How is the Force related to Energy

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SUMMARY

The discussion centers on the relationship between force and energy in the context of electric fields and capacitors. The participant expresses confusion regarding the conclusion drawn from the equations involving electric force and potential energy. Specifically, they reference the equation F = -∇U, which indicates that a constant potential energy in a capacitor leads to zero force. This conclusion is confirmed as correct, clarifying the misunderstanding regarding the relationship between electric force and potential energy in this scenario.

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  • Understanding of electric fields and forces
  • Familiarity with potential energy in capacitors
  • Knowledge of gradient operations in vector calculus
  • Basic principles of electrostatics
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  • Study the relationship between electric fields and forces using Coulomb's Law
  • Learn about the concept of electric potential energy in capacitors
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Students studying physics, particularly those focusing on electromagnetism, as well as educators looking to clarify concepts related to electric forces and potential energy in capacitors.

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Homework Statement



I'm confused as to how he makes the conclusion for the last portion of the question.

Homework Equations





The Attempt at a Solution



I would have had the following thought process,

[tex]\vec{E_{2}} = 0 = q\vec{F_{2}}[/tex]

[tex]q \neq 0[/tex]

[tex]\Rightarrow \vec{F_{2}} = 0[/tex]

Is this incorrect?

If so, where's the math behind his answer? I'm just not seeing it.
 

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Well, the fixed voltage and charges (on the upper & lower plates) imply that the potential energy stored in the capacitor is a constant.

Your professor is using the relation [itex]F = - \nabla \cdot U[/itex] to show that the constant potential implies zero force.
 

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