Potential Definition and 1000 Threads

1. Since the gravitaional field strength is 1/6 of that on Earth: W=mg W=90*9.81/6 W=90*1.635 W=147.15 ~ 147 N 2. ∆Ep=mg∆h ∆Ep=90*1.635*50 ∆Ep=7357.5 J I do not now whether this method would be suitable and if I should have instead used the formula for gravitaional Potential, V grav=-Gm/r? 3...

Potential energy is generally a function of position vector ##\vec r## and it is defined as ##\int_i^f \vec F(\vec r)d\vec r=-U(\vec r) \bigg| _{i}^{f}=U(\vec r_i)-U(\vec r_f)##, where the force is conservative. Using the fact that the integral of force is also the definition of work, I obtain...

I have a lot of questions about this single concept. You don't have to answer the questions in the order that I ask, if it is convenient to answer them in a different order. 1. When the dipole moment ##\vec{p}## is in the same direction as the electric field (uniform) it has the least potential...

Sorry - I wish I had some way of writing equations in this forum so the "relevant equations" section is easier to read. The answer to the first part is (a) so the rest follows from using the electric field given in B. If anyone is interested this question comes from Griffith's 3rd edition...

I've tried doing it but i haven't been able to find the resistance of the diode.

hello I would like some help with the first part of this homework. for the moment i have done this: E initial=m*g*h Efinal= 1/2 m*v ^ 2+1/2I*ω ^ 2 Ei=m*g*h+1/2I*ω ^ 2 Ef=1/2*m*v ^ 2 my doubt is with the potential energy since it confuses me when there is or not...

we know ##W_g = -\Delta U## but here to find ##\Delta U## we will need another equation won't it be wrong to write $$-\Delta U = -\int_1^{0.8}mgdy$$ as this equation is derived from ##W_g = -\Delta U## and as we have 2 unknowns we will need two equations. this is a rather easy problem but I am...

I'm reading Schutz's A First Course In General Relativity and in chapter 5 he discusses an idealized experiment in which an object is dropped from a tower, then turned into a photon and sent back up to its original height. In classical mechanics we would say that as the object falls it loses...

Here is what the solution says: As usual, quote the general potential formula: $$V(r,\theta)=\sum_{l=0}^{\infty}(A_lr^l+\frac{B_l}{r^{l+1}})P_l(cos\theta)$$ The potential outside the sphere is: $$V(r,{\theta})=\sum_{l=0}^{\infty}\frac{B_l}{r^{l+1}}P_l(cos\theta)$$, which makes sense to me...

Hello, I was going to solve numerically the eigenfunctions and eigenvalues problem of the schrödinger equation with Yukawa Potential. I thought that the Boundary condition of the eigenfunctions could be the same as in the case of Coulomb potential. Am I wrong? In that case, do you know some...

Hello, I was going to solve with a calculator the eigenvalues problem of the Schrödinger equation with Yukawa potential and I was thinking that the boundary conditions on the eigenfunctions could be the same as in the case of Coulomb potential because for r -> 0 the exponential term goes to 1...

Hello! I read in several papers (e.g. this one) that if we have 2 levels of fixed, opposite parities, which are the eigenstates of a P,T-even Hamiltonian, and we add a perturbing potential which is P-odd, T-even, the matrix element of the new potential between the 2 states of opposite parity...

This question is an example in Durcell's Electricity and Magnetism. The solution goes as follows: [In this case] there are four different types of pairs. One type involves the center charge, while the other three involve the various edges and diagonals of the cube. Summing over all pairs yields...

I tried finding the potential due to a small element dM of the ring let's say dV, the summation of dV for all the dM's of the ring will give the potential at the point P, but since every element dM of the ring is at a different distance from the point P I am unable to come up with a differential...

the gravitational potential energy of a body at any point is defined to be negative of the work done by the conservative force(gravity in this case) from bringing it to that point from a given reference point. if the reference point is taken to be at infinity and the potential energy at this...

In Tersoff Brenner formula: -Do I calculate the bij then bij or calculate bij only ? -In the figure , explaine to me wath are the neighbors atoms of atom 1 can we use for calculate bij ? - Wath is the range of bij ? - Can we use the Tersoff Brenner potential for silica?

The answer key says the correct option should be a, but I think it should be b. Because Y has a reduction potential same as the element B. An element is a good reducing agent only if its reduction potential is negative or less positive.

I know that (1/2)m(u^2) is KE and initially I thought this showed PE=KE but I don't think so anymore... I believe this has something to do with acceleration and Centripetal force but I'm so so confused

When I see explanations for quantum tunneling, the discussion is around the probability of an electron manifesting itself before the potential barrier, and after the potential barrier. However, looking at the curves draw, there is a non-zero probability (the evanescent part of the wave) inside...

Reference frame is an accelerated frame in SR (uniformly accelerated with "g" in flat spacetime). An object is falling with relativitic velocity of up to 0.8 c in the pseudo-gravitational field in this frame. From Newton's theory, I know the formula for potential energy in such a scenario: ##W...

Hi all, I got my Ph.D. a couple of years back (HEP physics) but for various reasons I never applied for any postdoc positions. I ended up working as a software engineer. It's been alright, it pays the bills, but I really don't give a damn about the work and feel quite unfulfilled and...

Let us connect a battery of potential difference V to a wire. There is no resistance. Nothing! Now the battery creates some potential difference and the charges in the conducting wire move due to the Electric field created in the conductor by the battery. So, as the charge moves, its potential...

I have a basic question in elementary quantum mechanics: Consider the Hamiltonian $$H = -\frac{\hbar^2}{2m}\partial^2_x - V_0 \delta(x),$$ where ##\delta(x)## is the Dirac function. The eigen wave functions can have an odd or even parity under inversion. Amongst the even-parity wave functions...

The dam is a series of massive re-bar and concrete wide base tapering to narrower top. Does anyone know if these structures are " tied" togeather via connecting rebar sections? I researched and apparently no piles were drive into bedrock so only the shear weight is anchoring the massive...

White House Coronavirus advisor Dr. Anthony Fauci said Tuesday that U.S. health officials are keeping an eye on a new strain of flu carried by pigs in China that has characteristics of the 2009 H1N1 virus and 1918 pandemic flu. The virus, which scientists are calling “G4 EA H1N1,” has not yet...

Recently I have encountered the following expression for the potential energy of a magnetic dipole of moment ##\boldsymbol{\mu}## placed in an external magnetostatic field B: $$U=-\boldsymbol{\mu} \cdot \textbf{B}$$. However, I was told that magnetic fields are non-conservative, so we can't...

The Wilson-Sommerfeld quantization rule claims (##\hbar=1##) $$\frac{1}{2\pi} \oint p(x)\,dx=n,\,n=1, 2, ...$$ where integration is done in the classically allowed region. Applying this to a square-well potential with a depth of ##V_0## and width ##a##, we get $$E=\frac{\pi^2 n^2}{2a^2}$$ This...

I was looking at this chart and I didn't understand how increased angular momentum of the test particle curves the spacetime around the center mass. If that is how it's interpreted. Now the way it looks like is that the curvature is dependent on the angular momentum of the test particle.

I know that in the case of central potential V(r) the hamiltonian of the system always commutes with l^2 operator. But what happends in this case?

I am struggling over a problem and i could really use some help in this. So it's about finding phase shifts in a localized sphere of coulomb and harmonic potential. I tried solving the radial Schrodinger equation for both of them by using power series method, but still i am having problem...

I would differentiate this twice and plug it into the S.E, but for that I'll need E. Which I don't have. Please provide me some direction.

My solution is making an analogy of the ##\text{Relevant equations}## as shown above, starting from the equation ##\vec \omega = \frac{1}{2} \vec \nabla \times \vec v##. We have ##\vec B = \vec \nabla \times \vec A = \frac{1}{2} \vec \nabla \times 2\vec A \Rightarrow 2\vec A = \vec B \times...

Not sure how the problem set up initially as no diagram was provided in the question. Please help me to start with the solution. Your assumptions and educated guess are appreciated.

Hello everybody! I want to check out if I've solved correctly: ##\Delta{V}=-E\Delta{x}## ##\dfrac{\Delta{V}}{\Delta{x}}=-E## ##\dfrac{15\;V}{10^{-2}\;m}=-E## ##1,5\times{10^3}\;N/C=-E## ##\vec{E}## direction it's oriented into the XY plane Thanks!

Hi, Is there a liquid/liquid junction potential between two liquids of same composition but different concentrations WHEN there is no external electrical circuit and then NO electrodes? (Of course this potential is not measurable). Thanks,

m.g.h = (GMm)/r how can we prove that mgh is potential energy and both equal to that?

I've marked the right answers. They mainly indicate at power carried by the particles being zero, and here is my doubt- why should it be zero? Shouldn't it have some definite value? I do understand that the kinetic energy is max at the y=0 and potential energy is max at y=A, but I don't know...

1. The student should use a rubber band, g-clamp, a retort stand, boss and clamp, a mass hanger, 100g masses and a metre rule. The rubber band should be positioned to hang freely from the retort stand, held in place by a g-clamp to the laboratory bench. Measure the length of the rubber band...

Greetings! Suppose I have 2 particles that interact via a Lennard Jones potential $$U(\mathbf{q}_{1}, \mathbf{q}_{2}) = 4 \epsilon \left[ \left( \frac{\sigma}{r} \right)^{12} - \left( \frac{\sigma}{r} \right)^6 \right] $$ with interparticle distance ##r=|\mathbf{q}_{1} - \mathbf{q}_{2}|##. The...

Hello folks, So my level of quantum knowledge is equivalent to what is covered in (year one) two short chapters introducing the topic in Knight's Physics for Scientists and Engineers. Ch. 39 introduces the idea of a wavefunction in a pretty simple way, and ch. 40 touches provides the basics of...

I quite understand the fact the EPE (Electrical Potential Energy) of a system of two charges are U = k*qQ/r, Q is fix. however when it comes to three charges i get lost. because my reasoning is : if q1 is fix then the EPE of the system when q2 is brought is U2 = k*q1*q2/r12, when q3 is brought...

Definition of conservative field I use:-it is a field in which potential energy of system is independent of path taken. I understand that it is independent because whenever we take some path than all the perpendicular displacements with respect to force are not counted and if we go further than...

Spring has more potential energy when it is compressed or stretched from its initially balanced state. As external work is done, it stores energy in the form of potential energy. Here, we know energy is stored in spring but For the Earth-ball system, where the energy stored?

I found out the equation of electric potential, that is V=\int_{-a}^a \int_{-a}^{a} \frac{σdxdy}{4 \pi \epsilon_0\sqrt{x^2+y^2+d^2}}=\int_{0}^a \int_{0}^{a} \frac{σdxdy}{\pi \epsilon_0\sqrt{x^2+y^2+d^2}} but I couldn't calculate the integral. It seems convenient if we use the polar coordinate...

For a system of two or more particles, it is customary to define potential energy functions ##V_{ij}## between pairs of particles, so that the total conservative force (not necessarily total) on any given particle is $$\mathbf{F}_i = \sum_{j\neq i} -\nabla_i V_{ij}$$as a sum over all other...

"The force is zero" means the total force act on the particle is zero? Then there must be an external force. If not, then Fx=0 ? since Fx = d(U(x))/dx, the answer of (b) should be (i), but how about (a)?

I think the right choice is c. I'll pass on my reasoning to you: We can think that if the formula of the potential is V(r)=\dfrac{kq}{r} If r tends to infinity, then V(r)=0. But the correct answer is d).

I thought the right choice was d). But when it comes to the solutions, it is b) and I don't understand why. My reasoning would be: the potential at a point is the work that the electric field does to transport a charge from infinity to that point, so if the field is zero, it does no work and...

a) \vec{F}=\vec{E}\cdot q \phi =\oint \vec{E}d\vec{S}=\oint \vec{E}d\vec{S}=\underbrace{\oint \vec{E}d\vec{S}}_{\textrm{FACES } \perp}+\underbrace{\oint \vec{E}d\vec{S}}_{\textrm{FACES } \parallel}=0+\oint EdS\cdot \underbrace{\cos 0}_1= E2S \dfrac{Q_{enc}}{\varepsilon_0}=\phi \left...

I'm falling at the first hurdle here; the time independent Schrodinger becomes $$-\frac{\hbar^2}{2m} \psi''(x) - \frac{\hbar^2}{m}\text{sech}^2(x) \psi(x) = E\psi(x)$$ $$\left(-\frac{d^2}{dx^2} - 2\text{sech}^2(x) \right)\psi(x) = \frac{2mE}{\hbar^2}\psi(x) = \mathcal{E} \psi(x)$$...