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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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 ...
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1answer
18 views

Circular Orbit in a spherical potential

If we some point mass of mass $M$, in a spherical potential given by $$\Phi(R,z) = \frac{GM}{R},$$ then under what condition would we get a circular orbit, supposing our initial radius from a central ...
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1answer
76 views

Relation between gravitational field and gravitational potential

The gravitational field is the negative differential of the gravitational potential. Now the gravitational potential due to a particle at a distance $r$ is $-Gm/r$ where $m$ is the mass of the ...
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1answer
24 views

Numerical calculation of electric field in dielectric medium

I want to numerically calculate the electric field between two parallel plates with finite length. Where parallel plates are connected to source of constant potential difference: I have boundary ...
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0answers
17 views

Electric octupole moment in cartesian coordinates

I'm trying to calculate the symmetric traceless tensor for the octupole moment in cartesian coordinates... I have to deal with the electrostatic potential of the form: $\Phi^{(4)}(\textbf{r})=\int d^{...
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1answer
180 views

Potential function - numerical simulation

Using MATLAB, I fixed the potential in a region inside a rectangular plate (100 V) and in the border (50 V). I got the following result of the potential along the plate: I can't find an intuitive ...
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2answers
236 views

Scalar and Vector Potential

I am a physics undergraduate student currently studying electromagnetics. I have previously studied electrostatics and magnetostatics yet the concept of scalar potential, $V$ and the vector potential, ...
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4answers
681 views

Increasing a potential causes increase in energy levels

Suppose a potential $V(x)$, and suppose a bound particle so the allowed energy levels are discrete. Suppose a second potential $\widetilde{V}(x)$ such that $\widetilde{V}(x) \geq V(x)$ for all $x$ (...
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1answer
44 views

Quantization of energy in semi-infinite well

Consider an electron with total energy $E>V_2$ in a potential with $$V(x)= \begin{cases} \infty & x< 0 \\ V_1 & 0< x< L \\ V_2 & x>L \end{cases} $$ ...
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1answer
538 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 ...
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1answer
45 views

Why is the energy shift due to a 'sagging' potential negative and independent of box size?

Consider a box of width $L$ and the composed of the following potential $$V(x)=\frac{V_0x(x-L)}{L^2}, x\in[0,L]$$ and $V(x)=\infty$ elsewhere. Using perturbation theory - with a square box as the ...
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1answer
63 views

Schrödinger's Equation with multi-part potential

I have this potential $$V(x) = \left\{ \begin{array}{ll} \infty & \mbox{if } x < -a \\ \frac{V_o}{a}x & \mbox{if } -a \leq x \leq a \\ V_o & \mbox{if } x \geq a \ \end{...
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2answers
336 views

Why not use the magnetic scalar potential?

In electricity and magnetism, we use the scalar potential to derive the electric field and the vector potential to derive the magnetic field because $\nabla\cdot B=0$ and $\nabla\times E=0$. I was ...
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1answer
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Potential Difference

Ohm's law: $$V=IR$$ Here $I$ is the current in the circuit, which is equal to charge flowing per unit time. $R$ is the resistance offered. $V$ is potential difference. What's the physical ...
7
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1answer
911 views

Child-Langmuir space charge law for non-zero cathode potential (non-zero initial electron velocity)

I'm trying to reconcile some conflicting results that I've found in publications that address the idea of the current in a vacuum diode in the case where the cathode has a non-zero potential, in other ...
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1answer
48 views

Questions About Quantum Delta Function Potentials [closed]

I didn't think that it would be possible for a wave function to get through the delta function because there is no "leakage" of the wave function through an infinite potential barrier. I can ...
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0answers
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Insulating cylinder with charge in a uniform electric field

Suppose that we have a very long insulating cylinder of radius $R$ on which we have placed some electrons such that it has a constant $\sigma_0$ charge per unit length. Assume that we then apply a ...
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1answer
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Potential and Field for a sphere with a central core of differing density [closed]

A spherically symmetric planet of radius $a$ consists of a central core of radius $b(<a)$ of uniform density $\rho_1$ surrounded by an outer region of uniform density $\rho_2$. Obtain an expression ...
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1answer
297 views

Dielectric sphere placed in another dielectric medium with uniform external field: is there a surface charge density?

Consider a dielectric sphere placed within a dielctric medium. There is a uniform electric field $E_0$ present throughout in the medium. Would there be surface charge on the sphere?
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1answer
311 views

Semi-infinite / Asymmetric potential well

I'm asked to come up with an ansatz and solve for the coefficients of a asymmetric infinite potential well, where: $$ V = \begin{cases} \infty \text{ for } x< 0 \\ V_0 \text{ for } 0 \leq x \leq L ...
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3answers
82 views

Spherical Conducting Shells, Potential

When we have a spherical conducting shell and charge on outer surface of the shell then the potential inside remains constant i.e, kQ/R (R=radius). But say the inner surface of the shell is charged ...
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1answer
110 views

Tricky particle in an infinite potential well question

For a particle in an infinite square-well potential in an energy eigenstate, the probability distribution relating to outcomes of position measurements vanishes outside the square well and takes a ...
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1answer
19 views

Connected and disconnected conductors spheres

I have an exercise in which I have the following situation: there are two conductors spheres (far apart) both of a given radius (R1, R2=2R1). The lesser sphere has a positive charge q and the other ...
2
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1answer
25 views

Is potential difference the difference in electric potential energy or electric potential?

Referencing the book Physics for Scientist and Engineers, Ninth Edition, the book says that "Potential Difference should not be confused with Difference in Potential Energy." I also reviewed several ...
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1answer
473 views

Is there any potential associated with magnetism

Can anybody please tell me if magnetism is a conservative force or if there is a field associated with it? How to reason? One thing I know is that the work done by a magnetic force is equal to $0$.
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2answers
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Why does there have to be an electric field if there is potential difference?

I read in a few books that there is always an electric field if there is an electric potential. I went through this but the question on this page only states that there is an electric field and it is ...
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0answers
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Doubt regarding scattering and bound states in quantum mechanics

I just started studying quantum mechanics from Introduction to Quantum Mechanics by D. J. Griffiths. At the beginning of the second chapter, he proves that we cannot have negative energies in the time-...
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1answer
225 views

How can energy be negative in a finite square well?

Say if the potential $V(x) < 0$ in the well but the sides or the scattered states its zero potential, anyways How is that the energy in the well is less than zero? Is it because the potential ...
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2answers
116 views

Ignoring constant potential energy

The reason why constant potential energy terms are dropped is because the derivative of a constant is zero. And since force is the gradient of potential energy, constant terms won't change what the ...
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2answers
384 views

Infinite square well that suddenly decreases in size

A well known exercise in basic quantum mechanics is the sudden (diabatic) increase of the length of an infinite square well. Now consider a particle in an eigenstate of an infinite well that is ...
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1answer
42 views

Electric potential in a wire

I am slightly confused on the physics of direct electric circuits. Here is what I have been taught: Batteries (sources of emf) provide a constant potential difference between its terminals; ...
0
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1answer
39 views

Quadrupole moment of point charges?

We know that due to expansion, the Quadrupole potential equals $$1/4\pi \epsilon r^3 . \int (r^\prime)^2(\frac32. \cos^2\theta^\prime-\frac12)\rho(r^\prime)d\tau$$ but what is the equation for point ...
7
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1answer
165 views

From Liénard-Wiechert to Feynman potential expression

When studying the potential of an uniformly moving charge in vacuum, Feynman proposes to apply a Lorentz transformation on the Coulomb potential, which reads in the rest frame $ \phi'(\mathbf r',t') =...
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1answer
49 views

Maximum Angular Momentum for an orbit in GR

[The reference for this question is the book Gravitation by Misner,Thorne, & Wheeler.] The trajectories of massive particles around a spherically symmetric body is governed by the effective ...
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1answer
495 views

Dirac Delta Potential and bound/scattered states

Why does the attractive Dirac Delta distribution (function) potential $V = \alpha\delta$(x) (for negative $\alpha$) yield both bound AND scattered states? Is this due to the definition of the Dirac ...
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1answer
127 views

What's my $\mathrm dM$? 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: $$\Phi=\...
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1answer
48 views

Do energy levels such as $E_c$, $E_v$ have negative values in semiconductors?

In energy band diagram of a semiconductor, do energy levels such as $E_c$, $E_v$ have negative values? Also, why electrons in semiconductor have energy? What is the formula for energy of an ...
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1answer
225 views

Explain confinement energy for a particle in a box

What is a "particle in a box"? How does confinement energy equal kinetic energy? How does confinement energy relate to the spectrum energy (the absortion/emission between energy)?
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2answers
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Why does a electric Potential have to be real, but not a Potential in quantum mechanics?

So I had this Problem when I had to learn about classical electromagnetism: Why is it, that we use complex numbers when calculating stuff, but in the end only the real part is important (for example ...
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3answers
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When Eigenfunctions/Wavefunctions are real?

When the Hamiltonian is Hermitian(i,e. beyond the effective mass approximation), generally under which conditions the eigenfunctions/wavefunctions are real? What happens in 1D case like the finite ...
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2answers
886 views

How does symmetry allow a rapid determination of the current between $A$ and $B$?

The following was originally given to me as a homework question at my physics 2 course: Consider the following circuit The difference of potentials between the point $V_{1}$and the ...
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1answer
175 views

Introducing cut-off in a renormalisation procedure for quantum mechanics

I've been reading a paper on renormalisation theory as applied to a simple one-particle Coulombic system with a short-range potential. In the process of renormalisation, the authors introduce an ...
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6answers
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Why is the electric field perpendicular to every point on the surface of a conductor?

I am reading Berkeley Physics Course, Volume 2 (Electricity and Magnetism by Edward M. Purcell). I am in chapter $3$, page $92$, and the book discusses conductors. The following is from the book: ...
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1answer
61 views

Solution for Schrödinger equation for constant box potential?

It is known that in a box potential, when we set $V = 0$ inside and $V = \infty$ on the boundaries, the solution to the equation $$ - \frac{\hbar}{2m} \bigg( \frac{\partial^2}{\partial x^2} + \frac{ \...
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2answers
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Potential difference between two assymetrically charged plates

What is the potential diff between two plates of charges $q_1$ and $q_2$ ($q_1$ $>$ $q_2$)? I know the equation is $V = \frac{q_1-q_2}{2C}$ where $C$ is the capacitance of the system but how has ...
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1answer
29 views

Electrical gradient

I'm a zoology minor and I'm trying to understand electrical gradient. I found this explanation in an authentic website but cannot undertand it fully. An unequal distribution of charges across the ...
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Why do we like gauge potentials so much?

Today I read articles and texts about Dirac monopoles and I have been wondering about the insistence on gauge potentials. Why do they seem (or why are they) so important to create a theory about ...
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1answer
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Lagrangian in a system with a specific velocity dependent potential

I have a system of a particle moving under the generalized central potential $$ V= \frac{1}{r}(1+\dot{r}^2) \tag{1} $$ The general Euler-Lagrange equations for such type of potentials are: $$ \frac{...
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Does the mass of a brick increase when you lift it? [duplicate]

If a person takes a brick, and lifts it to a height of 1 m, will the mass of the brick increase?
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1answer
97 views

Deriving the Lienard-Wiechert Potentials

Let $\mathbf{w}(t)$ be the trajectory of a moving charge. Let the observation event be $(\mathbf{r},t)$. The scalar potential is: $$\varphi = \frac{q}{4\pi\epsilon_0}\int \frac{\delta\left(\mathbf{r'...