How is the Force related to Energy

[jegues]

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,

$$\vec{E_{2}} = 0 = q\vec{F_{2}}$$

$$q \neq 0$$

$$\Rightarrow \vec{F_{2}} = 0$$

Is this incorrect?

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

 

[Redbelly98]

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 $F = - \nabla \cdot U$ to show that the constant potential implies zero force.