Questions tagged [conservative-field]

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The path-independence of work done by an electrostatic field

We know that work done by conservative forces is path-independent and so is work done by electrostatic force but how can we prove it using Coulomb's law? I know such a question has already been asked ...
Ayesha J.'s user avatar
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5 answers
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Physical meaning of line integral involving force

I'm curious about the physical meaning of the following equation: \begin{equation} \oint \mathbf{F} \cdot d \mathbf{s} = 0 \end{equation} What does this physically mean? I think is has something to do ...
Jan Oreel's user avatar
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Energy and Non-conservative forces

I understand that one cannot assign a potential energy to all points in space in the presence of a non-conservative force field due to the work done by the force being dependent on the path taken. ...
Cognoscenti's user avatar
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If a force depends on velocity, then why is the force not conservative? I need a formal proof [duplicate]

I am currently an undergraduate taking a course on Newtonian mechanics. The lecturer defines a force to be conservative if there exists a scalar function (we call it potential function), say $V(x,y,z)$...
IncredibleSimon's user avatar
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What the physical interpretation of negative work done in case of attractive force? Also how negative potential energy is related with negative work?

I want to ask why potential energy becomes negative in attractive forces along with the work done. As the meaning of potential energy according to my knowledge is the amount of energy required to keep ...
Shubhankar Mishra's user avatar
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Systematic drift in total energy in MD simulation

I have been simulating a system of 10 particles interacting among themselves via Yukawa potential using Molecular Dynamics technique. In addition to the Yukawa interaction, there is an exterally ...
bubucodex's user avatar
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Conservative force and change in the mechanical energy

Why is work done by a conservative force equal to change in the potential energy only? Why doesn't it account for all mechanical energy, what about kinetic energy?
GoodApp23's user avatar
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Is $F=-\nabla V$ a form of the least action principle? [closed]

Only for conservative systems, of course.
Reinhold Erwin Suchowitzki Tob's user avatar
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1 answer
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Conservative forces and Variation

I am currently studying "Classical mechanics by Goldstein" and have just started. The book introduced something simple. For a conservative force, the work done in taking a mass from one ...
Charu _Bamble's user avatar
2 votes
2 answers
126 views

Intuition behind the formula: $F = -∇V$ [closed]

I have been staring at the following formula for too long and I can't figure out the intuition behind it. I have watched courses about directional and partial derivatives as well as gradients and now ...
Bonsaï's user avatar
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2 votes
2 answers
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Conceptual misunderstanding of work and conservative forces and their relations

I tried to calculate the work done by friction along an arbitrary surface. and this is the result I got. This system is under the only force of gravity and friction. we can see that work done by ...
Hammock's user avatar
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The magnetic force is conservative when the magnetic field is static, what is its potential function then?

The magnetic force $\vec{F}$ can be conservative when the magnetic field is a static. That is $\vec{\nabla} \times \vec{F}=0$, so it follows that there is a scalar function $f$ such that $\vec{F}=q \...
Jack's user avatar
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Do conservative forces obey Newton's laws of motion? If we look closely, non-conservative forces like Friction etc follow 2nd law but Im confused [closed]

I have a small confusion, do conservative forces obey Newton's Second Law always? Because it depends on the end points and the path taken, the acceleration may vary path to path, but the force doesnt ...
Mini N's user avatar
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1 answer
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Conditions for a force to be conservative - Does the second condition imply the first? [duplicate]

John Taylor's Classical Mechanics says this... I was wondering if the second condition already implies the first? I mean, are there situations where the first condition is violated even though the ...
user266637's user avatar
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Can a non-zero curl vector force field still do a null amount of work?

I've been given a vector field $\vec{F}=(12xy^2, 12yz, 9z^2)$ in cartesian coordinares and I'm asked to calculate the work it would develop on a particle moving from point $A$ to point $B$ through ...
AlanFox86's user avatar
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Velocity-Dependent Forces and Generalized Potential

Is there any theorem about for which velocity-dependent forces a velocity-dependent generalized potential of the form $$F_k=\frac d {dt} \left(\frac {\partial U}{\partial \dot q_k}\right)-\frac {\...
gluon's user avatar
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How to define the potential energy, and conservative forces? [closed]

I understand that there are multiple questions under this name, but as far as I have seen, none of them answers what I am about to ask. If you came across a duplicate, please feel free to share the ...
gluon's user avatar
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Trouble understanding the electrostatic field's curl [duplicate]

I'm going over Griffiths Electromagnetism, and I've encountered a sort of proof about why we can state an electrostatic field is conservative, using Stokes' theorem. Of course, I do understand if you ...
AlanFox86's user avatar
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Very Basic Question: Relationship between Potential, Conservative Forces and Path Independency

I am studying for my exam and wanted to clarify if the following I got from Taylor are true, because we have written something different in my lectures: $$\nabla\times\vec F=0\ \ \Leftrightarrow\ \ \...
gluon's user avatar
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How can we define Magnetic Potential Energy if it is non-conservative?

I recently learnt that for a circular wire carrying electric current or for a magnetic dipole, if it is kept in a uniform magnetic field, we can define its magnetic potential energy. This would mean ...
Srish Dutta's user avatar
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Is this statement about conservative fields and parallel circuits correct?

I am wondering if this statement about parallel circuits and conservative fields is true?: The voltage drop over resistors in parallel is the same because the electric field is conservative, so the ...
user394334's user avatar
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1 answer
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Exact test for checking conservative forces

What is the nature of this force on the path $x^2+y^2=1$? $$\tag1\vec F=\frac{-y\,\hat{i }+x\,\hat{j}}{x^2+y^2}.$$ I tried two methods, but they give different answers: For this specific path it ...
Maths's user avatar
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Are all one-dimensional force fields conservative? [closed]

Just checking a rather small thing: given any open set $U$ of $\mathbb{R}$ and any force field $f:U\to \mathbb{R}$, then $f$ is conservative since it is the gradient of any of its antideratives. Right?...
Sam's user avatar
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Does a charge moving freely in an electric field's direction, produce a magnetic field?

Does a charge moving freely in an electric field's direction, produce a magnetic field? If so, then why is energy conserved in cases of distance of closest approach? If there is a magnetic field it is ...
ANSH NAYAL's user avatar
1 vote
1 answer
75 views

Is the conservativity of a force frame independent? If so, how do you show it?

If a force $\vec{f}$ is conservative in a frame $S$, is it such in another, generic, frame of reference $S'$? How do you show this, and how are the potential energies in the two frames related?
Due.Berto's user avatar
9 votes
5 answers
1k views

Intuition for vector calculus identities

I can follow the proofs for these identities, but I struggle to intuitively understand why they must be true: $$$$ 1. The curl of a gradient of a twice-differentiable scalar field is zero: $$\nabla\...
TunaSandwich's user avatar
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How can work be a function of position when non-conservative forces don't act the same way at each point?

My textbook and wiki/online articles all claim that work is given by the integral $$W=\int_\gamma\vec{F}\boldsymbol{\cdot}\text{d}\vec{s}$$ where the $\text{d}\vec{s}$ is some infinitesimal step along ...
Max0815's user avatar
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3 answers
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Why is the work done non-zero even though it's along a closed path?

So, in this problem I just solved there is a force field given by $\mathbf{F} = -x \hat{\mathbf{j}}$ and I need to compute the work done on a particle along a circular path of radius $R$, centred at ...
Dewd's user avatar
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How can we write Faraday's law if $\vec{E}$ is conservative?

From multivariable calculus you can assure that the line integral of a conservative field around a closed loop is always going to be zero. It is well known that the electric field is a conservative ...
rodryx11's user avatar
1 vote
2 answers
158 views

How might one interpret Feynman's comment about how all fundamental forces are conservative?

I know that there are several questions related to the topic of conservative forces. But I am trying to understand where Feynman might have been coming from when he said that "We shall take a ...
sasaak's user avatar
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0 answers
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Proof that gravitational force is conservative [duplicate]

It is a well accepted fact that gravitational force is conservative in nature, i.e, the work done on an object in gravitational field is independent of the path taken. To prove the above statement, I ...
PandaScientist's user avatar
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1 answer
78 views

Is a velocity-dependent force $\vec{F}$ that doesn't do any work on an object a conservative force? [duplicate]

Let's consider a point like object with mass $m$ upon which acts a force $\vec{F} = \vec{c} \times \vec{v}$ ($\vec{c}$ is supposed to be a constant vector). Given that $\vec{F}$ is perpendicular to $\...
PhyAC's user avatar
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2 answers
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What is the essence of the fact that the work in the potential field of forces to move to some point does not depend on the trajectory? [closed]

Is it something like a guarantee that somehow arriving from point A to point And you will have the same energy? For example, having a spaceship in the solar system with a fuel tank, you can fly to B ...
Kallipso's user avatar
1 vote
1 answer
73 views

Understanding material continuity

I am prepping for an exam in large scale fluid mechanics, and I struggle to understand what material conservation really means. In standard mechanics conservation would mean the variable in question ...
Nikolai Enok Anfeltmo's user avatar
4 votes
2 answers
423 views

Conservative Force: Translational Invariance

I have a question about the following. Why if there are two masses, $m_1$ and $m_2$ respectively, and the only force acting on them is from their mutual interaction which is conservative and central, ...
Terry Cho's user avatar
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1 answer
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${}$Conservative and Non-Conservative Forces

For work done by conservative forces ($W = F.S$), we consider $S$ as the displacement and not the actual path travelled. However for non conservative forces we consider the total path length and not ...
nerdygeek's user avatar
4 votes
1 answer
285 views

Is the conservation of the electric field mathematically derived?

I was studying electrical potential and was caught in a loop. In the book shows that the electric field is path-independent by an example with a point charge. I needed more, I wanted some universal ...
Moses Kim's user avatar
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2 votes
2 answers
139 views

Are non-contact forces conservative forces?

Some non-contact forces like gravity, electric force are conservative forces. Is this thing right for all non-contact forces?
abcxyzklmn's user avatar
2 votes
1 answer
130 views

Explain Feynman's explanation why KE + PE = constant

I'm reading Feynman's lecture on physics, and I'm having trouble following the logic. In section 14-4 he says: "Now we have the following two propositions: (1) that the work done by a force is ...
user745730's user avatar
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1 answer
594 views

What is the derivative of potential energy with respect to $x$? [duplicate]

I was reading an article which was proving the conservation of energy with calculus, but they did not explain why the derivative of potential energy with respect to $x$ is the negative force. $${dU\...
Adam's user avatar
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2 votes
2 answers
134 views

Intuition behind relation between intensity of gravitational field and gravitational potential

I found out that the gravitational field intensity, $\vec{I}$ is the negative derivative of the gravitational potential $V$ wrt to distance $r$ from (point) mass. Can someone provide some intuition ...
AVS's user avatar
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0 answers
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How to prove that work due to conservative forces are independent of path?

The Wikipedia article on conservative forces says, A force field F, defined everywhere in space (or within a simply-connected volume of space), is called a conservative force or conservative vector ...
arz's user avatar
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1 answer
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What is the vector field associated with potential energy?

The mere concept of a line integral is defined for a vector field, and I thus thought the following was a rigorous and general definition of potential energy: Definition: Given a conservative force ...
Sam's user avatar
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1 answer
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How do we visualise multiplication and division (reciprocal multiplication) in physical equations?

All formulas have terms generally multiplied or divided to represent another physical quantity. Like $F=ma$, $I=Q/t$, $W=F.s$ etc. Technically this is so because of ratios and proportionalities, the ...
Lumbini Ashutosh Tambat's user avatar
4 votes
3 answers
1k views

Is David Tong incorrect in this remark about classical mechanics in his QM lectures?

In page 11 of his Quantum Mechanics lectures, we have the following quote: It turns out that not all classical theories can be written using a Hamiltonian. Roughly speaking, only those theories that ...
agaminon's user avatar
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2 votes
2 answers
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How to show that a radially symmetric central force is conservative?

Let $U\subseteq \mathbb{R}^3$ be open and $f:U\to\mathbb{R}^3$ be a radially symmetric central force, that is, a force field such that $$f(p) = -g(r)u_r$$ where $r=|p|$ and $u_r$ is the unit vector ...
Sam's user avatar
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1 vote
2 answers
131 views

Let $U$ be the potential energy associated with the force $F$. Why is $\frac{d}{dx}U=-F$?

In a conservative force field, we may define a function $U:\mathbb{R}^3\to\mathbb{R}$ such that $$\int_CFdx = U(x_A)-U(x_B)$$ and we call $U$ the potential energy associated with the force $F$. I've ...
Sam's user avatar
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1 answer
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Why is the force being the differential of a potential equivalent to it being a conservative force?

I was reading Goldstein's book on mechanics and came across this theorem: $F(r) = - \nabla V(r)$ is a necessary and sufficient condition of the force field being conservative. So far, I have ...
physBa's user avatar
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12 votes
4 answers
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Does the Newtonian gravitational field have momentum analogous to the Poynting vector?

We can define the total energy of the electromagnetic field as: $$\mathcal{E}_{EM}= \frac{1}{2} \int_V \left(\varepsilon_0\boldsymbol{E}^2+\frac{\boldsymbol{B}^2}{\mu_0}\right)dV$$ which satisfies the ...
Davius's user avatar
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1 answer
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How to identify electrostatic field function out of some given functions? [closed]

Suppose I have a vector function $$\vec{v} = p(x,y,z) \ \hat{x} + q(x,y,z) \ \hat{y} + r(x,y,z) \ \hat{z}$$ How can I determine whether the given function represents an electrostatic field or not?
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