How is the Force related to Energy

In summary, the student is confused about the conclusion made in the last portion of a question and asks for clarification on the math behind it. The professor explains that the fixed voltage and charges on the capacitor imply a constant potential energy, and uses the relation F = -\nabla \cdot U to show that this implies zero force.
  • #1
jegues
1,097
3

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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  • #2
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.
 

1. How is the Force related to Energy?

The Force and energy are closely related concepts in physics. The Force is defined as any influence that can cause an object to accelerate, whereas energy is the ability to do work. In other words, the Force is a measure of change in energy, and energy is required to create a Force. They are two sides of the same coin, with the Force being the cause and energy being the effect.

2. Can energy be converted into the Force?

Yes, energy can be converted into a Force. This phenomenon is known as the principle of conservation of energy, which states that energy cannot be created or destroyed but can only be converted from one form to another. For example, potential energy can be converted into kinetic energy, which can then create a Force by causing an object to accelerate.

3. What is the role of energy in the Force?

Energy is essential for the existence of the Force. Without energy, there can be no Force. This is because energy is required to create a change in an object's motion, and a Force is the cause of that change. In other words, the amount of energy present in a system determines the magnitude of the Force that can be produced.

4. How does the Force affect energy?

The Force can affect energy in several ways. When a Force is applied to an object, it can change the object's energy by causing it to move or change its position in space. Additionally, the Force can also change the form of energy, such as converting potential energy into kinetic energy. The amount of Force applied also determines the amount of energy that is transferred.

5. Is the Force a form of energy?

No, the Force is not a form of energy. While energy is a measurable physical quantity, the Force is a concept used to describe the interactions between objects. The Force is not a physical substance that can be measured or quantified like energy. However, as mentioned earlier, the Force and energy are closely related, and energy is required to create a Force.

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