# Work done by a conservative force

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Does the work done by the force remain 0 even if it varies at all points on the loop ?

Yes. For example, the gravitational force.

Note, that in general fields are not conservative. So if you write an arbitrary force, the work will not be zero.

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### Rijul Gupta

Updated on June 20, 2022

• Rijul Gupta less than a minute

A conservative force is a force with the property that the work done in moving a particle between two points is independent of the taken path. Equivalently, if a particle travels in a closed loop, the net work done (the sum of the force acting along the path multiplied by the distance travelled) by a conservative force is zero.

Does the work done by the force remain 0 even if it varies at all points on the loop? From the definition given in wikipedia it seems as if it is defined for work done by a constant conservative force. Is the work done over a loop 0 for variable forces as well? Can it be somehow proven for a variable force?

• Rijul Gupta over 8 years
No I mean varying with point and for gravitational force we can take approximation that it is constant. I know the work is 0 even for forces varying extremely from point to point over a loop too, but can we just apply it everywhere ? How ?
• Rijul Gupta over 8 years
physics.stackexchange.com/questions/87621/… please take a look and tell me what I am doing wrong here then ?
• Rijul Gupta over 8 years
The field is electrostatic, I think it should be conservative only
• Rijul Gupta over 8 years
So if I set up an electric field which has a dependency on y as I mentioned then in that case it is possible that the field may not be conservative even though it is electrostatic in nature ?
• Rijul Gupta over 8 years
But just in case hypothetically, I did what will be its consequence ?
• Rijul Gupta over 8 years
Did you read this ? physics.stackexchange.com/questions/87249/… If somehow the field is proven my assigning energy crisis would be solved, as you said the laws would themselves proclaim formation of energy.
• Rijul Gupta over 8 years
Aside from the agreement with established laws, did you read it ? Any comments ?
• jinawee over 8 years
@rijulgupta I didn't read it because it's deleted. Still, my answer is the same. Aside from the agreement with established laws this site is about mainstream physics. Aside from established laws you can cure cancer if you drink water upside down, predict the future seeing tea leaves, etc. The scientific method has resisted hundreds of years, so it's very unlikely that some random person will destroy the foundations of Physics. So you can spread your ideas somewhere else, but not here. Anyway, if you're so sure why don't you build it and earn billions with it? Please stop being a crackpot.
• Rijul Gupta over 8 years
Maybe you are misinterpreting what I am saying, I have formulated a conceptual machine and I have been trying to explain the results on basis of established laws only, there is no need to call names or to say that I am trying to destroy established science. Only if I myself or someone else cannot explain it I havent discarded the idea, as far as building it goes, if you would have read it you would understand it would be an expensive and difficult device to build and I neither have the precision skills or the budget at the moment to test the machine practically