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Questions tagged [conservative-field]

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How do conservative forces conserve mechanical energy?

A force that conserves mechanical energy is known as a conservative force. Question: How do conservative forces conserve mechanical energy?
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Can someone explain how magnetic potential energy can exist even though the field is non-conservative?

$U=-B\cdot \mu$ is defined to be the magnetic potential energy, I saw this in my lecture notes, but we had already talked about the fact that since the work done to move a charge there is path ...
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Is friction an emergent phenomenon?

The microscopic origin of the frictional forces is due to contact between irregularities of the surfaces as seen here [1]. Electromagnetic interactions are the fundamental forces responsible for ...
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Meaning of “a force that derives from potential energy”

In mechanics course, when the idea of equilibrium was introduced they included the idea of a force that derives from potential energy which is the force $F$ which is related to the potential energy $...
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Electric Potential: Building system of point charges

How can we prove that the amount of work we have to do to build a system of point charges is same , whether we place the point charges one by one or all at once
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Static electric field which admits no potential

Conservative condition for (static) electric field $\mathcal{E}$ is usually defined as $\mathcal{E}$ being closed (curl-free). Now this clearly holds when for the given manifold $X$ we have $H_\text{...
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Nature of interaction of two magnetic dipoles

Is the force of interaction between two magnetic dipoles a conservative force? If not, how do we find that force?
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Can we define potential for all conservative forces?

I know that defining potential for non-conservative forces is not possible and we can define potential and potential energy for conservative forces only. But can we define it for all conservative ...
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64 views

What is the difference between Non-Conservative and Dissipative?

We often hear these terms. However, they are often confused to be synonyms, but they are not. What are the rigorous definitions of them?
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Do conservative forces obey Newton's laws of motion?

Do conservative forces obey Newton's laws of motion? Is the force between two charge particles a counterexample?
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Is surface tension a Conservative force?

Is surface tension a Conservative force? Can the work done by surface tension be recovered?
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70 views

Potential Energy of Conservative Forces [closed]

For a conservative force, its associated potential energy at position $\mathbf{r}$ is $$U(\mathbf{r}) = - \int_{\mathbf{r}_{0}}^{\mathbf{r}} \mathbf{F}(\mathbf{r'}) \cdot \text{d} \mathbf{r'}$$ ...
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Potential energy-Conservative forces

Does potential energy exist because conservative forces exist? Can a system of objects that interact with dissipative forces have potential energy?
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Path independence in a gravitational field

In all of the below remarks, I am considering an object (a "mass") moving around above the surface of the earth. What are some physical examples of situations that demonstrate path independence in a ...
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Relation between central force and potential energy

I read this in one of the comments at this site "Any force that admit a potential is conservative"- what does it mean? Because I want to know why central force is related with potential as I have ...
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1answer
132 views

Non-conservative electric fields

Is the electric field produced by uniformly moving charges non-conservative? And if it is, then why?
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Susskind & Hrabovsky: For any system $F_i=-\partial_{i}V$?

In the following $\left\{x\right\}$ means a configuration point in $3N\text{-dimensional}$ configuration space. Each $x_i$ represents one coordinate of one particle of the system of $N$ particles. ...
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Why exactly is work a path function?

This might be a stupid question, but why exactly is work a path function? In school, my teacher said it’s because it depends on the path. She gave an example of walking up a mountain, and said the ...
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All central forces are conservative forces, but are all conservative forces central forces?

I have just been introduced to the concept of central forces, and to the fact that they are per definition conservative forces. I have looked up several examples of central forces (gravity, electric, ...
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Is gravitational energy always conserved?

If I take a body to a height $h$ then I did the work $mgh$, but gravity does the work of $-mgh$, so the net work done would be 0. So why do we say that at that height $h$ the body will have potential ...
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Kinetic energy and conservative fields

If $W = E_1 - E_0$ for every force and a conservative field is a field such that the work on a closed path is 0, then every field should be conservative, since $W = E_0 - E_0 = 0$. I know that this ...
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Two-particle system: proof force on each particle can be derived from one potential energy

Suppose we have a two-particle system with particle 1 and particle 2 that obeys Newton's laws. Further assume that the force on particle 1 due to particle 2, $F_{1, 2}$, is conservative. I know then ...
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Conservative $E$-field and Kirchoff rule in practice

In undergrad physics, when analyzing an LR circuit, it is often considered that Kirchoff rule holds. However, as far as I understand, Kirchoff rule only holds when E field is conservative (curl of E ...
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1answer
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Do force fields come from potential fields, or do potential come from forces?

Please excuse me if this question is a duplicate. I tried my best but I didn't find an existing question for this. In physics class, I was first introduced to gravity in terms of a force, ...
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Are the gradient field are the only fields which are only conservative? [duplicate]

I have found that gradient fields are always conservative. But for my knowledge I wanna ask "are the gradient fields are only fields which are conservative"? I mean is it necessary that a field which ...
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How do many conservative forces come together to make a non-conservative one?

Consider the mysterious force of friction. It drives our cars and bikes, slows them down, allows me to walk to the nearest dominoes store, allows me to eat my delicious pizza while ensuring that I ...
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4answers
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A gravitational field is path independent. Why does a rocket not fly in serpentine lines? [closed]

in theory a gravitational field is path independent, a gravitational field is a gradient field and so conservative. why doesn't a rocket fly in serpentine lines to exit the gravitational field of the ...
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Defining potential energy for a non-conservative field with a global attractor

Consider a vector field $\vec{F}(\vec{x})$ that is not necessarily conservative (meaning that the line integral of this field need not be path-independent). If we now describe the motion of a particle ...
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Why work done against gravity is independent of it's path aquired?

I can't understand why work done against gravity does not depend on it's path acquired.
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Proof of Path-independence of work done by an electrostatic field using Coulomb's law

We know that work done by conservative forces is path-independent but how can we prove it using Coulomb's law?
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1answer
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Why are conservative forces responsible for elastic collisions?

In elastic collisions, such as the collisions of two snooker balls, it is stated that conservative forces are responsible for the collision being elastic. (See http://vlab.amrita.edu/?sub=1&brch=...
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Can work done by conservative forces change the mechanical energy of a system?

It is defined that a constant force is conservative. Does this mean that the work of this force won't change the mechanical energy of the system? Example: a constant force pulls an object from A to B:...
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4answers
208 views

Is potential energy a type of energy at all?

Is potential energy, whether it be that of a charge in an electric field or a mass in a gravitational field or anything like that, actually an energy that the particle itself contains, like kinetic ...
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3answers
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Why must a conservative force be able to be written as a derivative of the potential function?

Why must a conservative force be able to be written as a derivative of the potential function? Furthermore, what exactly is a potential function?
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1answer
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Conservative force definition

Classical Mechanics, by John Taylor defines a conservative force F as a force that satisfies: F depends only on the particle's position and no other variables. Work done by F is the same for ...
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1answer
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What is this thermodynamic property called: the thermodynamic state is independent from path/process

I'm trying to comprehend the discussion here about the internal energy of an ideal gas being only dependant to its temperature $dU=nc_vdT$. I have the feeling that there are some assumptions missing. ...
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Non-conservative forces in nature [duplicate]

We know that gravitational, electrical and magnetic forces are conservative in nature. We also know that friction is fundamentally Electromagnetic in nature. How is it then a non-conservative force?
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If non-conservative force is constant then is the work done by it independent of the path taken?

Here, does the writer mean conservative forces, because I think non-conservative forces do depend on path taken.
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1answer
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Work and mechanical energy

I have come across the following lines in "Introduction to Mechanics" by Kleppner and Kolenkow. A peculiar property of energy is that the value of mechanical energy $E$ is arbitrary; only changes ...
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1answer
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Forces acting on a point and change of reference frame

Given a point mass, with $\underline{x}$ the position vector, on which acts a force $\underline{F}$ such that it is conservative: $$\underline{F}= -\nabla U(\underline{x}) .$$ Then if I change frame ...
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Why is the electric field created by a battery non-conservative?

Electromotive force(emf) or $\mathcal{E}$ is defined as $$\mathcal{E} = \oint \frac{\vec{F}}{q} \cdot \mathrm{d}\vec{s}$$ Here, $\vec{F}$ is the force which pushes the charges through a conducting ...
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Non-conservative electric fields [duplicate]

When magnetic flux is changed linked with the coil the the electric field is produced inside the coil. But this electric field is non-conservative field whereas the electric field produced by the ...
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1answer
302 views

Electric Field conservative property equation

Hi I'm learning about Electric Potential, and the Work Done for moving a charge in an electric field. The last equation really does not make sense to me. Please see the image attached. I understand ...
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2answers
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Potential Energy is defined only in conservative fields?

I am currently preparing for my physics test and struck in this question Q. Potential Energy is defined: 1}only in conservative fields 2}As negative of work done by conservative forces ...
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1answer
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Linking the work-energy principle with potential energy in the context of gravitational fields

I am trying to derive the equation for gravitational potential energy $E=-GMm/r$. On the Wikipedia page for energy: https://en.wikipedia.org/wiki/Work_(physics)#Work-energy_principle it says that $W=-...
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7answers
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For what reason is the difference of potential energy $\Delta U=-W$ equal to the *opposite* of the work done?

In my classical mechanics physics textbook (a translation of the Walker-Halliday-Resnick Fundamentals of Physics) the difference of potential energy is defined as $$ \Delta U = -W \qquad (1) $$ I ...
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1answer
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Inconsistency of Equations while finding Velocity in Satellite projection from one planet to another [closed]

Here's a question that's creating some doubt to me. Suppose there are 2 big spheres A and B of mass M and mass 4M, each of radius, R separated by a distance of 6R. An object of mass, m is projected ...
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1answer
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Intuitivelty speaking, if a radial force is only inversely proportional to $r$, why is speed required for any orbit independent of $r$, intuitively? [closed]

The following exercise has made me question the properties of a conservative field: Going through the first steps quickly so I can get to my point: $$\vec a = \vec a_r = -\frac{\beta ^2}{r} \hat r$$ ...
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1answer
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Work Done by Gravitational Force

[Bit a long question] Here in this question, I need to know clear my doubts on Gravity, more precisely Work done by a Conservative Force(here, gravitational force). Ok, suppose there is an object ...
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Determining whether a force is conservative

From my understanding, most forces that are conservative are of the form $$\vec F = \hat i F(x)$$ Which means the force is only a function of one variable, which means the work done of the force in ...