An electron with an initial kinetic energy of \(400 \text{ eV}\) is injected into the region between two oppositely charged, horizontal parallel plates separated by a distance \(d\). The electron enters at the surface of the bottom plate with an initial velocity directed at an angle \(\theta = 30^\circ\) above the horizontal. A uniform electric field of magnitude \(E = 2.0 \times 10^4 \text{ N/C}\) is directed vertically upward between the plates. What is the minimum plate separation \(d\) required to prevent the electron from colliding with the top plate?