Potential Definition and 1000 Threads

Homework Statement We have two semi-infinite coplanar planes defined by z=0, one corresponding to x<0 set at potential zero, and one corresponding to x> set to potential ##V_0##. a) Find the Green function for the potential in this region b) Find the potential ##\Phi(r)## for all points in...

Homework Statement Four charges are arranged at the corners of a square as shown in the figure. Q1 is at (-L/2,L/2), Q2 is at (L/2,L/2), point a is at the origin and Q1=Q2=-Q3=-Q4. Which of the following statements correctly describe the electric field E and the potential at points a,b and c...

Homework Statement Find the electric potential of an infinitely long cylinder shell of radius ##R## whose walls are grounded, when in its interior a line charge, parallel to the cylinder, is placed at ##r=a## (with ##a<R##) and that has a lineal charge density ##\lambda##. Homework Equations...

Chemical potential is defined as the change in energy due to change in the number of particles in a system. Let we have a system which is defined by the following Hamiltonian: $$H = -t \sum_i^L c_i^\dagger c_{i+1} + V\sum_i^L n_i n_{i+1} -\mu \sum_i^L n_i$$ where ##c^\dagger (c)## are creation...

Homework Statement Find electric field at Point A its an arc with uniform density= lamda https://drive.google.com/file/d/14cBqE2dMe_w0nb9LtPG0h1cUOrzGWt6g/view?usp=sharing the problem Homework Equations E=intergal dq/r^2 The Attempt at a Solution I've tried using wolfram and cosine rule to...

Homework Statement An isolated parallel-plate capacitor of area ##A_1## with an air gap of length ##s_1## is charged up to a potential difference ##\Delta V_1## A second parallel-plate capacitor, initially uncharged, has an area ##A_2## and a gap of length ##s_2## filled with plastic whose...

Homework Statement What is the potential at the center of the sphere relative to infinity? The sphere is dielectric with uniform - charge on the surface of the sphere. Homework Equations ##k=\frac {1}{4\pi\epsilon_0}## ##V=\frac {KQ}{r}## The Attempt at a Solution If the distance r=0 it would...

1. Homework Statement A proton is released from rest at point B, where the potential is 0 V. Afterward, the proton: a. Remains at rest at B. b. Moves toward A with a steady speed. c. Moves toward A with an increasing speed. d. Moves toward C with a steady speed. e. Moves toward C with an...

Does anybody know if there is an analytical expression for the electrostatic potential produced by a charge distribution confined to a double cone shaped region. Think of a beam of charged particles converging to a focus and then diverging again. The total charge in each thin, cross-sectional...

I'm interested in the following general question: Assume x,y,z is an axes system, and that the y-z plane is occupied by a conductive plate at a known potential V with respect to the earth. Now, a conductive material M of neutral global electrical charge is placed at some distance of the plate...

Dear all, I cannot figure out my mistake with this thought experiment: Consider a ferromagnetic material (e.g.iron) in a magnetic field - or just any iron anywhere, since the range of magnetic fields is infinite. Between the ferromagnetic material and (permanent) magnets potential energy is...

Ok, I am stuck on understanding when to use a part of an equation and when not to. e = (P/rho) + (Ke/m) + (Pe/m) where P is pressure, Ke and Pe are Kinetic and potential energy divided by mass. Ok, if we look at P/rho and P is defined as rho(g)(h) then the rho's divide out and we are left...

Homework Statement CLASSICAL MECHANICS [/B]Homework Equations E=U+K[/B]The Attempt at a Solution Guys, can you please help me with part b) ? I am not sure how to find the velocity. Thanks

The Coriolis potential last term of (42) is obtained by integration through r and R from last term of (40). I do not understand why we do not need to integrate through v as well, since the Coriolis force depends on v? Homework Equations Equation (41) is wrong I think, L must be replaced by...

In quantum mechanics, there exist some systems where the potential energy of some particle is a Dirac delta function of position: ##V(x) = A\delta (x-x_0 )##, where ##A## is a constant with proper dimensions. Is there any classical mechanics application of this? It would seem that if I...

Homework Statement [a) Show that chemical potential in intrinsic semiconductor at T = 0 lies exactly in the middle of the energy gap. At what temperature is the chemical potential equal ##(3/4)(E_c + E_v)##, where ##E_c## and ##E_v## are energies od the bottom of the conduction band and of the...

Homework Statement When a point charge is positioned at the origin = 0 in an isotropic material, a separation of charge occurs around it, the Coulomb field of the point charge is screened, and the electrostatic potential takes the form \phi(r) = \frac{A}{r} \exp\left( -\frac{r}{\lambda}...

Do exist examples of attraction forces with such a type potential ##V(\boldsymbol r)\sim-\frac{1}{|\boldsymbol r|^2}, \quad |\boldsymbol r|\to 0## in physics ?

Hi All, The Potential Energy for two chemically bonding atoms is defined by ,U=1/2(k*q1*q2)/r So it means that when the atoms approach each other then, their Potential Energy will increase. Where am I doing wrong? I will be thankful for help!

I have read that postdocs are extremely hard to come by in Astrophysics, and is likely a dead end at the end of the PHD and that Condensed Matter is less competitive in academia. Would a Condensed Matter PhD also provide more opportunities in UK science industry - in particular the life sciences...

Lets suppose we put a point particle with a mass m here on earth. No energy was used to put it there. It makes sense it will go down, but where does gravity gets the energy to pull the particle? from the earth/particle mass?

Homework Statement Hence calculate the expectation value and uncertainty of the mutual potential energy of the electron and proton for a hydrogen atom in this state. This is the Coulomb model, and that is the question. I just need to know if 'mutual potential energy' means the effective...

1.Data: We have an truncated cone with a volumentric charge density ρ, and it's uniform. The image show the truncated cone and show some info of the radios. 2. Question. We need to calculate the potential on the vertical axis. note: adding an image of the problem but it's in spanish, hope...

HiI was reading about capacitors and potential energy. But the equation seems counter to how i thought. For potential energy you have: U = Q^2 / 2C or U = CV^2 / 2 But doesn't this suggest you lose potential energy the more capacitance you have? Since in the first equation as C increases U...

For this problem at t=0 Ψ(x,0)=Ψ1-Ψ3 Where Ψ1 and Ψ3are the normalised eigenstates corresponding to energy level 1 and 3 of the infinite square well potential. Now for it's time evolution it will be Ψ1exp(-iE1t/ħ)- Ψ3exp(-iE3t/ħ) And taking the time given in the question the time part of the...

Homework Statement Homework Equations For this question my ans. is coming option (3) since the time part of the wave comes out to be same for both the energy states which is (-1)^(-1/8) and (-1)^(-9/8) respectively (using exp(-iEt/ħ)). But the correct option is given option (4). Am I right...

My question is given an orthonormal basis having the basis elements Ψ's ,matrix representation of an operator A will be [ΨiIAIΨj] where i denotes the corresponding row and j the corresponding coloumn. Similarly if given two dimensional harmonic oscillator potential operator .5kx2+.5ky2 where x...

Homework Statement Suppose the potential in a problem of one degree of freedom is linearly dependent upon time such that $$H = \frac{p^2}{2m} - mAtx $$ where A is a constant. Solve the dynamical problem by means of Hamilton's principal function under the initial conditions t = 0, x = 0, ##p =...

Let's say the solution on the left hand side is a sinkx + b coskx = 0 We get one solution for each E if we omitted a and another solution if we omitted b. However, how to conclude that they are all the solutions? Will there be any solution of the 5 coefficients such that a and b are both not...

Homework Statement My main conceptual issue here surrounds positives and negatives as they apply to electric potential difference. I will post two questions that illustrate my confusion, if that's ok. 1) The electrons in an old TV picture tube are accelerated through a potential difference of...

Is the 100 J of electric potential energy actually greater than -100 J of electric potential energy?

Homework Statement I'm trying to do a problem two ways, and things aren't consistent, finding the electric potential difference in a linearly varying field. The electric potential difference between two points is often summarized in texts as ΔV = Vf - Vi = - ∫ E⋅ds where the lower bound of...

Homework Statement A toy car is held at rest against a compressed spring, as shown in the figure. When released, the car slides across the room. Let x=0 be the initial position of the car. Assume that friction is negligible. Sketch a graph of the car's kinetic energy from the moment it is...

Homework Statement A 1.00 kg ball is thrown directly upward with an initial speed of 16.0 m/s. A graph of the ball's gravitational potential energy vs. height, Ug(h), for an arbitrary initial velocity is given in Part A. The zero point of gravitational potential energy is located at the height...

1. The problem statement Two charges of 3μC and -2μC are placed 2cm apart. At what point along their connecting line is electric potential zero? Homework Equations Electric potential superposition Φ=Φ1-Φ2 since q2 is negative Φ=kq/r^2 The Attempt at a Solution Let’s say the charges are on the...

Consider the classical scenario a stone falling in the Earth gravitational field. Classically we attach a Potential Energy to the stone and using the law of conservation of (mechanical) energy we are able to evaluate the dynamic of the falling stone. This model assume a stone in a "external"...

Assuming generlized variables, q, we have a Lagrangian in mechanics as the kinetic energy, K, minus potential energy, U, with a dependency form such that L(q,dq/dt) = K(q, dq/dt) - U(q) Can someone provide examples of Lagrangians in other disciplines?

So the work done when charging up a capacitor is ##dW=VdQ## However, when we add a charge ##dQ## to the capacitor, ##V## also changes accordingly, so I was wondering why the work done wasn't written as ##dW=VdQ+QdV## (one that also takes into account t he change in ##V##). Thanks in advance.

There is no absolute electric potential. Is it due to classical ignorance (because we don't know the static fields, capacitive coupling, etc. of the surrounding environment) or is it due to quantum ignorance (the potential can fluctuate to any value due to HUP)? My question is valid because...

Homework Statement Consider a particle of mass m moving in a one-dimensional double well potential $$V(x) = -g\delta(x-a)-g\delta(x+a), g > 0$$ This is an attractive potential with ##\delta##-function dips at x=##\pm a##. In the limit of large ##\lambda##, find a approximate formula for the...

Homework Statement Question_________________________________________________________________________________ Find transmitted coefficient and reflected coefficient in case barrier potential E<V ? determine. ##Ψ_{I} = Ae^{ikx}+Be^{-ikx}## ##Ψ_{II} = De^{βx}+Ee^{-βx}## ##Ψ_{III} = Ce^{ikx}##...

Homework Statement A 3.20kg rubber ball drops from a height of 4.80m to the ground a bounces back to a height of 2.70m a) how much potential energy does the ball lose on the trip down? b) how much energy does the ball regain on the trip back up? c) what is the net loss of potential energy...

Homework Statement We have the cross section of a metal pipe that has been split into four sections. Three of the sections have a constant electric potential, Vo. The fourth section is grounded so electric potential is zero. We are looking for electric potential inside and outside of the pipe...

Homework Statement Four identical cells each having emf E and internal resistance r are connected in series to form a loop abcd as shown in figure (picture 1). Find potential difference across ab and ac. 2. Homework Equations V=IR equations for combination of cells and resistances The...

Homework Statement Does a point in a wire having higher potential necessarily mean that it has a higher electric field? For example consider the cases of question 27 and 31 in the picture attached below. Homework Equations E=V/L The Attempt at a Solution The potential at a and b is the same...

I’ve seen the uncertainty principle used to calculate the ground state energy for things like hydrogen and the harmonic oscillator, but can this be done for the Yukawa potential where you have an exponential?

Homework Statement The change in gravitational potential energy of a mass m as it moves from the surface to a height h above the surface of a planet of mass M and radius R is given by: ΔPE= GMmh/R(R+h) a) show that when h is very small compared to R , this approximates to the more familiar...

I have been reading the book "Nanostructures and Nanomaterials" by G. Cao and Y. Yang, and was intrigued by the following passage in page 33: "Assuming the vapor of solid phase obeys the ideal gas law, for the flat surface one can easily arrive at: μv − μ∞ = −kTlnP∞, where μv is the chemical...

Homework Statement I have a force ##\vec{F} = a_x\vec{i}+2a_y\vec{j}+3a_z\vec{k}##. Find the potential Homework EquationsThe Attempt at a Solution Lets suppose And we know that ##\vec {F} = ∇U## In this case I said that ##U_x=-\int F_xdx## ##U_y=-\int F_ydy## ##U_z=-\int F_zdz## and then I...

Homework Statement A particle of mass m in one dimension has a potential: $$V(x) = \begin{cases} V_0 & x > 0 \\ 0 & x \leq 0 \end{cases} $$ Find ##\psi(x)## for energies ##0 < E < V_0##, with parameters $$k^2 = \frac{2mE}{\hbar^2}$$ and $$\kappa^2 = \frac{2m(V_0 - E)}{\hbar^2}$$...