Questions tagged [conservative-field]

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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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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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Helmholtz decomposition of magnetic field generated by a infinitely-long line charge in uniform axial motion

Context In [1], I derived the magnetic field generated by a infinitely-long line charge that is in uniform motion in a direction co-linear to the line of charge. The method that I used was volume ...
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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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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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54 views

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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1answer
29 views

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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35 views

Friction or not?

Say I have a differential equation in $\mathbb{R}^n$, Newtons Equation : \begin{align} \frac{d\gamma(t)}{dt}=&\dot{\gamma}(t), \nonumber \\ \frac{d\dot{\gamma}(t)}{dt}=&-\...
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Direction of $r$ in $-dU/dr$?

While stating $F(conservative)= -dU/dr$; what is/are the condition(s) on $r$ of which $U$ is a function of. Does it need to be along (either parallel or antiparallel to) $F$? This can be critical when ...
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Form of the restoring force in a string which carries a wave

A string is stretched when a wave is traveling over it. We also calculate the potential energy in the string due to the restoring forces,which arise due to the fact that the string is stretched. Since ...
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Why did Feynman use a negative sign while defining the potential energy function?

Why is it ($-U$) and not ($+U$)? And how do we know it's going to help us if we take it to be negative beforehand?
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Torque produced by conservative forces vs Torque produced by non-conservative forces

One clear observation is that we could write torque in the following way for conservative forces: $$ \vec{\tau} = \sum_{i=1}^n \vec{r}_i \times (-\vec{\nabla} U(\vec{r}_i))$$ Where $U$ is the ...
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Why does an exact differential mean a force is conservative?

If you can express an integrand as an expression of just one variable i.e. $xdy + ydx = d(xy) = df$ then why does that mean that a loop integral on that will equal 0? Is it because if it is just a ...
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Is the force conservative which produced the torque $\Gamma=-k \theta$?

We've a body that's oscillating in a fixed plane such that the torque on it is $$\Gamma=-k \theta.$$ I went on an computed its energy ( kinetic + potential) and it was constant. Why was it constant? ...
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Conditions for a force to be conservative

Taylor's classical mechanics ,chapter 4, states: A force is conservative,if and only if it satisfies two conditions: $\vec{F}$ is a function of only the position. i.e $\vec{F}=\vec{F}(\vec{r})$. The ...
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Defining potential energy in Taylor's Classical Mechanics

I'm trying to understand this sentence in introducing potential energy in John Taylor's book: If all forces on an object are conservative, then can define a quantity called potential energy, $U (\...
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Why is are induced electric field's non-conservative while static electric fields are conservative?

I have learned that the $E$-field induced by changing magnetic flux, such as in 'motional emf', is non-conservative in nature. I am also aware that static $E$-fields are conservative in nature. What ...
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Relationship between force and potential energy

Consider a conservative force $\vec{F}=F_1\hat{i}+F_2\hat{j}+F_3\hat{k} $ acting through a displacement $\vec{ds} =dx\hat{i}+dy\hat{j}+dz\hat{k}$. The work done $dw$, will be equal to $F_{1}dx +F_{...
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Why can a force field only be conservative if it is spherically symmetric?

I saw in my textbook that a field can only be conservative if it happens to be spherically symmetric. Why is this so? Is there a good proof for this?
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How can you conclude that gravity is a conservative force?

A force field $F_i(x)$ is conservative if for every curve $C$ from a point $y_1$ to a point $y_2$, we have $\int\limits_C F_i(x)\mathrm{d}x^i$, so that the energy difference between $y_1$ and $y_2$ is ...
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In what case can we describe forces by potential?

Let's consider a particle in an $N$-dimensional space and let's assume that acceleration of this particle depends on its position. So, one can say that we have an $N$-dimensional vector field in an $N$...
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Help understanding forces in non-conservative systems

This might seem like a very simple problem, but it's stumping a few of us (myself obviously included). We have been tasked with showing the mechanical energy of a particle is dissipated under the ...
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Work is a path function: it cannot be expressed as a difference between the value of some property of the system in two states

Why do we not define work done as the difference between two quantities that depend entirely on the initial and final states. Why is work a path function? What is the reason?
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How can we choose any level for gravitational potential energy to be zero?

In my book, I read that we can choose any level as Zero Gravitational P.E. and measure height of objects above it and call its energy 'mgh'. But by saying that all the points on that level is of zero ...
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Is mechanical energy conserved in all Inertial frames? (Newtonian Mechanics)

Is total mechanical energy, i.e. Kinetic Energy + Potential Energy, conserved in a frame which is moving with constant velocity with respect to earth. Consider a ball dropped from a building. The ball ...
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51 views

How do we talk about conservation of energy when the potential field keeps changing with time?

The way it is taught in school, you have a mass moving under the influence of an unchanging potential field. It can be proven that if the mass moves from point A to point B in the field, the increase ...
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Why is the conservation of momentum not equivalent to the conservation of energy in Newtonian mechanics?

Conservation of momentum is Newton's third law. Conservation of energy is attained in theory by defining work, deducing the work-energy principle and specifying that if a force or system is ...
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Why is the centripetal force non-conservative while the centrifugal isn't?

Aren't both perpendicular to $R$? Also, doing $\nabla \times \vec{F}$ using $\hat{r}$, $\hat{t}$, $\hat{k}$ as versors (with $t$ tangent to $r$ and $k$ perpendicular to the surface) i get $0$ with ...
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Path independence of a conservative force

My book Halliday et al. gives a proof of the path independence (conservative force). It is said that the net work to move a particle from a to b and then from b to a is zero. Thus the work done from a ...
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234 views

Why is work done by non-conservative force around a closed path not zero? [duplicate]

If work done by a conservative force in a closed loop is zero then why is the work done by a non conservative force not equal to zero. Since in both the cases the body moves in a closed path so the ...
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1answer
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The curl of a friction force being zero

Consider the resistive force modelled by the function $\vec{F} = -b\vec{v}(t)$. The curl of this function, $\nabla \times \vec{F}$, is $$[\frac{\partial}{\partial y} (\frac{dz}{dt}) - \frac{\partial}{\...
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Why is the general definition of electric fields in dielectrics breaking down here?

According to the definition of the dielectric constant(k) for a dielectric, the electric field in the dielectric is defined as the corresponding electric field in vacuum divided by k. We are also ...
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$\nabla \times \bf{u} \neq 0$ but $\oint_{c} \bf{u} \cdot \textit{d}r \textit{=0}$?

Consider the vector field $\vec{u}=(xy^2,x^2y,xyz^2)$ The curl of the vector field is $$\nabla \times\vec{u}=(xz^2,-yz^2,0)$$ Consider the line integral of $\vec{u}$ around the ellipse $C$ $x^2+4y^2=...
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Can a static non-conservative vector field have scalar potential?

STATEMENT#1: A vector field can be considered as conservative if the field can have its scalar potential. STATEMENT#2 If we can have non-zero line integral of any vector field along with a single loop ...
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Why are Electric Fields an exact differential?

{$\vec E$ - Electric Field Vector ; $x^2$ is $x$ raised to the power $2$} When finding the Potential Difference between two points in a non uniform electric field, the equation of $\vec E $ given in ...
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A non-conservative electric field inside a conducting wire within a magnetic field?

We consider a region of space confined within a box, in which there is a time varying magnetic field $\mathbf{B}$ as well as a perfectly conducting loop of wire that passes into and out of the box to ...
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Is this true about potential energy?

Work done by an external force on a system equal and opposite to a conservative force is stored as potential energy within the system. We choose an arbitrary location x and define the potential ...
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Do all conservative forces act in the direction of decreasing potential energy?

Let us take two unlike point charges $q_1$(positive charge) and $q_2$(negative charge). When we decrease the distance between them, the potential energy between them also decreases according to the ...
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Why is friction non-conservative? [duplicate]

As electrostatic force is a conservative force, but friction, occurring due to electrostatic forces is non-conservative. A wider question would be: why is any force non-conservative if it is a ...
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$\text{div} \ \vec{F} = \vec{0}$ for a conservative force? [duplicate]

I saw from "Advanced Engineering Mathematics, 10th Edition" by Kreyszig, p. 400, that the solution $V$ of the Laplace's equation, $$\nabla^2 V = \frac{\partial^2V}{\partial x^2}+\frac{\partial^2V}{\...
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Relation between velocity and position vector in a central force

I am aware that the dot product of the position and velocity vector, $(\vec{r}\cdot\vec{v})$, in circular motion under a central force, $F(r)=-\frac{k}{r^2}$, is equal to zero as the two vectors are ...
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Conservative or non-conservative? Frame dependent?

Can a force which is conservative in one frame become non-conservative in another frame. Why/Why not? Basically what does it mean for work to be zero in closed loop? If I am thinking of coordinates ...
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Can changing EMI through a coil change the flux through it?

As the Lenz's law states, the magnitude of EMF $E=N\frac{d\phi}{dt}$, which means changing flux can change the EMF across the coil. I have the following questions: Across which points is the EMF ...
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Is tension a conservative force?

Are forces such as tension (from an in extensible string), normal reaction, and applied force from us, non conservative forces? If so why? I have read in few books that these forces are labeled as ...
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Is static friction considered to be a conservative force? [closed]

The work done by static friction is 0.So shouldn't it be a conservative force?
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Why can't conservative forces depend on velocity?

In my mechanics lecture notes, it is written that, for a force $F$, To be conservative, $F$ must be a function of position only: forces that depend on velocity, time, etc. cannot be conservative. ...
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What is a non-conservative system?

I've been searching a bit on the internet for a mathematical description of a non-conservative system, but I could not find it. I'm looking for a good description. Wikipedia does not have an article ...

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