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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2answers
88 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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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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0answers
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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0answers
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
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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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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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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2answers
77 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
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 ...
2
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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
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 ...
2
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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.
0
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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 ...
0
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1answer
61 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
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
59 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
18 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 ...
2
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1answer
100 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
74 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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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
60 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
56 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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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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0answers
31 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
45 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 ...
0
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1answer
34 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
33 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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1answer
82 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
47 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
57 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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3answers
64 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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36 views

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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1answer
54 views

Time dependent solution to infinite well

A particle of mass $m$ is confined within an infinite, one-dimensional potential well, $U(x)$, of width $a$. $$ U\left(x\right) = \left\{ \begin{array}{lr} \infty &\: x \leq ...
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70 views

Electric potential difference

From what I have read, since electrical potential is essentially EPE/unit of charge, it would be position dependent (relative to the electric field). Electrical potential difference is then defined ...
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1answer
16 views

electric potential at the other end of diode

I was brushing my basics about diode & got stuck at a point...my question is Consider a diode let the positive terminal of the diode be connected to +ve of battery Now in the figure let the ...
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1answer
64 views

Understanding electric field and potential inside an half-connected wire

Let's say we have a 9 V battery and a wire as shown in the image below: Let's assume H is the reference for measuring potential. I know the potential in F is 9 V, and I know the electric field in F ...
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2answers
141 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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0answers
34 views

Potential (which only depends on the length of a position vector) [closed]

a) A potential $U$ only depends on the length $r=|\vec{r}|$ of the position vector $r$. Show that $$\vec{\nabla}U(r)=U'(r)\frac{\vec{r}}{r}. $$ What properties does this vector field have? ...
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3answers
70 views

Parallel-plate capacitor working voltage $V={Qd\over{\epsilon_0 A}}$ relationship with plates' distance

I don't understand why the working voltage of a capacitor increases with the plates' distance. Suppose we have 2 capacitors in series where $C_1=12,0\mu F$ and $C_2=4,0\mu F$. The voltage over both ...
0
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1answer
47 views

Angular momentum & Energy using Yukawa's potential [closed]

I was doing my Gravitation problems and I found this one that I'm unable to solve. Yukawa's theory for nuclear forces states that the potential energy corresponding to the attraction force ...
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1answer
111 views

Electric field of two infinitely long and thin, straight wires

I know the formula of the electric field, however: suppose that we put two infinitely long and thin, straight wires symetrically into the coordinate system, so that y axis is between them. Now ...
2
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1answer
40 views

Is it possible for two polarizable bodies to induce dipoles in each other in the absence of an external electric field?

If there exist two initially neutral bodies (say atoms) some distance apart, with no external electric field applied, can they induce dipoles within each other?
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1answer
53 views

Potential and Electric field

I'm trying to find the electric field from the potential and vise-versa but I'm having trouble I know the electric field of a ring with radius a and charge Q to be $$E=\frac{Qx}{4\pi ...
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1answer
30 views

why isn't the net force considered while calculating potential due to a system of charges?

The textbook I'm reading defines potential at a point as work done per unit charge by an external agent to move the test charge from the reference point to the point under consideration (without ...
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1answer
37 views

Equipotential inside a conductor ring, but how do I determine the value?

I was mapping the potential lines of 2 cylindrical electrodes - one at 0 V, the other at 5 V. I have a metallic ring midway between the 2 electrodes. I know that the electric field inside the ring is ...
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1answer
69 views

Confusion with potential difference [closed]

I was trying to solve a hard problem involving a circuit like this: Find the reading on the voltmeter (red ones are resistors) I don't know how to think about potential difference across branches ...