Questions tagged [conservative-field]

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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 ...
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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 ...
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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 ...
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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 ...
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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 ...
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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 ...
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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 ...
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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 ...
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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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Fluid-mechanics: Scalar field associated with velocity field

I have just started studying fluid mechanics (without a proper physics education :) and came across the following equation for incompressible steady-state fluids. $$ \nabla\cdot \mathbf{u} = 0 $$ ...
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Do optical tweezers provide conservative forces?

So, either it seems I am mislead with the idea of the conservative and non-conservative forces or I never knew/understood it. What exactly does the work in optical tweezers to make object levitating? ...
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Why the change in gravitational potential energy of the two particle system remains same even when the both the masses are moving?

When we calculate Gravitational Potential energy of the two masses, we fix one mass and calculate the force acting on the other mass. Work done by the the force which is acting on the fixed mass is ...
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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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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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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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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 $\Delta ...
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$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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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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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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