Potential Definition and 1000 Threads

Homework Statement A beam of particles of mass m and energy E is incident from the right unto a square well potential given by ##V(x)=-V_0## for ##-a<x<0##, and ##V(x)=0## otherwise. Solve the Schrodinger equation to determine the wave function which describes this situation. Determine the...

In class while learning about electromagnetism, I was given the following two equations: U=-μ⋅B τ=μ×B where μ=IA First of all, what does μ stand for? How should I interpret the relationship between potential energy (U) and torque? Can someone explain this in terms of μ and B?

Homework Statement Homework EquationsThe Attempt at a Solution a. ##{ P }_{ avg }=\frac { 1 }{ 2 } \mu v{ \omega }^{ 2 }{ A }^{ 2 }=\frac { 1 }{ 2 } 0.075\frac { 10 }{ 3 } { 0.35 }^{ 2 }{ (10\pi ) }^{ 2 }=15.1W## b. Not sure how to calculate that... I'm guessing it'd be some integral over 1...

I have a discussion going on with some friends. The discussion goes like this: We have two identical tanks. One is empty. One is full of water. Both placed on the ground. They are connected with a hose at the bottom. There is a ball valve in line with the hose. The full tank has a given...

Homework Statement The volume charge density for some charge configuration is given as ## \rho (x,y,z) = \lambda \delta(x) \delta(z) [\theta(y+L)-\theta(y-L)]## where ## \theta(x)## is the step function, defined as ##\theta(x)=1## for x>0 and 0 for x<0. a) Calculate V(x,y,z), the potential...

Homework Statement I was going through a worked example in my textbook to gain a better understanding but after I had a go myself it is the opposite to what I have calculated. I have attached the worked example which asks you to calculate the gain in gravitational potential moving from a point...

Homework Statement A disc of radius R lying in the xy-plane is composed of an inner disc of radius R/2 carrying a uniform surface charge density +σ and an anulus (inner and outer radii of R/2 and R) carrying a uniform surface charge density -σ. Assume that the inner disc and the annulus are...

Homework Statement ( The following problem is taken from kleppner's " Introduction to mechanics" ) ( The question in the book talks about the velocity but my confusion is related to the Energy ) Homework Equations Conservation of Mechanical energy : Ef - Ei = 0 Consevation of Momentum : Pf -...

Homework Statement Find the potential at points P1, P2, P3, and P4 in the diagram due to the two given charges. Homework Equations VP =k∑qi/ri p = q ⋅ d The Attempt at a Solution I'm not sure how to approach the problem. I thought about using that given equation four times and adding it all...

Homework Statement What is the strength of the electric field between two parallel conducting plates separated by 1.00 cm and having a potential difference (voltage) between them of 1.50×104 V? Homework Equations ΔV = qΔU ΔV = -∫E⋅dl E = kq/r2 The Attempt at a Solution I am not sure where to...

I've been studying PEM fuel cells for a while and wondered if they could be used for electrolysis. I was surprised at first to find out the technique had been used for decades, but after watching this animation the dynamics make much more sense...

If we had a a sample of atoms in thermal equilibrium at a temperature, T, it would approximately follow a Maxwell-Boltzmann distribution and be isotropic. But if we now subject these atoms to a force in one direction (e.g. gravity, perhaps near a dense object), it will take the system out of...

Homework Statement A particle with mass m and spin 1/2, it is subject in a spherical potencial step with height ##V_0##. What is the boundary conditions for this eigenfunctions? Find the degeneracy level for the energy, when it is ##E<V_0## Homework Equations Radial equation \begin{equation}...

In the case of lifting a box, I know potential energy is negative because negative work is done by gravity. What does the negative part of -PE denote? Does it denote the direction of the energy or does it mean that energy is being lost? But how is energy being lost if the box gains more...

My book says: "Let us derive an expression for the potential energy associated with an object at a given location above the surface of earth. Consider an external agent lifting an object of mass ##m## from an initial height ##y_{i}##above the ground to a final height ##y_{f}##. We assume the...

Is the potential energy of a symmetric planar (x,y) charge distribution lower than any non symmetric distribution ? from the discussion on Gauss's law and symmetric charge distributions I would think so because the electric field could only be normal to the (x,y) plane in the symmetry case but...

Hi guys! I was wondering about the relation between the Gradient, Electric Potential, and Electric Field. I know that if you take the Gradient of a scalar field, you get a resultant vector field in which the vector points in the direction of greatest increase when you take a infinitesimally...

Homework Statement I have a few questions I'd like to ask about this example. (C1 was already derived before the second part) 1. What does the line "The rest of the coefficients make up the difference" actually mean? 2. What does "As one might expect...because of the admixture of the...

Homework Statement Determine the potential difference across the plates of the capacitor of the network shown in the figure. Homework Equations kirchoff's loop rule q=vc 3. The attempt at a solutio applying kirchhoffs law starting at bottom right point, q/c2-E1+q/c1+E2=0 =>E2-E1=-q/c1-q/c2...

work done in taking positive charge from A to B in electric field E= potential energy at B - potential energy at A OR potential at A-potential at B Am i correct in both formula?

How can I find the potential energy of a string of mass m and length L that has a block of mass M attached to it? The string is uniform, so I know its center of mass is at L/2.

Homework Statement When calculating the Fourier coefficients of the potential of the following lattice (the potential is a sum of deltas at the atom sites): I get the wrong coefficients if I choose the following primitve cell, with primitve vectors a1,a2: And the right coefficients if I...

From CNN: Powerful Hurricane Irma is rapidly intensifying in the open Atlantic and poses a major threat to the Caribbean and potentially to the United States next week. With the storm still five days away from the outermost Caribbean islands and at least a week away from any potential US...

My textbook states that an alternative definition of the change in potential energy is the work required of an external force to move an object without acceleration between two points. I am confused on why it says acceleration. Wouldn't that mean that the acceleration is 0 and therefore the...

Why there is the term ##\frac{3}{5}## in the formula of the electrostatic potential of a nucleus $$U_e = \frac{3}{5} \cdot \frac{(Ze)^2}{4 \pi \epsilon_0 R}$$

Homework Statement Two concentric spheres have radii a and b with b>a. The region between them is filled with charge of constant density p. The charge density is zero everywhere else. Hence, find the electric field of all points , then find the electric potential. 2. Homework Equations [/B]The...

Homework Statement In Fig. 26-5, how large must R be if the potential drop from A to B is 12 V? (The figure has been pasted into the attached file). The answer to this problem is 3.0 ohms. I keep trying to solve this problem but I get a wrong answer. The answer I get from my calculations does...

Homework Statement A molecule of nitrogen has a diameter of 3.2 x 10-8 cm and can be ionized upon absorbing 14.5 eV. what potential must be applied to a parallel-plate ion chamber operating at a pressure of 50mm of mercury, and with an electrode separation of 3.0 cm, in order to produce...

Homework Statement An electron that accelerates from a point near a collection of negative source charges toward a point near a collection of positive source charges experiences A) a decrease in electric potential energy as it moves toward a region at a lower electric potential B) a decrease...

Homework Statement A point charge of + 2.0 μC is placed at the origin of coordinates. A second, of − 3.0 μC, is placed on the x-axis at x = 100 cm. At what point (or points) on the x-axis will the absolute potential be zero? Homework Equations V= ko*∑ (q/r) The Attempt at a Solution My work...

Here is the Wikipedia page on electrode potentials. Here's how I'm reading it, which makes no sense: If a singly ionized atom of strontium donates an electron to the hydrogen in the standard hydrogen electrode, this will emit 4.101 eV of heat (395.68 kJ/mol). If cesium is used, there will be...

This might be either an obvious one, or I might be totally off track. I haven't seen, or been able to find neural action potentials being referenced as signal transductions. Aren't they signal transductions? And if not (say if action potential is only referenced to the change in potential)...

Potential of a body is defined as the amount of work done in bringing that body from infinity up to some point divided by its charge. The Earth has zero net charge, so the work done in bringing any charge from infinity till the Earth is zero. So what do statements like, "The potential of this...

when the external electrical potential difference is applied across the conductor ,electrons flow in the direction opposite to the current.Whether the number of free electrons in the conductor decrease?

Homework Statement I want to find the charge and potential drop across each capacitor Homework EquationsThe Attempt at a Solution I know both the capacitors are in series and hence have the same charge on them. However I don't know how to calculate the potential drop across the capacitors...

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 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...