Questions tagged [conservative-field]
307 questions
24
votes
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Are all central forces conservative?
It might be just a simple definition problem but I learned in class that a central force does not necessarily need to be conservative and the German Wikipedia says so too. However, the English Wikipedia states different on their articles for…
n3rd
- 393
22
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2 answers
What causes a force field to be "non-conservative?"
A conservative force field is one in which all that matters is that a particle goes from point A to point B. The time (or otherwise) path involved makes no difference.
Most force fields in physics are conservative (conservation laws of mass,…
Tom Au
- 333
22
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5 answers
Why should Conservative forces have their curl equal to zero? (intuition)
There are several conditions that must be met in order for a force to be conservative.
One of them is that the curl of that force must be equal to zero?
What is the physical intuition behind this?
If you can, please explain it to me via the magnetic…
TheQuantumMan
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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 work done by the force is independent of the…
satan 29
- 1,345
18
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5 answers
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 of starting and ending point and they can be…
AbsoluteZero
- 558
18
votes
1 answer
How do non-conservative forces affect Lagrange equations?
If we have a system and we know all the degrees of freedom, we can find the Lagrangian of the dynamical system. What happens if we apply some non-conservative forces in the system? I mean how to deal with the Lagrangian, if we get any external…
user58143
17
votes
4 answers
What exactly makes a force conservative?
I get that forces can be classified as either conservative or non-conservative, depending on whether the work done in a round trip is zero or non-zero.
What property of the force makes it to be, conservative or non-conservative, so that the work…
vs_292
- 957
14
votes
2 answers
What is a potential?
I am self-studying electrodynamics and am wanting to know what is meant by a potential. I understand the concept of potential energy but what is meant by a potential? Is it the same thing as a field, like gravitation or electromagnetic?
Steven
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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 described by
$\vec{F} = -\hat{x}\frac{y}{x^2+y^2} +…
Lucas Sievers
- 165
13
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5 answers
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 independent of the curve taken from one to the…
user276626
12
votes
4 answers
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 conservation…
Davius
- 1,700
12
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2 answers
Are fundamental forces conservative?
I wonder whether fundamental forces are conservative.
First of all, I'm not sure if we can talk about conservative forces, since to study electromagnetism, weak and strong interactions we need QFT.
For gravity, I'd that it's not conservative,…
jinawee
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Can a force in an explicitly time dependent classical system be conservative?
If I consider equations of motion derived from the principle of least action for an explicitly time dependent Lagrangian
$$\delta S[L[q(\text{t}),q'(\text{t}),{\bf t}]]=0,$$
under what circumstances (i.e. which explicit functional $t$-dependence)…
Nikolaj-K
- 8,873
11
votes
1 answer
Why is the electric field created by a battery non-conservative?
Electromotive force(emf) or $\mathcal{E}$ is defined as $$\mathcal{E} = \oint \frac{\vec{F}}{q} \cdot \mathrm{d}\vec{s}$$ Here, $\vec{F}$ is the force which pushes the charges through a conducting wire loop, $q$ is the magnitude of charge and…
Apoorv Potnis
- 1,419
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5 answers
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\times\nabla U=\boldsymbol0$$
Conservative forces…
TunaSandwich
- 148