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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Potential difference between 2 points in a loop containing changing magnetic field = 0?

I came across this question in an exam. The answer to this was given as YES. But I think otherwise. They say between A and B, there is zero potential difference. But if i simply alter the diagram a ...
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3answers
107 views

Why do wider double wells have a lower $\Delta E$ than thinner ones?

In this diagram, in which an $n=1 (E_{1})$ and $n=2 (E_{2})$ wave have been superimposed, the probability density of the new, combined wave changes with time. The period of its shifting density is ...
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2answers
116 views

movement of water in plants

Books say that water moves from places with a high water potential to places with a low water potential. The movement of water in plants are explained because water potential is lowest in leaves and ...
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1answer
47 views

Lower Voltage = Higher Potential?

I am doing problems from a textbook and one of the questions asks to determine where the higher potential is. (b) Find the potential difference between the points on the axis at and which of ...
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92 views

How do you find potential by Lagrangian formalism?

Suppose a ball is falling towards earth and hence by Lagrange equation we can find $T$ and $V$ where $V$ is $mgh$. But we know $V$ only because we know $F = mg$. Now since Lagrange equation doesn't ...
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1answer
19 views

What are the potentials of a battery with respect to earth?

Assume an open-circuit voltaic cell. We know that the cell maintains a potential difference between its terminals. That is $V_+ - V_- = E$. Now, if I connect $(-)$ to earth using the earth terminal ...
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1answer
180 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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236 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
75 views

What mistake am I making in plotting this graph of effective potential for the Earth-Moon system?

I am trying to create a graph of effective potential for the Earth-Moon system in Excel. It should result in a graph that looks like this: But this is not what I end up with. (I've made a Google ...
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2answers
124 views

What does Potential Difference between a load/resistor mean?

Guys this has been bugging me for ages and all the answers i found online were unsatisfactory. My questions is, what does difference in potential or potential drop after current passes through a ...
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1answer
33 views

Potential on a uniform

My doubt is in the part where he sets $V=V_s - \int{E dr}$. My idea is that he is summing two potentials, from the surface, and the one he's trying to calculate with the integral. Is that right? ...
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1answer
67 views

Does magnetic induction produce potential across zero resistance wire?

If magnetic field is increased at a constant rate inside a zero resistance wire loop, then, according to Faraday's law , $$\varepsilon = \frac{dΦ}{dt} $$ Thus, a potential difference is produced. ...
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80 views

Significance of imaginary mass

Can real mass be thought of as producing a deformation in spacetime leading to a stable equilibrium (valley curve in gravitational potential energy) of the massive body, and imaginary mass as similar, ...
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1answer
78 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: $\phi = \frac{q}{4\pi\epsilon_0}\int \frac{\delta(\mathbf{r'} - ...
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1answer
80 views

Acceleration due to gravity: what's the derivation? [closed]

Modelling the Earth as a symmetric, spherical body (and by using the law of gravitation), we come up with the equation $$w = F_g = \frac{Gm_Em}{R_E^2}$$ How do we arrive to the equation to get the ...
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0answers
41 views

Misbehaving singular isothermal sphere potential

The singular isothermal sphere (SIS) is a useful simple model often used in astrophysics. It has density profile: $$\rho(r) = \frac{\rho_0 r_0^2}{r^2}$$ This is well known to have some quirks ...
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2answers
335 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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2answers
202 views

Why does the superposition principle work in method of images?

Okay, let there be a conducting sphere having radius $a$ initially charged with $Q$ & insulated. Now, $q$ is brought in front of the conductor at $y$ from the center. Now, Jackson in his book ...
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465 views

Bound states of the $V(x)=\pm \delta'^{(n)}(x)$ potential?

The $\delta(x)$ Dirac delta is not the only "point-supported" potential that we can integrate; in principle all their derivatives $\delta', \delta'', ...$ exist also, do they? If yes, can we look for ...
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1answer
47 views

Mean squared velocity of a particle moving in a logarithmic potential [closed]

A particle of mass $m$ moves in the logarithmic potential $V(r)= C\ln(ar)$. $C$ and $a$ are constants. What is the mean squared velocity of the particle? Do I have to solve this in ...
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1answer
50 views

Potential energy function for high energy continuum?

For the hydrogen atom the quantised energy levels are: $$E_n = \frac{- 13.6 eV}{n^2}\quad\text{with}\quad n = 1,2,3...$$ One peculiar property of this quantisation is that for large $n$ the energy ...
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1answer
33 views

Effect of charge on electric circuit in free space

Assume I put some electronic device, a laptop for example, in free space. Now add electrons to the object. It will become progressively more negatively charged. At what point will the laptop (or ...
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2answers
199 views

How to predict bound states in a 1 D triangular well?

Assume we have a (single) particle in a potential well of the following shape: For $x \leq 0$, $V = \infty$ (Region I) For $x \geq L$, $V = 0$ (Region III) For the interval $x > 0$ to $x < ...
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2answers
64 views

The correspondence of potential energy with reality

I'm a bit in doubt about whether the concept of potential energy has any correspondence to the real world. Real world entities can't change their magnitude in an instant, nor without being affected ...
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1answer
252 views

Concrete example of the application of complex analysis in electrostatics [closed]

I've heard complex analysis can be useful in solving electrostatics problems, but despite doing some research I was unable to find any concrete examples. Would anyone be able to provide a simple ...
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1answer
167 views

Minima & maxima of Laplace's equation

I don't get the following sentence from David J. Griffiths' Introduction to Electrodynamics (the ambiguous sentence is in bold) Laplace's equation tolerates no local maxima or minima; extreme ...
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1answer
24 views

Obtaining central force from the potential of an off-orgin object

I was trying to go through a simple exercise and was getting tripped up on the mathematical intuition of my elementary physics. I thought I should be able to get any old central force from the central ...
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1answer
34 views

variation of electrostatic potential on moving radially outwards from the nucleus of an atom

I was wondering how would the electrostatic potential change on moving radially outwards from the nucleus in an atom, considering the effect of the electron clouds around it.
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1answer
60 views

Potential difference in a circuit of n cells = 0? How?

I was supposed to find the potential difference across any one cell in an arrangement consisting of n cells of EMF E connected in series in a closed circuit and internal resistance r. I proceeded by ...
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1answer
101 views

Why is the equation for electric potential energy so counter-intuitive?

The equation: $U_E = Vq$ or $(Eq)d$. This works the same way as the equation for gravitational potential energy: $mgh$ But to me, for charges of different signs, the potential energy also varies. ...
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2answers
40 views

Is this diagram in my textbook not constructed to scale?

Or am I having an illusion. Clearly, the distance from 6v to 4v is not the same as 4v to 2v. I know it should be based on: $V = k\frac{q}{r}$.
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1answer
245 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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1answer
74 views

Can a photon excite an electron via the uncertainty principle?

An electron is trapped in an infinite well potential with a width of $\Delta x$. A photon of wavelength $\lambda $ < $\Delta x$ is fired at the electron and misses or rather they don't interact. ...
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1answer
34 views

Zero of Electric Potential Energy

When you have a positive charge and a negative charge, the line that cuts perpendicularly between their separation distance is an equipotential line of 0 volts. The math indicates that at that point, ...
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53 views

Electic potential due to finite rectangular plate

I am trying to find the potential at any point (x,y,z) due to a rectangular plate with a constant surface charge density. Let's assume the plate is centered on the X-Y plane and extends from -n to n ...
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1answer
135 views

Why electron can not be found at some node locations in the infinite potential well?

Consider electron in an infinite potential well, studied in quantum mechanics. Position probability density of the electron is $$ P_n(x)=\left(\frac{2}{L}\right)\sin^2\left(\frac{n\pi x}{L}\right)$$ ...
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2answers
87 views

Where does the factor of $x$ come from in this formula for expectation value?

Given the normalised ground-state wave-function: $$\Psi(x, t)=\begin{cases} \sqrt\frac{2}{d}\cos(\frac{\pi x}{d})e^\frac{-i\hbar\pi^2t}{2md^2} & \ \lvert x\rvert<\frac{d}{2}, \\ 0 & ...
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28 views

Solutions to time-independent Schrödinger's equation with symmetrical (even) potential [duplicate]

A problem from Griffith's Introduction to Quantum Mechanics asks to prove the following: Given a symmetric potential $V(x)$ $(=V(-x))$, the solutions to the time-independent Schrödinger's equation ...
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1answer
118 views

If systems minimize their potential energy, why do people climb mountains?

A person climbs a mountain. They convert the stored chemical energy of food in their body and back pack into heat energy on the mountain, and gravitational potential energy as they move towards the ...
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2answers
64 views

Finding potential function of $f(x,y)=\hat i+ 2 \,\cdot\hat j$ [closed]

Find the potential function of $f(x,y)=\hat i+ 2 \,\cdot\hat j$ My attempt: $$\frac{\partial f}{\partial x}=1 \, , \frac{\partial f}{\partial y}=2 \, .$$ Integration with respect to $x:$ ...
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44 views

How does the idea of a scalar potential for a 3-vector field generalize to Minkowski space?

How does the idea of a scalar potential for a 3-vector field generalize to Minkowski space? As I guess, I thought one way would be to generalize 3-force to 4-force and replace the 3-gradient with the ...
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0answers
44 views

Developing an analytic equation set for a complicated solenoid

So, I'm a bit stumped by this. I've been asked to develop an analytic function for the magnetic field of a complicated axisymmetric solenoid with free parameters to be determined by making a fit ...
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1answer
78 views

Analytical non-separable solution for schrodinger equation

I am an undergraduate with the background of a first course in Quantum Mechanics. I want to find out if there exist non-unique solutions to Schrodinger equation. So I have to find potentials ...
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1answer
129 views

Proving assumptions used in 'method of image charges'

While studying the method of images for an infinite grounded plate, I came upon two assumption I can't seem to find the logic for: The test charge doesn't induce a charge density on the plate which ...
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1answer
52 views

Is the scalar magnetic potential continuos?

If we have two current-free spaces and separated by a surface current, we can solve the magnetic problem by solving two magnetic scalar potentials and then using matching conditions. My question is, ...
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1answer
43 views

Vector potential of a linear current

First of all, I apologize in advance for my English, as I know it is not very good. So thank you for making the effort of understanding me. Well, here is my problem. I am trying to prove that if I ...
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241 views

Gravitational potential in GR

Why in GR does the $g_{\mu\nu}$ describe potential?
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1answer
262 views

Q: Goldstein chapter 1 problem 16: Finding the generalized potential from the force

I have started to work through Herbert Goldstein's, Charles Poole's and John Safko's Classical mechanics, and I am having a bit of trouble with one of the problems (chapter 1 problem 16). The problem ...
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2answers
156 views

Why the electric potential energy the charges carry in a electric circuit does not vary with its distance to the opposite terminal?

I understand that with wires assumed to be ideal, there is no resistance and subsequently no force acting on electrons, hence no work done and p.d. across any segment of wire. However, as the ...
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1answer
110 views

Resistance and potential difference across it

I have this question that has baffled me for hours now. My question is what really happens when charge passes from one point to another in a circuit for eg what happens when it passes over a ...