# 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 ...
2answers
67 views

### 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 ...
1answer
46 views

### 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 ...
3answers
402 views

### 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 ...
0answers
10 views

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

Context In , 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 ...
1answer
28 views

### 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 ...
5answers
891 views

### 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 ...
2answers
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.
1answer
29 views

3answers
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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 ...
1answer
65 views

### 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 ...
0answers
24 views

### 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 ...
1answer
73 views

### 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 ...
1answer
123 views

### 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 ...
1answer
78 views

### 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 ...
0answers
50 views

### $\text{div} \ \vec{F} = \vec{0}$ 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}{\...
2answers
266 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 ...
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 ...
0answers
21 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 ...
2answers
2k 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 ...
1answer
267 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?
2answers
252 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. ...
4answers
1k 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 ...