Force fields and law of conversation of energy

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SUMMARY

Force fields, including magnetic, electric, and gravitational fields, do not violate the law of conservation of energy. The forces acting on particles within these fields arise from the derivatives of the coupling terms, specifically the gradient of potential energy in electromagnetic fields. Classical field theory provides a comprehensive framework for understanding these interactions, where both the fields and matter fields possess energy and momentum, ensuring conservation during interactions.

PREREQUISITES
  • Understanding of classical field theory
  • Familiarity with electromagnetic (EM) fields
  • Knowledge of potential energy concepts
  • Basic principles of energy and momentum conservation
NEXT STEPS
  • Study the principles of classical field theory
  • Explore the gradient of potential energy in electromagnetic fields
  • Investigate the energy and momentum of dynamic fields
  • Review conservation laws in physics
USEFUL FOR

Physics students, educators, and anyone interested in the principles of force fields and energy conservation in classical mechanics.

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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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