GATE Electronics and Communications (EC) 2016 Shift 2 Solved Paper

A positive charge $\mathit{q}$ is placed at $\mathit{x}=0$ between two infinite metal plates placed at $\mathit{x}=-\mathit{d}$ and at $\mathit{x}=+\mathit{d}$ respectively. The metal plates lie in the yz plane.

The charge is at rest at $\mathit{t}=0$, when a voltage $+\mathit{V}$ is applied to the plate at $\mathit{–}\mathit{d}$ and voltage $-\mathit{V}$ is applied to the plate at $\mathit{x}=+\mathit{d}$. Assume that the quantity of the charge $\mathit{q}$ is small enough that it does not perturb the field set up by the metal plates. The time that the charge $\mathit{q}$ takes to reach the right plate is proportional to