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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What is the relationship between potential energy and electrical potential?

I actually always thought this was trivial, now I am not so sure. For a potential $\phi$ the potential energy is $V=q\phi$ where q is a test charge. Now I am thinking this may work differently in two ...
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20 views

Working with the problems related to potential energy

Consider a spring mass system. A block is attached to a light vertical spring which is stretched under the load of block and this system is at a height $h$ from the ground. Now my problem is ...
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118 views

If systems minimize their potential energy, why do people climb mountains?

A person climbs a mountain. They convert the stored chemical energy of food in their body and back pack into heat energy on the mountain, and gravitational potential energy as they move towards the ...
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1answer
33 views

Understanding electric potential in the context of gravitational potential?

I'm trying to understand the concept of electric potential and the significance of an electric field being related to the gradient/derivative of an electric potential. I found this question that ...
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1answer
132 views

How can energy be negative in a finite square well?

Say if the potential $V(x) < 0$ in the well but the sides or the scattered states its zero potential, anyways How is that the energy in the well is less than zero? Is it because the potential ...
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Is 12-6 Lennard-Jones potential smooth confining potential? [on hold]

It's obvious that 12-6 LJ is a 2-body potential. The potential $V$ is said to be a confining potential $V(\pmb{q}) \to \infty$ whenever $\pmb{q}_i \to \infty$ or $||\pmb{q}_i - \pmb{q}_j|| \to ...
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Self enery of a sphere [on hold]

If we have a sphere of radius 2R in which there is a cavity of radius R with concentric centre . Now we have to find self energy. I searched and got 3 methods : 1) U'' + U' + U* = U In this we ...
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64 views

Does contracted spring weigh more than stretched one?

(One of examples that potential energy contributes to mass.) Does hot object weigh more than cold one? (One of examples that kinetic energy contributes to mass.) If these are true and justified by ...
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449 views

Mass in special relativity?

Is the mass of a object at rest defined by $$E=mc^2$$ where $m$ is the rest mass. I.e. does the rest mass include every thing from thermal to gravitational potential energy and every other possible ...
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44 views

What is the difference between the potential difference and potential energy of an electron?

What is the difference between the potential difference and potential energy of an electron? Let's take an example the potential difference (PD) across a resistor. if there's a current flowing, the ...
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2answers
64 views

Whats the meaning of this equation relating electric field and potential energy?

My electrodynamics teacher was explaining that it is required to apply some energy (or do some work) on charges in order to arrange them in space. When he stated an example about energy in a capacitor ...
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1answer
235 views

Potential energy of springs and gravity, and work of a force

I am currently really stuck on this problem and I am not sure how to actually solve it, I think I can reason it out logically but I do not know how to show it. Here it is and under I will show what I ...
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19 views

Does a charge difference necessitate a potential difference?

Consider two metal objects, X and Y that when connected by a conducting wire results in a transfer of electrons from Y to X. What can be concluded about X and Y before the connection was made: ...
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1answer
20 views

Problem involving Energy Method and Non-conservative Forces [closed]

I've got a problem in my physics I class that's got me stuck at the moment. A box is placed onto an angled plane so that it compresses a spring. When released, how far up the plane does the box go? ...
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2answers
27 views

Trouble understanding non-conservative force and work

I am having some trouble defining whether a force is conservative or not. In the example that we are working on a mass on a pulley system is used to cause a slender bar to rotate from rest to a ...
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6answers
148 views

When we write that $F = -\nabla V$ , what would happen if we ommit the (-) minus sign

I have had this question for a long time. In classical mechanics, if we choose $\mathbf F = -\mathbf \nabla \, V,$ with the minus sign, we can proof the work - kinetic energy theorem. What are the ...
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2answers
39 views

Potential Energy of Point Charges in a Square [closed]

So, an AP Prep book for the Physics 2 test has the following problem: My reasoning is as follows: The total potential energy = the sum of the PE of each of the 4 charges Which will equal 4x the PE ...
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What is the physical meaning of potential energy in a band diagram of a semiconductor?

According to this slide (from this website), the potential energy of an electron in a semiconductor is defined by the difference between the Energy level of the conduction band and the fermi level. ...
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6answers
81 views

Why does positive work done by internal conservative forces $\implies$ decrease of potential energy?

Potential energy can be thought as the amount of work that the force can potentially do on the point because of its position. $$W=-\Delta U=U_{initial}-U_{final}$$ A positive work done by a force ...
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1answer
35 views

Energy diagram of a planet with fixed mechanical energy

Consider the following energy diagram for the motion of a planet about a star. The centrifugal potential curve can be represented once I fixed the angular momentum $\vec{L}$ of the planet. To fix the ...
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4answers
2k views

Why should Conservative forces have their curl equal to zero?(intuition)

There are several conditions that must be met in order for a force to be conservative. One of them is that the curl of that force must be equal to zero? What is the physical intuition behind this? If ...
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2answers
49 views

What is the relationship between potential energy and inertia?

It seems to me that the two are very similar! Potential energy seems to either explain, or partially explain, directly or indirectly, the law of inertia. I already know that bodies do not move because ...
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3answers
923 views

Electrostatic energy integral for point charges

The electric energy stored in a system of two point charges $Q_1$ and $Q_2$ is simply $$W = \frac{1}{4\pi\epsilon_0}\frac{Q_1Q_2}{a}$$ where $a$ is the distance between them. However, the total ...
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1answer
56 views

Energy stored in electric field [duplicate]

I know that energy stored in electric field / unit volume = $\frac{1}{2} \epsilon\,E^2$. so can I say that for any configuration calculating $\int \frac{1}{2} \epsilon\, E^2 \,d^3r$ over whole space ...
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78 views

Zero Potential Energy Change in Raising a Mass

Suppose I am able to lift a body of mass $m$ up using a constant force $F=mg$ so that net acceleration is zero on it. I want to find the potential energy and the total energy of the body when I have ...
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Relation between Electric field and potential

I am unable to understand from this - sign comes. Which step I have done wrong?
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31 views

Inconsistency in solving energy in free space given electric potential

So we have the equation $$ W= \frac{1}{2} \int_{volume} \rho_v V\,dv$$ and then after applying a vector identity which is $$\nabla \cdot (V\vec{D})=V(\nabla\cdot \vec{D})+\vec{D}\cdot (\nabla ...
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The “potential energy” degree of freedom?

I'm reading Schroeder's "An Introduction to Thermal Physics" and he mentions the vibrational degrees of freedom of a diatomic molecule: A diatomic molecule can also vibrate, as if the two atoms ...
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Why doesn't an object, despite having a non-zero potential energy stored in it, fall by itself from the elevation?

When an object is at a certain height, it has some energy stored in it as we have done some work on it to get it to that height. So when it already has energy, then why doesn't it fall off from the ...
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4answers
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What is $V(x)$ in Schrödinger's equation?

In the time-independent Schrödinger equation it is stated that $$-\frac{\hbar^2}{2m}\frac{d^2\psi(x)}{dx^2}+V(x)\psi(x)=E\psi(x)$$ And it is common to give $V(x)$ some standard "forms": the infinite ...
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32 views

When should gravitational potential energy be included in the law of conservation of energy

I have a problem that says: A block of mass 0.249 kg is placed on top of a light, vertical spring of force constant 4 975 N/m and pushed downward so that the spring is compressed by 0.090 m. ...
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Interaction between magnetic moments and magnetic field

Consider a particle with a magnetic moment $\vec{m}$. For simplicity, suppose that this particle is a circle in the plane $xy$ which can rotate around its center of mass along the $z$ axis. If this ...
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436 views

Center of mass error - calculating systematic error in change in PE

Suppose we have to calculate systematic error in change in PE. Let's suppose systematic error due to scale is 1%. I'm confused about the center of mass error. \begin{align} \Delta PE = m*g*h_1 - ...
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2answers
55 views

How does conservation of energy work?

I understand that the law of conservation of energy states that energy cannot be created or destroyed, it can only change from one form to another. This means that the total energy before a certain ...
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Potential energy of a shell & point system

Consider the system of a point particle with charge $q$ and a spherical shell with uniform charge $Q$ and radius $R$ whose center is a distance $r > R$ away from the point particle. I'm trying to ...
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2answers
39 views

Relationship between work and energy in an electrostatic system

I am having problems understanding the relationship between the concepts of Work and Energy in a electrostatic system. As I know, the definition of Potential Energy is the ability to do work. In a ...
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32 views

Meaning of centrifugal term in the mechanical energy of a orbiting planet [duplicate]

For a planet under the effect of gravitational force the mechanical energy can be written as $$E=\frac{1}{2}\mu {\dot{r}}^2+\frac{L^2}{2\mu r^2}-\gamma \frac{m M}{r^2} \tag{1}$$ Where $\mu$ is the ...
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1answer
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Why can't I use conservation of energy to find ratio of final velocities on different planets?

The question is An object of mass $m$ is allowed to slide down a frictionless ramp of angle $\theta$, and its speed at the bottom is recorded as v. If this same process was followed on a planet ...
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1answer
249 views

Finding the components of the tensor for potential and kinetic energy

I have a rather poor understanding of what a tensor is, but enough to apply it to the biggest part of the classical mechanics I'm studying. However, I've run into a small problem while studying "Free ...
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4answers
230 views

How is energy converted when massless spring is attached to a rigid support

Say a massless spring of length l is attached to a rigid support. It is extended to length l + x. Now at this position, the ...
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13 views

Electric potential energy of a charge

Potential energy is the work done by the particle against a conservative force. Isn't it? when a charge is fixed on a free space and then when we bring another charge from infinity to a distance r ...
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2answers
773 views

Work done by a non-conservative force and change in potential energy

I know that the work done by a non-conservative force is equal to the change in total mechanical energy (from Work-Energy Theorem). But I read in a place that "Non-conservative forces don't affect ...
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144 views

Help understanding the solution to a problem regarding kinetic energy of a group of point charges

The problem provided by my professor goes as follows: "Now consider a situation in which all charges are equal to q and they simultaneously become "unglued". What speed will each charge have when a ...
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2answers
87 views

Physical meanings of kinetic energy

While studying energy on Sears & Zemansky's University Physics, I came up with a doubt on the meaning of kinetic energy. The book gives two possible physical interpretations of this quantity. ...
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1answer
30 views

Total potential energy in electric field?

if there are 2 charges generally potential energy of the system should be the sum of individual potential energy. but why the potential energy is half of the sum of every individual charge's potential ...
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1answer
29 views

Directional derivative of the potential energy in the direction of the displacement in three dimensions

For a conservative force $\vec{F}=-\vec{\nabla } U \implies \mathrm dW= -\vec{\nabla} U \cdot \mathrm d\vec{s} $ Where $\mathrm d\vec{s}$ is the infinitesimal displacement. For a differentiable ...
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Why do a conservative force try to reduce potential energy?

Mathematically I understood the reason why, for a conservative force, $\vec{F}=-\vec{\nabla}U$. Physically this means that a conservative force is always oriented in the direction of greatest ...
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Why is the longitudinal term removed to form the Lorentz force equation?

Beginning with the expression for interaction energy, and deriving the potentials form for the force on a test charge moving at velocity $\vec v$ yields: $$\vec F = q(-\nabla\phi - {D\vec A \over ...
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About Electric potential

when we bring a unit positive charge from infinity to a point in the electric field EF does work on the charge and external work is also done on the charge in same amount but in opposite sign. then ...