-ph/0703040 as an example. Anyhow, the formulas only cover the Schrödinger equations ...
0
votes
1answer
27 views

Which is the right sign convention for the potential difference?

The circulation of the electric field gives the potential difference, but is it : $$V_B-V_A = \int_A^B\vec{E}.\vec{dOM} \hspace{1.5cm} (1)$$ or $$V_B-V_A = - \int_A^B\vec{E}.\vec{dOM} \hspace{1cm} ...
1
vote
1answer
56 views

Potential difference between Earth's surface and 2 meters above

Assuming Earth is a charged sphere of radius $R = 6400\times10^3$ m with uniform surface charge density $\sigma = -10^{-9}$ C/m2 and with $\epsilon_0 = 8.85\times10^{-12}$ F/m I find that ...
6
votes
2answers
109 views

Triangular barrier in infinite potential well

Suppose I am looking to solve the wavefunction for the following 1D potential: $$U(x) = \begin{cases}V_0\frac{a-|x|}{a}&\quad\text{for}\quad|x|<a ...
0
votes
0answers
31 views

What justification is necessary for convolutional variational principles to be considered legitimate?

I recently asked a related question and was interested in why/or why we cannot use convolutional variational principles in practice or in theory. Summarizing the points I made in the earlier post: ...
0
votes
0answers
30 views

Is it possible to get the (Pauli) repulsive term in the Lennard-Jones potential from theoretical considerations?

Title says it: Is it possible to get the form of the (Pauli) repulsive term in the Lennard-Jones potential from theoretical considerations, or is it purely found experimentally through fits?
0
votes
1answer
30 views

potential inside a cylindrical shell in terms of the surface potential?

Given a potential distribution $V(\phi)$ at the surface of an infinite cylindrical shell, is there an easy way to derive the potential inside the cylinder. No charges or currents anywhere.
3
votes
2answers
140 views

How to formulate variational principles (Lagrangian/Hamiltonian) for nonlinear, dissipative or initial value problems?

Although this questions is very much math related, I posted it in Physics since it is related to variational (Lagrangian/Hamiltonian) principles for dynamical systems. If I should migrate this ...
0
votes
1answer
49 views

Fermions in a well

I have two identical fermions in an infinite potential well. They are non-interacting. How should I show that the first excited state is four-fold degenerate? Is the wavefunction just the ...
0
votes
1answer
17 views
0
votes
2answers
51 views

What is the purpose of knowing the value of ground state energy of a potential well?

Using the formula $$E ~=~ \frac{\pi^2\hbar^2}{2 m a^2}$$ where $a$ is the length of an infinite potential well. It is apparent that as $a$ get smaller i.e. from a metal to the size of an atom, the ...
0
votes
0answers
38 views

Potential difference and voltage

Is potential difference between two points the voltage? (or) Is voltage the potential difference between two points? (or) Are they both the same?
0
votes
1answer
30 views

What's the Relation between Potential of mechanics and electricity?

As we know that for a conservative force field, there is associated a Potential with the force. But we know there is a potential in electricity (That's voltage). My question is that is there any ...
1
vote
2answers
48 views

What kind of potentials can be used in Schrödinger's equation?

I have a couple of questions about what kind of potentials can be used in Schrödinger's equation: How about the potential from a magnetic field? Isn't Dirac's equation more appropriate in that case, ...
2
votes
0answers
36 views

Asymptotic Analysis of 1-D Schrödinger Equation [closed]

I'm looking to do a small personal project regarding the time independent Schrödinger equation in 1-D: $$y'' +V(x)y=Ey$$ $$y''=Q(x)y$$ where $ Q(x):=E-V(x) $. There is obviously nothing stopping ...
0
votes
0answers
35 views

How would you define a difference in potential?

I'm currently in 12th grade, and am required to write an essay about physics and biology. The topic of the essay is the artificial brain (with the researches of the Human Brain Project in Switzerland ...
0
votes
2answers
33 views

Is work needed to bring a test charge from a higher potential to a lower potential?

I don't understand whether work is needed to bring a test charge from a higher potential to a lower potential. It seems that no work is needed because the positive test charge will be under the ...
0
votes
0answers
34 views

Why does charge build up at the boundary surface of two media?

On a homework problem, we are asked to to use the first two Maxwell equations, $$\nabla\cdot \mathbf{B} = 0$$ $$\nabla \cdot \mathbf{D} = \rho$$ to show that along the boundary surface of two ...
1
vote
1answer
133 views

Position and momentum expectation values for the stationary states of the infinite square well [closed]

I'm really lost in figuring out how to solve the integral for the expectation value of $x$ and $x^2$ $$\int_0^a x \sin(\frac{n\pi}ax)^2 dx $$ This equation is from the $n$th stationary state ...
1
vote
2answers
41 views

Electrostatics Basic Question

Why ,if we increase the charge on a conductor its potential also increases? That is, Q directly proportional to V. Why ,if an insulated conductor is given some charge it acquires a certain ...
1
vote
2answers
67 views

Using Electric Potential to Float an Object

I've been trying to answer the following question but I'm stuck at one step. The question essentially states that a magician is trying to perform a "floating objects" act, for which she has a thin ...
1
vote
1answer
46 views

Calculating electrostatic potential [closed]

A continuous charge distribution is spherically symmetric and has a volume charge density $$\rho(r) = \rho_oe^{−\alpha r}$$ I need to find the potential as a function of '$r$' i.e. $V(r)$. It seems ...
0
votes
1answer
55 views

How should I interpret the math in showing that the potential difference and the emf in an ideal battery are the same?

I was reading Griffiths' Introduction to Electrodyamics where he says that in order to have the same current through out a circuit there are two force per unit charges acting on the circuit, $f=f_s+E$ ...
0
votes
1answer
30 views

How is the electric potential of a localized charge distribution scaled when scaling the geometry of the problem?

I am trying to find the potential at a point on the surface of a charged polygon (rectangular). I have find a solution to the problem, but it relies on the following statement: If the potential at ...
1
vote
0answers
89 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 ...
0
votes
0answers
39 views

How to compute minimum shallowness of quantum well to have at least one bound state?

Given a potential $V$, how does one compute how shallow the potential can be such that it allows at least one bound state?
2
votes
1answer
49 views

Is there a mathematical explanation for why there occur bound states if the effective potential falls below zero?

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 ...
1
vote
5answers
125 views

Physical interpretation of the statement $\oint E\cdot dl=0$

Can anyone provide me with a physical interpretation of $\oint E\cdot d\ell=0$ in electrostatics?
3
votes
1answer
84 views

Estimate for minimum potential depth required for bound states in 3D attractive potential well

Consider a 3D spherically symmetric potential well, $$H = \frac{p^2}{2m} + V(r)$$ with $V(r) = - V_0$ for $r < a/2$ and $0$ else, for some $V_0 > 0$. Now, it is well known that $V_0$ needs to ...
3
votes
1answer
79 views

Maxwell's Equations, cast in terms of magnetic vector potential [closed]

Derive $$ \nabla \times \frac{1}{\mu_r} \nabla \times A + \mu_0 \sigma \frac{\partial A}{\partial t} + \mu_0 \frac{\partial}{\partial t} \left( \epsilon_0 \epsilon_r \frac{\partial A}{\partial t} - ...
1
vote
1answer
69 views

Realistic Potential Wells

What is meant by the term "realistic" potential wells? I got stuck into the term as I don't know what are the limitations of the word realistic in this case. For example mentioned in line We ...
3
votes
1answer
30 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 ...
0
votes
1answer
35 views

Can you derive reaction rates from the potential difference across a battery?

There were several cases where I was able to (relatively easily) derive potentials for interactions in my statistical mechanics course. I know that there is no real way to derive the kinetics of a ...
1
vote
1answer
49 views

Current in a fluorescent tube that is not in a circuit

In Walter Lewin's 8.02 Electricity and Magnetism course, he places a fluorescent tube pointing radially outwards from a large Van der Graaf (VDG) generator. Due to the VDG's E-field, this causes a ...
2
votes
5answers
205 views

General question about the potential barrier problem: Why does $\exp( kx)$ diverge when $x>0$ in the case when $E < V(x)$?

For the two images below, the first potential barrier has particles approaching it where $E > V_o$ & the second has a particle that has $E < V_o$, where $E$ is the energy of the particles ...
1
vote
1answer
59 views

Induced electric field due to a moving wire

An infinite wire carrying a constant current $I$ in the $\hat{z}$ direction is moving in the $y$ direction at a constant speed $v$. Find the electric field, in the quasistatic approximation, at the ...
0
votes
2answers
63 views

Is electric potential a form of potential energy?

As I understand it, the concept of potential energy arises from analytical mechanics. Yet I often see the concept of electric potential $\phi$ introduced without mention of analytical mechanics. For ...
1
vote
1answer
89 views

Deriving Voltage from Electric Field

I'm trying to derive the point charge equation for voltage by integrating the point charge equation for an electric field over distance ($dr$) traversed:$ \int (KQ/r^2)\cdot dr$ This is my ...
1
vote
1answer
117 views

Need of vector potential in quantum mechanics

I need your opinions. Why is the vector potential of a magnetic field important (or even necessary) to quantum mechanics? Why it has to be defined everywhere? Is there any fundamental reason you can ...
1
vote
1answer
49 views

Allowed energies for semi-harmonic oscillator

Question: If a particle is attached to a semi-harmonic oscillator (that is, for example, the spring is stretchable but not compressible) such that the potential $V(x)$ is infinity for $x\leq0$ and ...