Questions tagged [conservative-field]

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3
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2answers
66 views

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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5answers
2k views

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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0answers
19 views

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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2answers
294 views

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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1answer
58 views

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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2answers
93 views

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. ...
3
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4answers
101 views

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 ...
2
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0answers
33 views

What happens to the potential energy of an object if the conservative force associated with it vanishes [closed]

Now, some textbooks have been telling me that when you do work against a conservative force, ("it is stored up as potential energy") Apparently this gives the ability to do work, because when the ...
0
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4answers
181 views

Non-conservative EMF around a circuit and delocalization of motional EMF

Around a circuit, the EMF is non-conservative. In fact, we are in a closed loop and "its" work (the EMF is actually the work itself per unit charge) is non-zero (contrarily to conservative forces/...
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2answers
89 views

Feynman says “The total work done in going around a complete cycle should be zero for gravity forces”

I am reading "The Feynman lectures on physics volume 1". Feynman says "The total work done in going around a complete cycle should be zero for gravity forces" When gravity forces are given, I ...
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1answer
67 views

Why is it called “Conservative” field?

I understand -mathematically- what a conservative field is; it is a vector field that can be expressed a gradient of some scalar function OR it is a vector field whose line integral is path ...
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2answers
51 views

Kinetic Energy in a Conservative Field [closed]

My problem states that $\vec{F}$ is a conservative field, ie: $F = \nabla \phi$ for some scalar potential $\phi$. $$\begin{align}\vec{F}&=m\vec{a}\\ &=m\frac{\mathrm{d}^2\vec{r}}{\mathrm{d}t^...
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1answer
28 views

In order for a force to be derived from the gradient of a potential energy the work done by such force must be invariant of the path?

Suppose a force F = F(r, t) where r is a three dimensional space vector and t is time. I understand that in order to a force be conservative two conditions must be satisfied: The force must be ...
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3answers
115 views

How to check if a given force (in vector form) is conservative or not? [duplicate]

How to check if a given force is conservative or not ? Is there any mathematical way of doing the same?
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2answers
78 views

Potential Minimum Confusion

Today my lecturer mentioned the notion of vector field and potential, he also said that if the vector field is a force field then there is a potential energy given by: $F(x)=-\dfrac{dU}{dx}$. (I have ...
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1answer
120 views

If the work done by a force along a closed path is zero, is it necessarily conservative?

I just had a simple doubt. If a force is conservative, we know that the work done by it around a closed path is zero. I believe the converse should also be true. I can't think of any counterexamples ...
1
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1answer
25 views

Is the relation between change in potential energy and work by internal conservative force can be used even in presence of non conservative forces?

We know that work done by internal conservative forces is the negative of change in potential energy of the system stored in conservative force field. But does this logic still hold when there are non-...
1
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1answer
68 views

Why is the electric field induced due to a Time varying magnetic field non-conservative?

As the title states, Why is the Electric Field which is induced due to a time varying Magnetic Field Non Conservative in nature ? Everywhere I read the answer that the line integral over a closed ...
4
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1answer
73 views

Conservative field vs conservative force

For a conservative field (e.g. electrostatic field) the circulation of the field (along a closed line) is zero. For a conservative force (e.g. macroscopic elastic force) the work performed on a ...
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2answers
54 views

What is the three dimensional generalisation of a conservative force?

I was studying about conservative forces from a physics book (NCERT, a standard Indian textbook) and came to a para which is as follows: A force is conservative if it can be derived from a scalar ...
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2answers
100 views

In electrostatics, $\nabla\times\mathbf E=0$. Why is this?

I can understand why this is mathematically but I do not understand the actual why, like in words why this is.
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2answers
67 views

Proof for condition of a Force being conservative

While studying Mechanics, I came to know about a way to test whether a force is conservative. Check whether the expression for the Work done is solvable without the path of the object that is $\int \...
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0answers
55 views

Conservative force as negative gradient of scalar potential

In Classical Mechanics by H. Goldstein it is mentioned that “To satisfy the strong law of action and reaction, $V_{ij}$ can be a function only of the distance between the particles $i$ and $j$, i....
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3answers
159 views

Derivation of Conservation of Energy from Newton's Second Law [duplicate]

Given Newtons's Second Law: $$ \frac {d}{dt} (m \boldsymbol{\dot r}) = \mathbf F $$ How is it possible to derive the conservation of energy equation with a constant mass? That is how can you derive $ ...
0
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1answer
64 views

Point of stokes theorem - conservative field

I am working through electrodynamics at the moment and I have a rather elementary question - which I apologize for. But after some research on google I am still not sure if I have understand "the ...
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2answers
75 views

Can a conservative force do not conserve mechanical energy?

Let us define a conservative force as being a force whose work is path independent. Then, in particular, a vanishing force is conservative. If a force acting on a particle can be written from a ...
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0answers
18 views

Are radial forces always conservative? [duplicate]

Well both gravity and coulombic electrostatic forces are radial forces (acting along the line joining the sources) and their potential energy is defined whereas magnetic force is not radial force and ...
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0answers
74 views

Can a cat be non-Lagrangian?

It is obvious to regard a cat to a system of masspoints (particles) with forces acting between point-pairs satisfying Newton's third law, and assuming that these forces can be arbitrary functions of ...
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1answer
51 views

Definition of non-conservative force [duplicate]

In defining conservative force, we say that "The potential energy difference is path independent." However, as far as I understand, potential energy only exists when there is a force field. ...
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3answers
75 views

Work done over a closed loop

Is it true that the work done in the motion of a body over a closed loop is zero for every force in nature?
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0answers
33 views

Can non-conservative field store energy when work is done?

Taking a non-conservative field like magnetic field (in presence of current density), when work is done can it store energy? If so how?
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0answers
41 views

Is the Casimir force a conservative or a non-conservative forces?

If the Casimir force is a non conservative forces, how can this affect the polarized vacuum theory in the universe's evolution?
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1answer
51 views

Electric field conservation

I was reading on the topic electric field at that time i came up with a question "why electric field is conservative in nature? ". Then i searched it on google but it has been given in terms of work ...
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1answer
82 views

Conservation of mechanical energy proof (Kleppner Kolenkow)

On page 168 of Kleppner and Kolenkow's mechanics they give a proof of the conservation of mechanical energy theorem which starts roughly as follows: The work done by a conservative force depends only ...
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1answer
53 views

Is this understanding of potential energy correct?

I am studying basic mechanics and have reached the chapter on potential energy. However I am a bit confused about the difference between potential energy and the formula for the potential energy due ...
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1answer
43 views

What is the reasoning behind saying the magnetic field is non conservative

I remember hearing this and believing it but I cant seem to show it. If i consider a positive test charge moving around in a uniform magnetic field, then the field always seems to do no work. How can ...
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1answer
62 views

How do conservative forces conserve mechanical energy?

A force that conserves mechanical energy is known as a conservative force. Question: How do conservative forces conserve mechanical energy?
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1answer
216 views

Can someone explain how magnetic potential energy can exist even though the field is non-conservative?

$U=-B\cdot \mu$ is defined to be the magnetic potential energy, I saw this in my lecture notes, but we had already talked about the fact that since the work done to move a charge there is path ...
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1answer
68 views

Is friction an emergent phenomenon?

The microscopic origin of the frictional forces is due to contact between irregularities of the surfaces as seen here [1]. Electromagnetic interactions are the fundamental forces responsible for ...
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1answer
39 views

Meaning of “a force that derives from potential energy”

In mechanics course, when the idea of equilibrium was introduced they included the idea of a force that derives from potential energy which is the force $F$ which is related to the potential energy $...
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1answer
26 views

Electric Potential: Building system of point charges

How can we prove that the amount of work we have to do to build a system of point charges is same , whether we place the point charges one by one or all at once
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0answers
219 views

Static electric field which admits no potential

Conservative condition for (static) electric field $\mathcal{E}$ is usually defined as $\mathcal{E}$ being closed (curl-free). Now this clearly holds when for the given manifold $X$ we have $H_\text{...
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0answers
35 views

Nature of interaction of two magnetic dipoles

Is the force of interaction between two magnetic dipoles a conservative force? If not, how do we find that force?
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2answers
62 views

Can we define potential for all conservative forces?

I know that defining potential for non-conservative forces is not possible and we can define potential and potential energy for conservative forces only. But can we define it for all conservative ...
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1answer
144 views

What is the difference between Non-Conservative and Dissipative?

We often hear these terms. However, they are often confused to be synonyms, but they are not. What are the rigorous definitions of them?
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3answers
166 views

Do conservative forces obey Newton's laws of motion?

Do conservative forces obey Newton's laws of motion? Is the force between two charge particles a counterexample?
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4answers
72 views

Potential Energy of Conservative Forces [closed]

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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1answer
47 views

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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2answers
371 views

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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1answer
134 views

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 ...