Relationship: Force on a charge at some distance from capacitor Plates

[Minhtran1092]

Homework Statement

Two capacitor plates (infinite plane) with uniform charge distribution but different charges (one positive, one negative) are distance "d" apart. A charge is place at d/2 and feels force |F1|. A charge is placed at d/4 and feels force |F2|. How does |F1| compare to |F2|?

Homework Equations

F=qE (Force on a test charge is proportional to the electric field at the point charge)
E = η/ε₀ (η = Q/A, charge distribution); Electrical field between two parallel plate capacitors

The Attempt at a Solution

The electrical field between two parallel plate capacitors is constant and uniform in direction at any point. Since F=qE, E is constant and 'q' is negligible, F≈E everywhere. Thus, |F1|=|F2|.

 

[TSny]

That looks good except for the statement F≈E. q is assumed negligible in the sense that it is assumed q does not disturb the uniform charge distributions on the plates. But that doesn't mean that you can ignore q in the equation F = qE. Do you see that your answer is still valid even for F = qE?