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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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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57 views

Concrete example of the application of complex analysis in electrostatics

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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184 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
212 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
39 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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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
97 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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20 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
96 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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1answer
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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
161 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
56 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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38 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
56 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
96 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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1answer
16 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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21 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
508 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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1answer
129 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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2answers
69 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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5answers
144 views

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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0answers
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
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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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11answers
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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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0answers
26 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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30 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
85 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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183 views

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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1answer
186 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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6answers
930 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 ...
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3answers
115 views

Semiclassical quantization of bouncing ball

Consider an elastically bouncing ball of mass $m$ and energy $E$. This has a triangular potential $$ V(x)~=~\left\{\begin{array}{ll} mgx & \text{if } x>0, \\ \infty & \text{if } x<0, ...
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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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7answers
737 views

Why do two ends of a long conducting wire have the same electric potential?

I am not seeing the "big picture" here. If I have two conducting spheres separated by a long conducting wire, why would the spheres share the same electric potential? I think of the spheres as point ...
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1answer
43 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
34 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
33 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
31 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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2answers
68 views

Importance of bound states

While solving a potential well problem we get scattering states and bound states (if exist). Number of the bound states we get depends on the potential profile. What I want to ask is, what is the ...
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1answer
43 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 ...
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2answers
982 views

Particle in a 1D Box with Symmetric potential: How find solutions?

I am working on a problem in which I shall find the normalised solution to the 1D particle in a box. Solving for the particle in an asymmetric potential is quite straight forward, but I run into ...
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2answers
36 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
49 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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3answers
62 views

How to decide if a potential is a scalar?

I know that ${\vec E}=-{\vec \nabla} V$. If a potential is scalar, I can find its electric field strength. The question is how can I know if a potential is scalar? Do all point charges result in ...
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159 views

Why are the dineutron and diproton unbound?

It is known that there is no diproton and dineutron nuclei. Does this mean that two protons or neutrons are not actually attracted to each other? Even if the attraction was weak, wouldn't it cause ...
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1answer
151 views

Eigenvalues of the radial Schrödinger equation on a finite integration interval

There are numerous ways to estimate the eigenvalues of a radial Schrödinger equation, see http://arxiv.org/abs/math-ph/0703040 as an example. Anyhow, the formulas only cover the Schrödinger equations ...
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Electron's Frame Aharonov-Bohm Effect

In the electron's inertial frame the solenoid moves past it in the Aharonov-Bohm Effect. That means the electron sees a time varying vector potential which, by: $\vec{E}$ = ...
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9k views

How can you have a negative voltage?

How can you have a negative voltage? I don't really understand the concept of negative voltage, how can it exist?
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579 views

Potential energy of a dipole in a uniform electric field convention?

When finding the potential energy of a dipole in a uniform electric field, I was told by my lecturer that the convention is that the potential energy is 0 when the dipole moment and electric field ...