Potential Definition and 1000 Threads

1. Homework Statement We have an infinitely long wire with charge density ##\lambda## located at ##x=0,y=h##. We also have a semi-infinite strip of a conductor ##|x|<a/2, y<0##. We need to find the potential in all space. The hint is to use conformal maps. Homework Equations $$\nabla^2 = 0$$...

Homework Statement I have a curve $$\Psi(t) = \hat h_\alpha$$ where the coordinates are $$\alpha=0, \beta=t$$ and $$\gamma=t$$ in the system. Additionaly $$x=\sqrt2 ^\alpha \cdot(sin\beta-cos\beta)\cdot \frac{1}{cosh\gamma}$$ $$y=\sqrt2 ^\alpha \cdot(cos\beta+sin\beta)\cdot...

Homework Statement Homework EquationsThe Attempt at a Solution In case of uniform E, torque ##\vec N = \vec p \times \vec E \\ U = \int_0 ^ \theta N d \theta = pE \int_0 ^ \theta \sin \theta d \theta = - pE \cos \theta \text { Here, I assumed that the direction of } \vec N ~ and ~ \vec d...

Homework Statement I'm trying to digest the concept of change in potential energy being set equal to a change in kinetic energy. Does this relationship always hold? Please see below for more details. Homework Equations PE = mgh KE = .5mv^2 W = ΔKE = -ΔPE W = f*d The Attempt at a Solution...

To find potential energy in 3 dimensions why do we take partial derivative and not total derivative?

Homework Statement [/B] I am trying to identify every force in this system and prove that it is in mechanical equilibrium when tan(θ)=⅓. Initially I had to solve it by finding when the derivative of potential with respect to θ was 0, but now I am just trying to resolve the forces. Homework...

Homework Statement I am currently reading a textbook on solving the Schrödinger equation for the harmonic oscillator using the series method; $$-\frac{\hbar^{2}}{2m}\frac{\mathrm{d}^2 \psi }{\mathrm{d} x^2}+\frac{1}{2}m\omega ^{2}x^2\psi =E\psi $$ It starts by using these two dimensionless...

Hi, friends! Under particular conditions on ##\phi:\mathbb{R}^3\times\mathbb{R}\to\mathbb{R}## - I think, as said here, that it is sufficient that ##\phi\in C_c^1(\mathbb{R}^4)##: please correct me if I am wrong - the following equality holds$$\frac{\partial}{\partial r_k}\int_{\mathbb{R}^3}...

Homework Statement A + q = 5 pC charge is uniformly distributed on a non-conducting sphere of radius a= 5 cm , which is placed in the center of a spherical conducting shell of inner radius b = 10 cm and outer radius c = 12 cm. The outer conducting shell is charged with a -q charge. Determine...

It is said that a negative potential energy gives stable equilibrium but a positive potential energy gives an unstable equilibrium. why is it so?

Homework Statement An Electron enters a parallel plate apparatus that is 8cm long and 4cm wide. The electron has a horizontal speed of 6*10^7 m/s. The potential difference between the plates is 6*10^2 V. Calculate the electrons velocity as it leaves the plates. (ans. 6*10^7 m/s [E 3.3° N])...

Homework Statement Action attached: To find the EoM of ##\phi ## / ##\phi^* ## Homework Equations The Attempt at a Solution [/B] Without deriving from first principles, using E-L equations I have: ## \partial_{u}\frac{\partial L}{\partial_u \phi} - \frac{\partial L}{\partial \phi} =0 ##...

Homework Statement A region of space has a non-uniform electric field that points in the +x-direction and has magnitude as shown in the figure (Figure 1) As a reference point, take the potential at the origin to be -140 V . Calculate the electric potential at x=3.0m. Express your answer to two...

1. Homework Statement This is my first question and I'll try to stick to the forum rules as much as possible. imgur.com/a/2JyZC Imagine a cylinder filled with air which is uniformly distributed and a piston above it, so the air can expand vertically. Let the system be the air itself, so the...

I bought this book "Idiot's Guide to Quantum Physics" I bought it because I know I am an idiot in quantum physics. Now I have a question about the contents. It says that: "The four fundamental forces in nature (gravity, electromagnetism, plus two more that we'll formally introduce in Chapter...

Homework Statement An electric field is given by Ex = 2.2x + 5x2kNC-1. Find the potential difference between two points on the x-axis at x = -2.0 m and x = 2.0 m Homework Equations ∫5x2+2.2x from -2 to 2 The Attempt at a Solution I got the answer of 27V. Solution said - negative 27V Can...

Homework Statement Homework EquationsThe Attempt at a SolutionThe position of the point (where V is to calculated) on the z-axis would be ##u = z_0 + l/2##.So in cylindrical coords, $$V(u) = \int_V {k \rho \over (s^2 + (u -z)^2)^{1/2}} dV = k \rho \int_0^L \int_0^{2\pi} \int_0^R {k \rho...

Homework Statement Can there be a point in space where there is an electric potential but not electric field? Can there be a point in space where there is an electric field but no electric potential? Explain you answer. What would the electric field lines look like if the electric field was...

Homework Statement A solid conducting sphere having a charge Q is surrounded by an uncharged concentric conducting hollow spherical shell.Let the potential difference between the surface of the solid sphere and that of the outer surface of the hollow shell be V.If the shell is now given a...

In the 'Particle in a box' system, with the well being extremely narrow, why does the particle path have to follow certain energy levels compared to the classical system? Thanks in advance.

Homework Statement In the circuit shown, what is the potential difference VPQ? Homework Equations No relevant equations given in question The Attempt at a Solution Tried kirchhoffs law. Tried to find equivalent battery and resistance but that doesn't seem to be possible.

Homework Statement Consider a finite,uncharged,insulated conductor placed near a finite positively charged conductor.The uncharged body must have a potential A)less than the charged conductor and more than at infinity B)more than the charged conductor and less than at infinity C)more than the...

Hello Guys! This is my first post so bear with me. I am currently studying the basics of electrostatics using the textbook "Introduction to electrodynamics 3 edt. - David J. Griffiths". My problem comes when i try to solve problem 2.21. Find the potential V inside and outside a uniformly...

currently working on format.. sor i was not preparedHi I think this question would be much related to calculus more than physics cause it seems I'd lost my way cause of calculus... but anyway! it says, Q=- \frac{\partial{U}}{\partial{q}}+\frac{d}{dt}(\frac{\partial{U}}{ \partial{ \dot{q}}} )...

Can a potential energy curve be vertical ?

Homework Statement A particle carrying charge +q is placed at the center of a thick-walled conducting shell that has inner radius R and outer radius 2R and carries charge −3q. A thin-walled conducting shell of radius 5R carries charge +3q and is concentric with the thick-walled shell. Define V...

hey guys! i am very confused about the concept of potential energy and gravity. we know that as an object is continuously lifted above ground, its potential energy increases. but i was wondering if that potential energy is physically affecting the body, like if the potential energy increases...

Homework Statement I must calculate chemical potential using the Boltzmann equation in relaxation time approximation $$f=f^0-\tau v_z^2 \partial f^0/\partial z,$$ where ##f^0## is given as $$f^0 = 2(\frac{m}{2\pi\hbar})^3 \frac{1}{\exp{\beta(z)(\frac{mv^2}{2}-\mu(z))}+1}$$ I have to consider...

At non-relativistic speeds is the elastic potential energy of a compressed spring frame-invariant? That is, would all reference frames agree on how much elastic potential energy is stored in the spring?

The more I think about it the less clear the respective natures of kinetic energy and potential energy (and of their sum, the so-called total energy) become. The thing is I have the impression that once you try to go a bit further than the usual description of "scalar values assigned to systems...

Homework Statement Which of the following Graphs BEST illustrates the potential energy vs. time for the system in Figure 1, where t=0 is defined as the time at which the incident box 1st contacts the box on the spring? My question is why can't the Elastic PE be negative? The answer is A...

Hi All, Perhaps I am missing something. Schrodinger equation is HPsi=EPsi, where H is hamiltonian = sum of kinetic energy operator and potential energy operator. Kinetic energy operator does not commute with potential energy operator, then how come they share the same wave function Psi? The...

Homework Statement A line charge has the total charge Q evenly distributed over a circle boat with radius a and sector 2β, placed according to the figure Find the Electric field E and the potential V in the origin. Homework Equations I know for this case that E(r) = (1/4πε) ∫ (λ(r')/R2)R...

Dear friends, I have found a derivation of the fact that, under the assumptions made in physics on ##\rho## (to which we can give the physical interpretation of charge density) the function defined by $$V(\mathbf{x},t):=\frac{1}{4\pi\varepsilon_0}\int_{\mathbb{R}^3}...

Homework Statement Consider a uniformly charged cube with uniform charge density ρ.The ratio of electrostatic potential at the centre of the cube to that of one of the corners of the cube is? A hint on how to approach the problem's solution would be appreciated.(whether to use gauss law or not...

My question is: If gravitational potential energy is normally negative, and E=m•c^2, doesen't that means that negative mass could exist? (I don't know much about general relativity so please explain as simple as posible)

Homework Statement A battery of emf 2V and internal resistance 0.1ohm is being charged with a current of 5 ampere. In what direction will the current flow inside the battery?What is the potential difference between the two terminals of the battery? Homework Equations If a battery of emf E and...

Homework Statement The resistivity of a potentiometer wire is (40×10^-8) ohm-m and the area of cross section is (8×10^-6)m^2.If 0.2 amp current is flowing through the wire,then the potential gradient will be?? Homework Equations 1.Resistance=[(Resisitvity)×(Length)]/(Cross-sectional area)...

Homework Statement Consider the Earth as 1. with a constant density of matter, 2. as a thin shell empty sphere and 3. with a constant linear density of matter ##\rho(r) = \rho_{0}r##. In all cases, calculate the gravitational potential and the gravitational field everywhere and make a...

Homework Statement [/B] Inside a sperical dielectric mass there is a electric dipole on the center of the sphere. The sphere has radius a. This dieletric sphere is inside and on the center of a conductive spherical shell of radius b. The problem asks to find the potentials and then the...

I read that : An electric potential (also called the electric field potential or the electrostatic potential) is the amount of work needed to move a unit positive charge from a reference point to a specific point inside the field without producing any acceleration. Typically, the reference point...

Homework Statement An electron in a hydrogen atom does not fall to the proton because of quantum motion (which may be accounted for by the Heisenberg uncertainty relation for an electron localized in the volume with size r). This is true because the absolute value of the Coulomb potential...

Homework Statement (i) Consider a non-conducting sphere of radius R with non-homogeneous charge density ρ = ρ(r) = r, where r is the radial co-ordinate. (a) Find the electric field inside and outside of the sphere(b) Find and plot the electric potential inside and outside of the sphere...

Homework Statement (The complete problem statement and solution are inside the attached picture) Two isolated, concentric, conducting spherical shells have radii ##R_1=0.500 m## and ##R_2=1.00 m##, uniform charges ##q_1=2.00 mC## and ##q_2=1.00 mC##, and negligible thicknesses. What is the...

In a barrier potential with sections: I: V(x)=0 (x<-a), II:V(x)=V (-a<x<a) and III:V(x)=0 (a<x) you can write the solution in this form: Ψ(x)=Ae^(ikx)+Be^(-ikx) (x<-a) Ψ(x)=Ce^(ik'x)+De^(-ik'x) (-a<x<a) Ψ(x)=Ee^(ikx) (a<x) and with boundary conditions solve, but why do you can write this...

Homework Statement A nonconducting sphere of radius r0 carries a total charge Q. The charge density ρE increases as the square of the distance from the center of the sphere, and ρE=0 at the center. a) Determine the electric potential as a function of the distance r from the center of the...

Homework Statement Q7. Some lead shot with a mass of 50 grams is placed into a card board box the distance from one end to the other being 1m. The ends are sealed with rubber bungs in order to prevent the lead shots from falling out, the tube is rotated so the lead shots fall down from one end...

Homework Statement Plot the electric potential ##V(r)## due to a positively charged particle located at the origin of an XY plane. Homework Equations ##V=\frac 1 {4πε_0} \frac q r## The Attempt at a Solution I'm unfamiliar with 3D coordinates at this time, but I like to know how can I plot it...

potential energy is the work done by an external force in taking a body from a point to another against a force. on the surface of a conductor the electrostatic charges arrange themselves in such a way that the net electric field is always zero. so if there isn't any force to act against why...

Say, we have two particles of equal and opposite charge in an isolated system in which we neglect gravity. The energy of particle 1 is: E1 = U1 + T1 Where U1 is electrostatic potential energy and T1 is the kinetic energy of particle 1. The energy of particle 2 is: E2 = U2 + T2 Where U2 is...