Force fields and law of conversation of energy

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Force fields, such as magnetic, electric, and gravitational fields, do not violate the law of conservation of energy because they arise from the potential energy associated with the interactions of objects. The forces experienced by particles in these fields result from the gradients of potential energy, indicating that energy is conserved within the system. In classical field theory, both the fields and the matter they interact with possess energy and momentum, which are conserved during interactions. The discussion emphasizes that energy is a product of these forces rather than the cause of them. Overall, the conservation of energy remains intact when considering the dynamics of force fields and their interactions.
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Why aren't force fields such as magnetic, electric and gravitational fields considered as a violation to law of conversation of energy?? :confused:
 
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Why would they be?
 
Drakkith said:
Why would they be?
After I wrote the topic It came on my mind that my question is illogical since all these forces arise due to the potential gained by the body.
 
Actually I think energy is the result of these forces interacting with objects, not the other way around.
 
Drakkith said:
Actually I think energy is the result of these forces interacting with objects, not the other way around.

No, the OP had it correct. Given a field, the forces on particles coupling to the field arise from derivatives of the coupling term(s). In the simplest cases (e.g. EM), this would be (minus the) the gradient of the potential energy. A more general treatment can be found in the formalism of classical field theory.
 
The fields themselves have energy and momentum (dynamic fields anyways), this combined with the energy and momentum of the matter fields is conserved assuming all interactions are mediated by the field.
 

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