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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Feynman's explanation of virtual work given in his book Feynman's lectures on Physics

In his book Chapter 4 Conservation of Energy, on Gravitational potential energy the discussion goes... "Take now the somewhat more complicated example shown in Fig. 4-6. A rod or bar, 8 feet long, ...
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Electric Potential produced by Hollow Sphere

Let there be a hollow sphere (Throughout the question we will ignore the thickness of the sphere) which is positively uniformly charged,q of radius, R. Suppose there to be a test positive charge, q' ...
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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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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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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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Sturm Liouville potential [on hold]

How to determine the potential function of a Hamiltonian, given by a general second order differential equation using the Sturm-Liouville theory? Of course, any other approach is also appreciated. ...
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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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Transformer primary and secondary coil current problem [closed]

A step up transformer has 300 turns on its primary coil and 90,000 turns on its secondary coil. The potential difference of the generator to which the primary circuit is attached if 60 V. The ...
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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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187 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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217 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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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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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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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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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
74 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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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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170 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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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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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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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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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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628 views

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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295 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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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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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'...
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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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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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How does voltage produce current?

I am studying electric current and i dont understand how does voltage(potential difference )produce current? PS : I am a 10th grade student so please avoid complicated terminologies.
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291 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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Wavefunction of electron in 3D infinite well with non-zero potential

Consider an electron moving in a potential $V$ defined by $$V(x,y,z) = \left \{ \begin{array}{ll} \alpha(x^2 + y^2) & 0 \leq z \leq a \\ \infty & \text{otherwise} \end{array} \right. $$ ...
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Degeneracy in one dimension

I'm reading this wikipedia article and I'm trying to understand the proof under "Degeneracy in One Dimension". Here's what it says: Considering a one-dimensional quantum system in a potential $V(...
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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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why potential becomes equal when capacitor are connected

If we have a circuit as shown in which two capacitor are connected of unequal potential. Now if we close the switch the charge will flow till potential becomes equal. But as we know $Q=CV$, $V=Ed$...
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Final potential difference between plates of capacitor [closed]

If the plates of a parallel plate capacitor are given charges 4Q and -2Q . The capacitor is then connected across an uncharged capacitor of the same capacitance as first one (=C) . Now we have to find ...
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As distance increase why no change in electric field in parallel plate condenser [duplicate]

If the distance between the plates of a parallel condensor is 4mm and the potential difference is 60 volts. Now if we increase the distance between the plates to 12mm, then: Why the electric field ...
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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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Can someone explain me magnetic potential? [duplicate]

I don't understand why we can write the magnetic field as a potential vector A, and what exactly this potential is. Is it just a mathematical thing? And how can it help me calculate the magnetic ...
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How to Explain the the following situation?

I have thought a simple thing: consider a system of a planet and its natural satellite revolving around it in a perfectly circular orbit(assumed) and this is happening in an isolated space in some ...
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The Zero Electric Potential of the “Earth”

I know its the potential differences that matter and generally we define the zero of the electric potential according to our convenience. I would like you to look at this standard problem: Charge $-...
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Electric potential due to something

What is the diffrence between "electric potential at some point due something" and "electric potential of something" ?
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Determine potential function given initial conditions?

Assuming a radially symmetric circular disk (let's say r=1). Given two simple initial conditions: Potential at the centre is 4 V Potential at the edges is 0 V How would I determine the potential ...
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Why electric potential at equatorial point of a dipole is 0?

Well ok I know that electric potential at equatorial point of a dipole is 0. It is a derived conclusion. Q1. But how this can be explained "theoretically"? Another question that electric potential ...
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What does a voltmeter actually measure?

For time varying fields (even quasistatic ones) the electric field is given by $${\bf E} = - \nabla \Phi - \frac{\partial {\bf A}}{\partial t}$$ So what does a voltmeter measure? Does it measure a ...
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Why do we use gauges in Maxwell equation?

While solving the Maxwell's equation we often use the Lorenz or Coulomb gauge, but why is that? Are the equations unsolvable if the gauge is not fixed? Or is it just for the simplicity?
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why does the Lennard-Jones potential fail to accurately describe forces between simple molecules, eg ammonia?

I have found only one reason, this being polarisation isn't accounted for. See for example this PDF - it is in the middle of the second paragraph, first page. What other reasons lead to the failure ...
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Under what condition is angular momentum conserved in both classical and quantum physics?

Classically, angular momentum is only conserved in a central potential by considering the torque (correct me if I am wrong). In quantum mechanics, it is also true, isn't it? If this is the case, ...
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Grounding system of conducting plates

So, I always make mistakes on problems such as this (the grounding part), so I'm hoping someone could really explain to me how the process works . There are n large parallel plate conductors carrying ...