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How is gate-screened Coulomb potential derived?

I've been stuck on the same problem for about three months, and was just able to derive the results. The key is to read Jackson's E&M chapter 3.9 to 3.11 where he talked about how to deal with ...
Yusen Ye's user avatar
2 votes
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Why does the curvature change with respect to the sign of the wave function?

Note the curvature is varying based on the sign of the second derivative. $\kappa=\frac{y''}{(1+y'^2)^{3/2}}$ The sign of the curvature is the sign of the second derivative. So if you have $\frac{-\...
R. Romero's user avatar
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1 vote
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Boundaries of finite potential well

You are correct that this definition of finite potential well is not well-defined. In the best traditions of quantum mechanics boundary condition should be omitted, because particle state at these ...
Agnius Vasiliauskas's user avatar
4 votes
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The Kerr metric applied to a solid rotating body

The Kerr metric strictly only applies to the spacetime of a black hole with spin. There are alternatives for the spacetime around axisymmetric rotating solid bodies. These are approximate solutions to ...
ProfRob's user avatar
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2 votes
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Vector Magnetic Potential and pointwise current density source

The notes I'm following proceed to define the current density as: $$\mathbf{J}=\delta(x)\delta(y)\delta(z)\hat{\mathbf{a}}$$ which I totally agree it only exists at the origin, but my question is: ...
Thomas Fritsch's user avatar
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Sign conventions for the electric potential, the tension and the current

It's clear to me now: I just have to define $$ U_{AB} = \phi_A - \phi_B $$ which is the convection (tension is of course not a vector)
user172501's user avatar
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Sign conventions for the electric potential, the tension and the current

The first thing to note is that neither potential or current are vectors so vector addition does not hold. The next thing is that you have defined $U_{\rm AB} = \phi_{\rm B} - \phi_{\rm A}= 0-(+10) = -...
Farcher's user avatar
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1 vote
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Problem with understanding the definition of electric potential

The electrostatic field is defined as a gradient of a scalar potential: $$\vec E(\vec r)=-\nabla V(\vec r).$$ Thus there is considerable freedom in how one might a scalar potential for any given ...
Albertus Magnus's user avatar
2 votes

Problem with understanding the definition of electric potential

Potential is uniquely defined up to an arbitrary additive constant, so it doesn't matter which starting point you use or the value of the potential at this point. The value of the potential at any ...
Puk's user avatar
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1 vote
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Understanding matrix element calculation in Schwartz (4.18) -- (4.21)

The term you get corresponds to a ‘nothing happens’ process where there’s only one particle propagating, this by definition is not a scattering event thus should be discarded. See this post S-matrix ...
Mmmao 's user avatar
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1 vote
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Sign choice for line element while finding potential due to point charge

Canonical or not, I find the approach you give a bit convoluted. As I see it, the potential, $V(R)$ due to point charge $Q$ at displacement $\mathbf R$ from $Q$ is the amount of work per unit test ...
Philip Wood's user avatar
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Is there no sense of 'absolute' in the universe?

Yes, there is a sense of absolute. The "potential" that has an absolute zero point is the thermal potential, that is the absolute temperature. In an irreversible process the dissipated work $...
hyportnex's user avatar
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1 vote

Is there no sense of 'absolute' in the universe?

After writing an equation involving $dQ$ and $dx$, you write: Mathematically, this also indicates that Q is a function of x . No, it indicates that $dQ$ is a function of $dx$.
WillO's user avatar
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1 vote

Is there no sense of 'absolute' in the universe?

It makes perfect sense to say that the total charge $Q$ along a length of string from $x=0$ to $x=l$ is given by $\displaystyle Q(l) = \int^l_0 \rho_q(x) dx$ And if we want some value of $l$ for which ...
gandalf61's user avatar
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2 votes

Can the potential depend on $\hbar$?

The Coulomb potential: $$ V(r) = \frac 1 {4\pi\epsilon_0} \frac q {r^2} $$ but the fin structure constant is: $$ \alpha=\frac 1 {4\pi\epsilon_0}\frac{e^2}{\hbar c} $$ so: $$ V(r) = \frac{\alpha \hbar ...
JEB's user avatar
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1 vote

Can the potential depend on $\hbar$?

$\hbar$ does not have units of energy and it is a constant so it’s not clear what you mean by “non-constant” part of $V(x)$ but take $$ V(x)=-V_0 e^{-m \omega x^2/\hbar}\, , $$ which depends on powers ...
ZeroTheHero's user avatar
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2 votes
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For these gauge transformations in electromagnetism, $\phi\to \phi-\partial_t \lambda$ and $\vec A\to \vec A+\nabla\lambda$, why do the signs differ?

We already know the 4-position is $x^\mu = (t, \vec{x})$ and the 4-gradient is $$\partial_\mu = \frac{\partial}{\partial x^\mu} = \left(\frac{\partial}{\partial t},\vec{\nabla} \right) \tag{1a}$$ or ...
Thomas Fritsch's user avatar
1 vote

For these gauge transformations in electromagnetism, $\phi\to \phi-\partial_t \lambda$ and $\vec A\to \vec A+\nabla\lambda$, why do the signs differ?

The perhaps underwhelming answer is, it doesn't matter, but you need to stick with the convention that you choose (when raising and lowering indices.) To see why, consider the following thought ...
TLDR's user avatar
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2 votes

For these gauge transformations in electromagnetism, $\phi\to \phi-\partial_t \lambda$ and $\vec A\to \vec A+\nabla\lambda$, why do the signs differ?

This sign comes from the fact that ($g^{00}=+1$ assumed) $$\partial^\mu = \left ( \frac{d~}{dt}, -{\vec \nabla} \right ) \,.$$ You can avoid such issues by using covariant notation throughout.
my2cts's user avatar
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2 votes

For these gauge transformations in electromagnetism, $\phi\to \phi-\partial_t \lambda$ and $\vec A\to \vec A+\nabla\lambda$, why do the signs differ?

Your result is almost correct, you just have two sign errors. Lets start with your transformation (B) and be careful with the signs. The four derivative is defined in such a way, that they have a ...
Eru's user avatar
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0 votes
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Depth of dipole trap

The trap depth is generally a energy, as stated here: https://arxiv.org/abs/physics/9902072 It is the energy difference from a free particle (no trap) to the trap bottom (lowest energy level). The ...
kai90's user avatar
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4 votes
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Magnetic vector potential in 1+1 spacetime dimensions

In 1+1D there is no magnetic field, while the electric field $E=-\partial_x\phi-\partial_tA$ and the magnetic potential $A$ have only 1 component, cf. e.g. my Phys.SE answer here. The 2-vector gauge ...
Qmechanic's user avatar
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4 votes
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Discontinuity in integrand while calculating the electric field of a uniformly charged sphere

The volume factor around the problematic point is is $4\pi |r-r'|^2 d(r-r')$ and the $|r-r'|^2$ cancels against the $1/|r-r'|$ to give a finite integrand.
mike stone's user avatar
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1 vote

Do electrons move faster towards the end of a circuit?

If that circuit is an accelerator beam pipe, then: yes, that's the point. If it's something with plain old resistance, then they loose $IV\tau = 1\,{\rm J}$ of energy to resistive heating, where tau ...
JEB's user avatar
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Does work equal to the amount of energy transported by potential difference?

In physics 'work' is said to be done when force applied on an object results in it's displacement (with positive component of displacement in direction of applied force). Less precisely it's formal ...
Qwerty's user avatar
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Does work equal to the amount of energy transported by potential difference?

A few remarks linked to your numbered statements. Work transfers energy by means of a force moving through a distance in the same direction as the force. Example: a gas at low pressure in one half of ...
Philip Wood's user avatar
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Can the electric potential of any body be calculated using the same formula?

As $$\underbrace{\left(\frac{\partial^2}{\partial x_1^2}+\frac{\partial^2}{\partial x_2^2}+\frac{\partial^2}{\partial x_3^2} \right)}_{=:\Delta} \frac{1}{|\vec{x}-\vec{x}^\prime|}=-4 \pi \delta^{(3)}(\...
Hyperon's user avatar
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3 votes

Is the electromagnetic 4-potential a Lorentz 4-vector in the Coulomb gauge?

but I don't understand how this can say that $A$ isn't a 4-vector Because the four-tuple is defined, in all frames, in such a way that it obeys $$ \nabla\cdot \mathbf A = 0, \varphi=0 $$ (in all ...
Ján Lalinský's user avatar
6 votes

Is the electromagnetic 4-potential a Lorentz 4-vector in the Coulomb gauge?

It's rather that the Coulomb gauge is not Lorentz invariant. If you fix the gauge in a given frame, then if you boost to another frame, the new 4-potential obtained by the Lorentz transformation does ...
LPZ's user avatar
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Will a charge move if it has electric potential but the field is zero?

The absolute value of the potential is irrelevant. It's its derivative that matters. Let $s$ be the side length of the square and $r=s\sqrt{2}/2.$ By symmetry on the z-axis, the electric field is $\...
R. Romero's user avatar
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2 votes
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Will a charge move if it has electric potential but the field is zero?

What you describe is an unstable equilibrium. A charge exactly at that point will feel no force. But any slight deviation in position from the exact center will produce a small force that accelerates ...
Dale's user avatar
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-1 votes

Energy balance turbine

FIG 1 below is an example of the application of the first law to a general open system. FIG 2 narrows the example to adiabatic turbines, compressors, and pumps. $$\dot W_{OUT}=\dot m(h_{1}-h_2)=-\dot ...
Bob D's user avatar
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Energy balance turbine

You need to review the derivation of the open system (control volume) version of the first law of thermodynamics. In this version, the work is subdivided into two parts, the work to push material ...
Chet Miller's user avatar
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-1 votes

Energy balance turbine

Let's follow a rigorous way, in few steps: integral balance of total energy for the geometric volume inside the machine where the fluid flow manipulation some terms of the integral balance, to make ...
basics's user avatar
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0 votes

Energy balance turbine

Enthalpy is defined as the internal energy of a system plus the work required to push the surroundings out of the way. In a control volume with an inlet and an outlet, the change in enthalpy is the ...
Chemomechanics's user avatar

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