Final answer:
To cause the negatively charged particle to accelerate downwards while it's between charged conducting plates, none of the provided options (A, B, C, D) are correct. The particle is balanced by the electric force and gravitational force, and changing the potential difference would, in fact, result in the opposite movement (upward) as the electric force would become stronger.
Step-by-step explanation:
The scenario described involves a negatively charged particle in a state of equilibrium between two charged conducting plates. The particle is not moving because the electric force exerted by the plates is exactly counterbalanced by the gravitational force acting on the particle. For the particle to start accelerating downwards, the electric force (upward) must become weaker than the gravitational force (downward).
To achieve this, increasing the potential difference between the plates is the correct course of action (Option D). With an increase in potential difference, the electric field strength will increase; since the particle in question is negatively charged, this means that the upward force on the particle will also increase, disturbing the balance. However, since the question asks for what will cause the particle to accelerate downwards, this is not the right choice. Decreasing the charge on the particle (Option A) would not directly affect this scenario since the particle is already at rest, and changing the separation or the length of the plates (Options B and C) doesn't affect the balance of forces directly. Therefore, none of the given options will cause the particle to accelerate downwards.