Understanding the Relationship Between Force and Potential: Proving F = -dv/dx

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Discussion Overview

The discussion centers on the relationship between force and potential, specifically exploring the equation F = -dV/dx. Participants seek to understand the implications of this relationship in both classical and quantum contexts.

Discussion Character

  • Exploratory, Technical explanation, Conceptual clarification, Debate/contested

Main Points Raised

  • One participant questions how to prove the relation F = -dV/dx and seeks clarification on the meaning of force being equal to the change in potential per distance.
  • Another participant points out a potential ambiguity in the notation, suggesting that "v" might be misinterpreted as velocity instead of potential difference (V), and provides a derivation involving the electric field and electrostatic potential.
  • A third participant connects the concept of force to work done, stating that force multiplied by distance equals the change in energy, leading to the expression F = dE/dx.
  • A later reply introduces a question regarding the interpretation of potential in quantum mechanics, specifically asking about the implications of a particle having V = 0.

Areas of Agreement / Disagreement

Participants express varying interpretations of the relationship between force and potential, with no consensus reached on the implications of potential in quantum mechanics or the clarity of the notation used.

Contextual Notes

There are ambiguities regarding the notation used for potential and velocity, as well as unresolved questions about the implications of a zero potential in quantum mechanics.

sciboudy
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how can we prove this relation F= -dv/dx
could some one explain what we mean by the force equal to the change it potential per distance and
 
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sciboudy said:
how can we prove this relation F= -dv/dx
could some one explain what we mean by the force equal to the change it potential per distance and

Your question is ambiguously presented, because it appears as if "v" is velocity, rather than "V" as in electrical potential difference.

You should know that the electric field E is E = -d\Phi /dx in 1-dimension. Since F=qE, then F=qE= -q d\Phi /dx, where \Phi is the electrostatic potential. But q \Phi is V, the potential difference. Thus, F=- dV/dx.

In 3D, the derivative in 1D is replaced by the grad operator.

Zz.
 
If you accept that energy (work done) is basically Force x distance then:
Force x distance = change in energy
F x dx = dE so F = dE/dx
 
OK thank you sir ZApperz and thank you truesearch
now i have another question based in the meaning of potential in the quantum mechanics
what is the potential for example whe i say a particle have V=0 ? is that mean the particle will never stop any time ?? or what
 

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