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Questions tagged [conservative-field]

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Potential Energy of Conservative Forces [on hold]

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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Sufficient condition for conservative fields of class $\mathcal C^1$

I would need help for a complete and detailed demonstration of this theorem if it is possible. I found several handouts on the net but I wondered if there was a demonstration not too long and ...
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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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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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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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2answers
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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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Can you give an example of a “non-conservative field force”? [duplicate]

I need an example of a non conservative field force,if there exists any. If in the case of conservative field force work done is stored as potential energy then what can we say in the case of non-...
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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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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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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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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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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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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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1answer
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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
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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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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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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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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 ...
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Understanding conservative forces

I'm trying to better understand conservative forces. I have a decent intuitive idea of what they are, but I've recently learned the mathematical rigor behind it which has made me have some questions. ...
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Help me overcome my confusion in Maxwell's treatise

I am reading Maxwell's treatise vol 2 page 157 and I have a doubt to clear in the following page: My analysis of this derivation: $\vec{ds}$ and $\vec{ds'}$ are the elements of circuits; $\...
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Does the field has to satisfy both conditions to be a conservative field or just either 1st or 2nd?

For the field to be a conservative field, does the field have to satisfy the both conditions? Work done is independent of path followed by the body. Work done in a closed path is zero.
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Why is potential energy defined for only a conservative force? [duplicate]

I want direct answer for this and some interpretation with example. why do we need conservative force to define potential energy? what is wrong with non-conservative force and other? I have seen many ...
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Is the weak force conservative?

Does it make sense to talk about "conservative" potentials and forces in (quantum) field theory? If yes, to what extent? Is (for example) the weak force conservative and what would it mean ...
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What exactly makes a force conservative?

I get that forces can be classified as either conservative or non-conservative, depending on whether the work done in a round trip is zero or non-zero. What property of the force makes it to be, ...
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Would this hypothetical field be conservative?

Let's say there's a field that acts perpendicularly to the direction of velocity of a particle (& it does not depend on the speed; it's a constant force) and hence does no work. Would this field ...
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Does path independence of line integral imply that the given vector field is conservative (that is, it is negative gradient of some scalar potential)?

For a vector field, is path independence of line integral a necessary and sufficient condition for the field to be conservative or is it just a necessary condition? Please provide proof if possible.
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What is a potential?

I am self-studying electrodynamics and am wanting to know what is meant by a potential. I understand the concept of potential energy but what is meant by a potential? Is it the same thing as a field, ...