# Questions tagged [conservative-field]

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### The conservative force [closed]

I read about the definition of the curl. It's the measure of the rotation of the vector field around a specific point I understand this, but I would like to know what does the "curl of the ...
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### Rigorous definition of potential energy of a system

In the mechanics textbook by Kleppner and Kolenkow, the concept of potential energy is introduced by considering the behaviour of particle under the action of a force $\vec{F}(\vec{r})$ that depends ...
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### How does one prove that the electric field is conservative when it is not defined on simply-connected regions?

I apologize for the ignorance and the rough English in advance, I have an issue understanding how to match both what happens in physics and what I am seeing in calculus. In my calculus class we ...
1 vote
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### Under what circumstances the work done by an external force gets stored as potential energy?

Consider earth and a block as a system. The block is accelerating downward under gravity. Now I apply a force against gravity which is less than the force of gravity. Would the work done against ...
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### Do conservative forces obey Newton's laws of motion? If we look closely, non-conservative forces like Friction etc follow 2nd law but Im confused [closed]

I have a small confusion, do conservative forces obey Newton's Second Law always? Because it depends on the end points and the path taken, the acceleration may vary path to path, but the force doesnt ...
1 vote
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### Conditions for a force to be conservative - Does the second condition imply the first? [duplicate]

John Taylor's Classical Mechanics says this... I was wondering if the second condition already implies the first? I mean, are there situations where the first condition is violated even though the ...
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### Can a non-zero curl vector force field still do a null amount of work?

I've been given a vector field $\vec{F}=(12xy^2, 12yz, 9z^2)$ in cartesian coordinares and I'm asked to calculate the work it would develop on a particle moving from point $A$ to point $B$ through ...
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### How can we define Magnetic Potential Energy if it is non-conservative?

I recently learnt that for a circular wire carrying electric current or for a magnetic dipole, if it is kept in a uniform magnetic field, we can define its magnetic potential energy. This would mean ...
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### Is this statement about conservative fields and parallel circuits correct?

I am wondering if this statement about parallel circuits and conservative fields is true?: The voltage drop over resistors in parallel is the same because the electric field is conservative, so the ...
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1 vote
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### Exact test for checking conservative forces

What is the nature of this force on the path $x^2+y^2=1$? $$\tag1\vec F=\frac{-y\,\hat{i }+x\,\hat{j}}{x^2+y^2}.$$ I tried two methods, but they give different answers: For this specific path it ...
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### Are all one-dimensional force fields conservative? [closed]

Just checking a rather small thing: given any open set $U$ of $\mathbb{R}$ and any force field $f:U\to \mathbb{R}$, then $f$ is conservative since it is the gradient of any of its antideratives. Right?...
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### Does a charge moving freely in an electric field's direction, produce a magnetic field?

Does a charge moving freely in an electric field's direction, produce a magnetic field? If so, then why is energy conserved in cases of distance of closest approach? If there is a magnetic field it is ...
1 vote
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### Is the conservativity of a force frame independent? If so, how do you show it?

If a force $\vec{f}$ is conservative in a frame $S$, is it such in another, generic, frame of reference $S'$? How do you show this, and how are the potential energies in the two frames related?
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### Intuition behind relation between intensity of gravitational field and gravitational potential

I found out that the gravitational field intensity, $\vec{I}$ is the negative derivative of the gravitational potential $V$ wrt to distance $r$ from (point) mass. Can someone provide some intuition ...
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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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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 ...