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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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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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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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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87 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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114 views

Potential difference between Earth's surface and 2 meters above

Assuming Earth is a charged sphere of radius $R = 6400\times10^3$ m with uniform surface charge density $\sigma = -10^{-9}$ C/m2 and with $\epsilon_0 = 8.85\times10^{-12}$ F/m I find that ...
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202 views

Why does the potential difference between two charged plates increase as they move further apart?

Suppose a uniform electric field $E$ exists between to oppositely charged metal plates (one is positively charged and one is negatively charged). If the plates move apart, and the charges on each ...
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243 views

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 ...
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What is the relationship between keV and kVp?

On X-ray topics we get used to talk about "energy", but what is keV? and what is the relationship between keV and kVp?
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534 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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24 views

History of delta barrier in QM [migrated]

I'm interested in finding something out about the history of the problem of the delta potential barrier in QM. Which was the first study to propose this problem, and perhaps any particular motivation ...
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19 views

Transfer matrix method in a rectangular potential well [closed]

I am trying to follow an algorithm that is described in Elementary Quantum Mechanics in 1D. I wanted to compute eigen energies and functions in bound states in the basic case in rectangular potential ...
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2answers
43 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
95 views

Does the electric field inside a circuit cause a potential drop with distance?

We know that when the system reaches steady-state(current does not change with time),the electric filed inside the circuit is constant. In many textbooks and lectures,professors make a graph like this ...
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1answer
31 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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33 views

Boundary conditions for laplace's equation rectangular conductor

Find the potential inside a rectangular conductor that is subject to the boundary conditions $$ (i)\ \phi (x = a,y,z) = \cos(\beta y)\cos(\gamma z) \\ (ii)\ \phi (x, y = b,z) = V_0\ (constant)\\ ...
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1answer
201 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
36 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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568 views

When is energy discrete/quantized for a potential well?

Specifically, my question is: Should one expect energy quantization for a particle in the following potential well? More generally, how can one tell whether or not energy should be ...
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1answer
124 views

Finite potential well, parity of solutions

I'm working through some problems for a QM exam and I've realised I don't really understand the concept of parity of solutions. I'm looking at a simple finite potential well problem: $$V(x)=0, \quad ...
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1answer
29 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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3answers
2k views

Barrier in an infinite double well

I am stuck on a QM homework problem. The setup is this: (To be clear, the potential in the left and rightmost regions is $0$ while the potential in the center region is $V_0$, and the wavefunction ...
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1answer
119 views

Quick question on sketching wavefunction in well

Usually for an infinite well, the sketch for n=3 level is this: Now I think if one side of the potential barrier is higher, the particle will be more likely to spend time on the left side than ...
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1answer
63 views

Current in a fluorescent tube that is not in a circuit

In Walter Lewin's 8.02 Electricity and Magnetism course, he places a fluorescent tube pointing radially outwards from a large Van de Graaff (VDG) generator. Due to the VDG's E-field, this causes a ...
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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
138 views

Why do electric field lines point in the direction of decreasing electric potential?

Why do electric field lines point in the direction of decreasing electric potential? I came across this sentence in my school book but am trying to understand this ever since. I know that dV=-E.dr ...
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1answer
24 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
79 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
199 views

How the electric potential of a charged body depends on the surface area of the body?

I have studied in the book that electric potential of a body depend on the surface area of the body, that is as the surface area increases potential decreases keeping the charge as constant and vice ...
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1answer
225 views

In a positively biased PN junction, where do the injection carriers come from?

I am not quite understand i-v character of PN-junction diode. Here is the model in textbook. The PN junction diode can be divided into three regions. They are One depletion region near the PN ...
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1answer
42 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
19 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
98 views

Electric Potential Energy

When work is done on a positive test charge by an external force to move it from one location to another, does the potential energy increases or decreases, and does the electric potential increases or ...
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1answer
25 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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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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1answer
179 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
60 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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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
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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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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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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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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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The potentiality of the electric field

Could you please explain using just words why electric the field is potentially? I know the proof using integral: $$A = \int_{12}q\vec{E}\cdot{d}\vec{r} = qQ\int_{12}\frac{\vec{r}\cdot{d}\vec{r}}{r^3} ...
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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
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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
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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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What is the difference between electric potential, potential difference (PD), voltage and electromotive force (EMF)?

This is a confused part ever since I started learning electricity. What is the difference between electric potential, potential difference (PD), voltage and electromotive force (EMF)? All of them have ...
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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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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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Meaning of “Grounded”

In my opinion, "grounded" means having the same potential as the potential at infinity, which is usually set to zero. Now if we consider a conductor inside a uniform electric field, what is the ...
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970 views

Gibbs free energy intuition

What is Gibbs free energy? As my book explains: Gibbs energy is the energy of a system available for work. So, what does it want to tell? Why is it free? Energy means ability to do work. What is ...