Questions tagged [potential-energy]

Potential energy is the energy of a body or a system due to the position of the body or the arrangement of the particles of the system.

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Deriving the Lagrangian of a set of interacting particles only from symmetry

In section 5 of Landau and Lifshitz's Mechanics book, they show that the Lagrangian of a free particle must be proportional to its velocity squared, $\mathcal{L} = \alpha\mathbf{v}^2$ using only ...
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Dilemma in Theory of Superposition of Electric potential

Electric potential is the amount of work done in bringing a unit charge from infinity to a point. Here we take infinity as a reference point. The unit charge might have higher or lower potential ...
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Does potential energy break Poincare invariance down to invariance under Lorentz boosts?

Landau and Lifshitz (Mechanics, Vol. 1) derive the form of the Lagrangian for a free particle by requiring invariance of action under Galilean transformation and assuming homogeneity and isotropy of ...
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What is the relationship between velocity-dependent potentials and non-Abelian gauge fields?

My (limited) understanding of non-Abelian gauge fields is that they arise from the construction of a theory using a non-Abelian Lie group (as a generalization of the Abelian group underlying E&M) ...
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What is a good analogy for electric potential?

When the electrical field was defined I could totally relate to $\vec{E}$ being like $\vec{g}$ in mechanics. But for the electric potential I don't know what would be equivalent analogy. Any ...
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Why does the law of conservation of energy not hold true when the work-function $U$ depends explicitly on $t$?

[...] the infinitesimal work $\overline{\mathrm dw}$ comes out as a linear differential form of the variables $q_i$: $$\overline{\mathrm dw}= F_1~\mathrm dq_1 +F_2~\mathrm dq_2+ \ldots + F_n~\mathrm ...
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How to efficiently cool down simulated gas by time-dependent potential?

I'm trying to simulate condensation of a highly diluted gas (a model gas, not any real one). For simplicity I restrict the simulation to 2 dimensions. To setup the simulation I take some interparticle ...
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Gravitational potential energy and center of mass

I've been reading about the Nordtvedt effect, and how Gravitational Binding Energy (GBE) affects total mass. According to the WP article, experimental evidence rules out the existence of this effect. ...
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Reference needed for effective gravitational potential in General Relativity

In Wikipedia ( https://en.wikipedia.org/wiki/Two-body_problem_in_general_relativity ) one can find the following expression for the effective gravitational potential in the Schwarzschild approximation ...
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1answer
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Charge on the plate of the capacitor

I was reading parallel plate capacitors in my book today and there I saw that the battery provides +Q charge to positive plate and -Q charge to negative plate? But we know that only electrons can flow ...
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1answer
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Intuiting qualitatively the shapes of the eigenfunctions of a finite well-like potential, using the infinite well eigenfunctions as an inspiration

Consider, for example, the third excited state of an infinite square well: Now consider the following potential: If we wanted to sketch the rough shape of the third excited eigenfunction of this ...
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1answer
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Doubt on calculation of a “general expression” on the energy of a travelling wave in a column filled with gas

I) SOME FACTS When we study mechanical waves, we essentially have to deal with $dm$ mass increments; then we can "expand" they as: $$ dm = \rho(x,t)dV.\tag{1}$$ Also, I think that it's pretty ...
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Why potential energy of a non-relativistic particle in an expanding universe is $ma^2\phi$?

I have been reading a paper on neutrino clustering in an expanding universe: see section 3, particularly 3.3.2 of this paper. In this paper for non-relativistic neutrinos, which travel through a ...
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156 views

Rotational potential energy on a system of two masses

On a homework assignment, we were given the following problem: This system is held at equilibrium according to the configuration in the image; initially the body B is at rest, and the body A is ...
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87 views

Total potential energy and equilibrium

Suppose a deformable body is under an external load. If there is no inclusion of gravity. When the body reach an equilibrium state, will the total potential energy be equal to zero? The total ...
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Binding energy in Euclidean Gravity

I suppose I'm asking in the context of classical gravity, but an answer in the effective GR quantum theory would be fine too. I can't seem to find much on the attractive nature of the gravitational ...
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1answer
161 views

Why does mass increase when gravitational potential energy increases?

I saw a solved example in a book (Concepts of Physics by H.C. Verma, volume 2), where there is a body near surface of the earth, the problem is to calculate the increase in mass of the body when it is ...
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2answers
841 views

Perturbation theory with infinite potential

I'm trying to solve an excercise that involves first order perturbation theory and an infinite potential. To ease the problem, I tried to consider an easier one dimensional model. Consider an infinite ...
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1answer
74 views

what is difference between region around a charge and region out of it?

Basically I want to know what makes a region around a charge particle so affective that another charge will have energy when brought in this region or it will experience a force when enters into this ...
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497 views

Conservation of Energy in Capillary Tube

The capillary action lets a liquid rise in a narrow tube to a certain height. In this, the liquid gains some potential energy. According to the Conservation of Energy, the energy must come from ...
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250 views

How can the levels of an asymmetric double well be understood qualitatively?

Consider the potential energy profile above (blue). There are two minima which can be thought of as wells, one much deeper than the other. In the diagram there are a few energy levels that I drew in ...
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157 views

Transform QM radial equation to spherical Bessel equation

I'm currently learning about spherical potentials (ex. hydrogen and hydrogen-like systems) and am trying to work through the problem of a generic spherical potential well such as: $$V(r) = \left\{\...
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1answer
134 views

Potential Energy in a System and its Relation to the Total Energy

In this answer it was stated that potential energy is a property of a system and not an individual particle. If we have two particles (1 and 2) interacting via a conservative force, we can write an ...
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342 views

Question about defining potential energy of a magnetic dipole placed in a magnetic field

We know that magnetic field is a non-conservative field, since it exists in closed loops. Then how can we define the potential energy of a magnetic dipole placed in a magnetic field ?
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297 views

Generalization of Feynman's derivation of the formula for gravitational potential energy in FLP volume I

In the Feynman Lectures on Physics, Feynman derives the formula for gravitational potential energy by applying a line of reasoning he borrowed from Carnot on reversible weight lifting machines (FLP I, ...
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Modelling gravitational potential of a galaxy

I am interested in modelling the gravitational potential of a disc-shaped galaxy with radius $R$, i.e. solving the 2D Poisson equation numerically by Gauss-Seidel relaxation: $$\nabla^2 \phi = 4\pi G ...
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What is the minimum physical distance between two electrons?

If electrons repel, then it seems to me that energy is required to decrease the distance between two electrons. Since energy and mass are equivalent, adding energy to a system also adds some mass. ...
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Differences between time-independent and time-dependent Schrödinger equation for potential generation

Suppose I wanted to develop a potential describing the interaction between two lithium atoms. One way to do this is to calculate the energy between the two lithium atoms for various distances and ...
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Potential energy and atomic units in the Bohr model

I have a question regarding the final sentence written in the solution to part iii) (found below) for the question given below. In the Bohr model of the hydrogen atom, the radius of the electron ...
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1answer
29 views

Nature of stability in a conservative system

In CM, a conservative system can be described by a potential energy function, $V(x)$ The states of the system which will be in equilibrium will be found at the extrema of this potential where: $\frac{...
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2answers
53 views

Law of conservation of energy and potential energy

I completely understand how this law goes and how energy is changed from one form to another. But there is something that I thought about, we all know how the potential energy works and when an object ...
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30 views

Elastic force expression

I would like to know how to properly write the elastic force in the classic x and y axes. I know that the global formula is $\vec{F_{el}}= -k\vec{x}$, but sometimes the situation is little bit ...
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Form of the restoring force in a string which carries a wave

A string is stretched when a wave is traveling over it. We also calculate the potential energy in the string due to the restoring forces,which arise due to the fact that the string is stretched. Since ...
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1answer
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Calculating the amount of energy lost

I am trying to finish up an problem dealing with loss of energy. It is a mini-lab where you take out a bouncy ball and drop it from an already recorded height and then also collect how high it bounces....
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Need help understanding a statement about energy in capacitors

The electric potential energy stored in a charged capacitor is just equal to the amount of work required to charge it—that is, to separate opposite charges and place them on ...
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How much potential energy is in a tritium glowstick?

I have a small tritium key chain light I got for my birthday. It will glow for decades, so I thought it would be fun to try to figure out how bright it is in lumens, and how much energy is stored in ...
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26 views

How can I find the potential energy and force between a steel sphere and a magnet?

I'm fine with certain simplifying assumptions being made, I currently only know high-school level physics (the simpler the better). Also, if anyone can explain the intuition behind formulae, I would ...
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36 views

How to calculate the total gravitational potential energy of a vertical object (do we use integration?)

Hello I was reading another question asked by zach466920, and when he was trying to calculate the total GPE of a water 'tower', he used this explanation: He basically used integration to calculate ...
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1answer
81 views

True meaning of negative energy

Any body in a bound system tends to possess negative total energy, like a satellite in Earth's orbit, according to classical physics. An external agent needs to expend energy in order to bring such a ...
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Landau & Lifshitz 'Mechanics': How is the potential energy related to additive property of Lagrangian?

By additive property of Lagrangian, I mean following: Let a system consist of two parts A and B which are not interacting with each other, so A and B will have separate Lagrangians $$L_a,L_b$$ and in ...
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82 views

Efficient calculation of potential energy of $n$-body system

Consider $n$ bodies which interact solely through Newtonian gravity/Coulomb force, then the total potential energy of the system can be obtained as: $$U =\pm \sum_{1\leq i<j\leq n}\frac{G\alpha_i\...
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53 views

What happens to the potential energy of an electric circuit during a voltage drop?

Is it accurate to say $$ W=\int{Fdx}=\int{EQdx}=\int{\frac{dV}{dx}Qdx}=QV$$ so voltage is like g*h it is a potential field and charge is like mass. We know that the energy flux(vector) is given by the ...
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1answer
44 views

Momentum probability distribution for $V(\mathbf{r})$ vs $V(\mathbf{-r})$ is the same?

Checking a thought I had... Given two potentials, $V(\mathbf{r})$ and its mirror potential $V(\mathbf{-r})$, the momentum probability distributions would necessarily be equivalent, right? I'm ...
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Is the relation between change in potential energy and work by internal conservative force can be used even in presence of non conservative forces?

We know that work done by internal conservative forces is the negative of change in potential energy of the system stored in conservative force field. But does this logic still hold when there are non-...
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27 views

Equipotential and Work on Electric Charges at Rest

Why exactly do lines of equal potential exist on a point charge at rest? This doesn't make sense to me if the point charge is hypothetically a lone charge undisturbed by other charges. I'm reading ...
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3answers
106 views

Velocity not affecting heat produced by impact

A bolt of mass 0.3 kg falls from the ceiling of an elevator moving down with an uniform speed of 7 $\text{m s}^{–1}$. It hits the floor of the elevator (length of the elevator = 3 m) and does not ...
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Can I add a classical potential to S-matrix

I'm a junior learner of QFT, and I wonder if I can add a classical approximated potential (like Coulomb potential) to a total interaction \begin{equation}V=V_{\mathrm{Coulomb}}+V_{\mathrm{internal}} \...
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1answer
243 views

Two Opposite Point Charges: Infinite Potential Energy?

If I had a fixed point-charge ($q_1$, +) and I placed another free-moving charge ($q_2$, -) some distance away, what is the potential energy between them? The opposite charges attract drawing $q_2$ ...
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1answer
106 views

Potential Drop across Inductor VS Potential drop across Rotating coils in $B$-Field

I was trying to understand the difference between the Back emf generated across Inductor due to change in current and Back Emf Generated across a coil that is rotating in presence of B Field. ...
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Potential Energy Graph for Nuclear Force

when you draw PE energy graph wrt to distance between two interacting nucleons, at distance $r$ around 1 fm, graph has the lowest PE and is point of stable equilibrum. For $r >$ around 1fm, nuclear ...

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