Questions tagged [conservative-field]

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Velocity- and time-dependent forces can not be conservative [duplicate]

I have already seen many posts about this specific question but in only a few of those mathematically rigorous answers were given. Unfortunately none of them are accessible at my level (first year ...
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Conservation and potential with non-cartesian forces

I understand how to determine if a force is conservative from \begin{equation} \nabla\times \mathbf{F}=0 \implies \mathbf{F}\text{ is conservative} \end{equation} When $F$ is in cartesian coordinates. ...
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How can a time-dependent gravitational field be conservative?

Let's consider 2 point particle graviting the one around the other. Can that gravitational field be considered conservative? I can go from A to B and then, after a time $\Delta t$ come back to A with ...
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Conservative electric field must be static?

My question means, by Maxwell equations: $$\nabla\times \vec{E}=0\stackrel{?}{\implies} \frac{\partial \vec{E}}{\partial t}=0$$ I think that is right, this is my explanation, Intuitive explanation: A ...
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Find the curl if the vector field depends on a parameter

Given the following vector, \begin{align} F(x(t),y(t),z(t)) &= \begin{bmatrix} \omega_1^2 x_o\cos(\omega_1 t) \\ \omega_2y_0\sin(\omega_2 t)\\ 0\\ \...
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What is the property of a counterpart of conservative vector field in Minkowski space?

As we know, a conservative vector field is defined by a vector field ${\displaystyle \vec {v} :U\to \mathbb {R} ^{n}}$, where ${\displaystyle \vec {v} =\nabla \varphi}$. It is also an irrotational ...
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2 answers
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Is net force conservative?

From the work-energy theorem, $$\int_{C}^{}\vec{F}\cdot d\vec{r}= \frac{1}{2}mv^2_f -\frac{1}{2}mv^2_i$$ Is velocity the gradient of position, and if so, does that make this force a conservative ...
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Do action-reaction conservative forces come in pairs?

If $\ \vec{F_{12}}\ $ denotes the force on particle 1 by particle 2 and is conservative, is $\ \vec{F_{21}}\ $conservative too?
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Orbit Equation of a particle moving under a central force [closed]

I want to prove that the orbit of a particle of mass $m$ that is moving under a central force $\vec{F}=f(r)\hat{r}$ is given by the differential equation: $$\frac{d^2r}{d\theta^2}-\frac{2}{r}(\frac{dr}...
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Why are most vector fields "found in nature" conservative?

So I got the mathematical aspects down of what it means for a vector field to not be conservative, but I'm trying to make sense of the physical intuition. Why are so many vector fields found in nature ...
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Conservative magneto-static field on a current carrying wire?

$$\nabla \times \mathbf{B}=0$$ I am asking why although magneto-static $B$ fields in total are considered as non-conservative fields by most of the literature, the magnetic field of a d.c. current ...
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Form of potential $V$ for conservative forces

Goldstein, Pg 21,3rd E.d writes only if $V$ is not an explicit function of time is the system conservative That means $V(r,\dot{r})$ is a conservative potential, however I think that only potentials ...
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What is the intuitive pictorial explanation of a conservative force's criteria of having zero curl and a value equal to the gradient of a potential?

A conservative force should be satisfying these two criteria. I want to understand the intuitive or pictorial form of why the criteria of only having zero curl not necessarily mean the force is ...
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3 votes
2 answers
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Proving if a force is conservative and non-conservative

recently I have studied conservative forces and non-conservative forces in halliday book and while doing some exercise I saw some questions asking for proving if a force is conservative so after doing ...
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4 answers
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Can non-conservative fields store potential energy?

I was taught that a time-varying magnetic field generates an electric field which is non-conservative in nature, and my teacher also told me that when a conducting coil is placed in a region with a ...
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Is force corresponding to surface tension conservative?

Suppose you have a structure like shown in the figure. Is the force corresponding to surface tension, $2\gamma l$, conservative? If it is not then by work-energy theorem, for the system consisting of ...
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Path Independence using the stokes theorem

If I have a vector field $\vec{F}= A(x,y)\vec{\imath} + B(x,y) \vec{\jmath}$ which satisfies the following condition: $$\frac {\partial A(x,y)} {\partial y}= \frac {\partial B(x,y)} {\partial x}.$$ I ...
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Proof $E$ field is path independent [closed]

From fundamentals I am trying to prove $E$ field is Conservative. Without the use of spherical coordinates, purely in cartesian as I have no knowledge of the spherical gradient. or the spherical line ...
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Proving $F = -(dV)/(dx)$ for conservative forces and application

How could we prove that $F=-\frac{dV}{dx}$ for conservative forces? I tried to it with: $W=F\Delta x$ with Work-Energy theorem, we get $W=\Delta K$ $\Delta K = F \Delta x$ Now from the law of ...
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Interpreting Stokes' theorem using the energy of a particle looping around a closed curve

We know that the work for a particle moving along a path $L=\partial S$ is $\int_{L} \vec{F} \cdot d\vec{s}$. Suppose the particle loops around this path once: $$ \int_L \vec{F} \cdot d\vec{s} = \int_{...
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Interaction forces always depend on positions only through the distance, therefore conservative?

Suppose that two point masses $A_1,A_2$ are in interaction with each other, resulting in forces $F_1$ (acted upon $A_1$) and $F_2$ (acted upon $A_2$). Let $\bf{x}_1$,$\bf{x}_2$ be their respective ...
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Relation between potential energy and conservative force

Does potential energy only happen when the work done is by a conservative force? Or does work done by non-conservative forces also create potential energy?
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Correlation between conservative forces, non-conservative forces and potential energy

So I recently learned the definition of conservative forces, and how the work done by such forces depends only on the initial and final position of the particle but then we learnt about definition of ...
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Do Electrostatic Charges build up at the ends of an Inductor in closed circuit?

I was watching this video from YaleCourses youtube channel. At around 41.00 minutes, the professor introduces the notion of charge buildup at the ends of an Inductor in a closed circuit. Is the ...
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Position from non-conserved potential

I have a non-conservative potential $U_x(x, t)$ in one dimension and that is it (there is no conserved counterpart). Thus, I arrive at the conclusion that the kinetic energy gained in the time $\Delta ...
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2 votes
2 answers
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$V=\int _C\vec{F}d{x}$ where $C$ is a path that "goes to infinity". Does the path chosen matter?

According to Wikipedia "The gravitational potential $V$ at a distance $x$ from a point mass of mass $M$ can be defined as the work $W$ that needs to be done by an external agent to bring a unit ...
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Why isn't constant pull a conservative force?

Consider the following diagram: The force $\mathbf{F} = 1 \textrm{ N} \hat{\imath}$ is being applied all time as the ball goes from A to B (assume positive $x$ to the right.) Now, there are a few ...
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How can the strong force, which is conservative, not follow the inverse square law?

In terms, which someone with a background in chemical physics & quantum chemistry might understand, what is the evidence that the strong force, across whatever its range is, follows something ...
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Path independence and Spherically Symmetric Force [closed]

This problem is from John Taylor's Classical Mechanics. I can't figure out how to prove that a series of paths consisting of paths moving radially or in the angular direction. I understand ...
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Friction is also a conservative force?

I have asked a recent question about how spring force is conservative and in that I learnt that for a force to be conservative the work done by the force should be path independent given the initial ...
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Is spring force really a conservative force?

Let us consider this picture. $\Rightarrow$ The first picture shows the initial position of the block when the spring is in its natural length and is kept on a smooth horizontal table. $\Rightarrow$ ...
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Why is $f = -\frac{du}{dx}$?

I am studying Newtonian Mechanics and I am familiar with single variable calculus. I came across the concept of conservative and non conservative forces and potential energy. Here is what I understand:...
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1 answer
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Potential energy and force [duplicate]

Why force is negative gradient of potential energy? Why negative sign is involved in this definition?
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Mechanical energy in a body moving upwards

Why is it that mechanical energy is always conserved, I mean when an object is thrown in air, why does the kinetic energy convert to potential energy and not any other form of energy?
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Why is the curl of an electric field zero?

I'm asking this question only to make sure that my understanding is correct. I know that that curl of an electric field produced by a stationary charge is zero and I also know that that work done in ...
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How to show that interaction potential depends only on separation of particles in system with position translation symmetry?

System 2 particles with mass moving in one spatial dimension $x$. Positions of particles are $x_1$ and $x_2$ respectively and they are only acted on by a conservative interaction force corresponding ...
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Can anyone tell me how does conservative forces work? Confused

From vector calculus, I'd learnt that a conservative vector field satisfies $$ \textbf{F} = \boldsymbol{\nabla} g $$ which $\textbf{F}$ is the gradient of some scalar-valued function, and $g$ is the ...
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Work done for conservative forces is path independent Proof

So I’m looking at the proof for work that is path independent. There is a line were the integral Partial derivative V dr from r1 to r2 becomes Partial derivative V r’ dt from t1 to t2 I’m a bit ...
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3 answers
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Can a non-conservative force be an internal force of a system?

Are all internal forces conservative? Is it possible for a non-conservative force to be an internal forces? If yes, please give a few examples.
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4 votes
2 answers
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Is there a symmetry between scalar and vector formulas for electrostatic and gravitational potential, potential energy, field and force?

Formulas for electrostatic potential, potential energy, field and force, bearing the subscript 'E': Electrostatic potential $V_E=\frac{U_E}{q}$ Electrostatic potential energy $U_E=k\frac{q_1\,q_2}{r}...
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Relationship between conservative and non-conservative forces with internal and external forces

Are there any kinds of relationship betweeen conservative and non-conservative forces with internal and external forces? If yes,please explain in detail.
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2 votes
1 answer
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What is the relationship between state variables and conservative force fields?

State variables are defined as being independent of path, just like conservative force fields. Is there any relationship between state variables and conservative force fields? Is it because there is ...
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Work done by gravitational field and and proof of gravity being conservative force [closed]

We know gravitational force is a conservative force. So work done by the field in moving an object form one position to other and again moving it bact to the initial position should be zero. But while ...
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Can we define potentials for non-conservative force?

I have just started out on Quantum Cavity Optomechanics from this EdX course , and have learnt that radiation pressure force is non-conservative. But, while dealing with the optical spring effect we ...
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5 votes
3 answers
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Deriving the work-energy theorem in three dimensions from Newton's second law of motion and justifying moving around differentials

I wanted to prove the work energy theorem in three dimensions starting from Newton's second law of motion. I am having some trouble understanding differential swapping and deriving the kinetic energy ...
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Conservative nature of electric field

It's a straightforward question. Electrostatic force is conservative, but I've read that the electric field generated according to Faraday's law of induction is not. What's the difference between ...
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12 votes
5 answers
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Why the work done in a conservative field around a closed circle does not vanish when calculated in cylindrical coordinates?

I was solving problem 2.4.13 from the book "George B Arfken, Hans J Weber - Mathematical Methods For Physicists- Sixth edition" and the problems was that: Problem 2.4.13 A force is ...
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1 vote
2 answers
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Conservative Force in a loop

Could someone prove mathematically that why in this situation a charge could move in a loop with net work done. Could someone explain this paragraph to me.
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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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Conservation of angular momentum and central forces

We review the statement and derivation of the law of conservation of angular momentum of a system of particles. $\textit{Theorem:}$ Consider the system of particles $$S := \{ P_i | P_i \; \text{is a ...
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