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12 votes

Is work done by a charged particle not gauge invariant?

Good question! Let's go by parts. The definition of electric work is $$ W_{x_1 \to x_2} = q \int_{x_1}^{x_2} d\mathbf{r}\cdot\mathbf{E},\tag{1} $$ which in the $\mathbf{A = 0}$ case (not the static ...
Gabriel Ybarra Marcaida's user avatar
6 votes

Can a positive charge have a negative potential?

First: The concept of your point B does not make sense to me, the static coulomb field of the charge does not stop at some point, it will just get weaker the further away you are. Secondly: Arguing ...
Zaph's user avatar
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5 votes
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Series Solution of Laplace Equation in Spherical Coordinates

You need both solutions in general. Your potential is not uniquely defined by being harmonic, you need to append boundary conditions. If your domain is a ball (includes the origin), this excludes the $...
LPZ's user avatar
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4 votes
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Can a positive charge have a negative potential?

First, you need to understand that electrostatic potential (or, indeed, any type of potential energy) is an attribute of a system or configuration of charges - you cannot ascribe it to any individual ...
gandalf61's user avatar
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4 votes

Can a positive charge have a negative potential?

The work done by an external force in moving unit positive test charge is the change in potential. The test charge has two equal magnitude, opposite direction forces acting in it as shown in the ...
Farcher's user avatar
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3 votes
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What is the potential of a conductor between two eletrically-charged plates?

Perhaps it helps to draw the induced charges, like this: The normal $E$-field component must be equal to those surface charge densities and then you need to assume that the middle conductor has no ...
Jos Bergervoet's user avatar
3 votes

Mirror image Electric field and potential

In principle, you have to find the solution of the Laplace equation in the half-space of the point charge which fulfills the boundary condition for the potential zero on the grounded plane. The image ...
freecharly's user avatar
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2 votes
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Potential of a conductor when the charge distribution is uneven due to induction

The electric field inside a conductor is zero (as long as no current is flowing). Electric fields add, so the field inside the conductor is the sum of the external field plus the field created by the ...
John Rennie's user avatar
2 votes
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Charge transferred from Sphere and Disc after being brought into contact

When you touch the charged conducting sphere with the small isolated metal disc, the disk practically becomes part of the surface of the sphere so that its charge per area is equal to the charge per ...
freecharly's user avatar
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2 votes
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How do we write the potential difference between the final and initial points?

As already pointed out there appears to be no absolute consensus on which is used (though personally I’ve seen the first equation more often). In any case, the magnitude of the potential difference is ...
Bob D's user avatar
  • 72.5k
2 votes

Can a positive charge have a negative potential?

B will always be at infinity as per the convention we take. But if you want to change it for some reason, then it is possible that potential becomes negative once you go further away. Logically, you ...
Aaditya Shah's user avatar
2 votes

Can a positive charge have a negative potential?

I shall give an explicit example where a positive point charge interacts with a test charge so that the potential of that test charge is negative for any $r\gt 0$. For example, as is noted in many of ...
Albertus Magnus's user avatar
2 votes

Where does the four-vector potential $A^\mu$ originate?

I see (at least) two questions here. Why is a four-vector such as $A^\alpha$ often written as a "scalar+vector" quantity, in this case $(\phi, \vec{A})$? Where does $A_\alpha$ come from? ...
SvenForkbeard's user avatar
2 votes

Is work done by a charged particle not gauge invariant?

You are correct that the expression $q\phi$ is not gauge invariant. Only expressions in E and B are, with the caveat that B does not contribute to the work except if it is time dependent. Then it is ...
my2cts's user avatar
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1 vote

The electrostatic potential due to a pair of oppositely charged infinite thin conducting plates

Your assumption of a potential value of V in both A and C is incorrect. The potential difference between these regions is V. For a finite system you can assume that the potential far away from the ...
my2cts's user avatar
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1 vote
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Why does the stopping potential correspond to zero current?

Your intuition would be right, if the circuit used in photoelectric experiments were closed. That is to say, in a closed circuit, it doesn't matter in which way the electrons flow, we will always ...
Lagrangiano's user avatar
1 vote
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Electric potential energy, Electric potential and self-energy of a body

When you divide the electrostatic potential energy of a charged body by its total charge, you don't "get the electric potential of the body". (1) If the body is not a conductor, there is no ...
freecharly's user avatar
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1 vote

Gravitational potential due to arbitrary shape

In short, no. The fact that a spherical mass distribution produces a field that acts as if all the mass were concentrated at the center is a consequence of the spherical geometry and the inverse ...
Albertus Magnus's user avatar
1 vote
Accepted

Gravitational potential due to arbitrary shape

No. This is characteristic to the sphere only. A more complicated shape will have a completely different potential, and you need to use the gravitational analog of Coulomb's law to compute it.
Níckolas Alves's user avatar
1 vote

Where does the four-vector potential $A^\mu$ originate?

The only reason one would ever define something like $A^{\mu}$ is "an effort to go and pull electrodynamics into a four-dimensional framework. Now, in order to do that, one can notice that you ...
Zo the Relativist's user avatar
1 vote

Where does the four-vector potential $A^\mu$ originate?

The four-vector ${\bf A}$ with components $A^{\mu}$ arises from the expressions for the electric field $\vec{\bf E}$ and the magnetic induction field $\vec{\bf B}$, which are three-dimensional. The ...
Physics_Et_Al's user avatar
1 vote

Does it make a difference whether potential difference is denoted as a negative or positive value in an answer, since it's just a scalar?

Potential is a scalar and you are free to choose an additive constant in any way that might make your problem easier to solve. However, in calculating a potential difference, that additive constant ...
ProfRob's user avatar
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1 vote
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Apparent contradiction while calculating potential inside shell due to off center charge

travelling in the first path gives 0 work done by the field due to Q Here is the mistake. $Q$ is not the only charge you need to consider. You must also consider the charge induced on the inner ...
Dale's user avatar
  • 102k
1 vote
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Reflection of quantum particle colliding with a potential barrier

Your last statement is basically correct. For a single particle, the current $\vec{J}$ is measuring a current of probability density $|\psi|^2$. However, to physically interpret what such a ...
Andrew's user avatar
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1 vote

How do we write the potential difference between the final and initial points?

Certainly, both notations are utilized. The outcome remains identical; one must simply exercise caution regarding the symbols preceding the potential.
Gorga's user avatar
  • 161
1 vote
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Confusion about reference point for potential difference

$\dots$ I know it should be $\frac{Q}{4\pi \epsilon_0}\cdot \left( \frac {1}{R_1}- \frac {1}{R_2}\right)$ is an incorrect statement and your integration gave you the correct answer. Since you are ...
Farcher's user avatar
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1 vote

Insertion of dielectric inside capacitor when capacitor is connected to a battery

The energy density is $$u=\tfrac 12 \epsilon_0 \kappa E^2$$ in which $\kappa$ is the dielectric constant (relative permittivity). [For a vacuum $\kappa=1$.] There is no contradiction. Note that we can ...
Philip Wood's user avatar
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1 vote

Electric Potential in circuit confusion

The equation applies when the potential is assigned a value of zero at infinity, which makes sense when you are looking the potential due to the contribution of many point charges. But the assignment ...
Bob D's user avatar
  • 72.5k
1 vote

How to find the wavefunction that solves an infinite square well with a delta function well in the middle?

There is also a solution possible for $E<0$. Define $\kappa^2 = 2m |E|/\hbar^2$ with $\kappa > 0$. Then for $0<x<L/2$ we have $$\psi(x)=Ce^{\kappa(x-L/2)} -Ce^{-\kappa L/2)}$$ and for $L/2&...
Hubert van Luytelaar's user avatar

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