Two large oppositely and uniformly charged parallel plates are separated by \(10 \mathrm{~mm}\). An electron is projected halfway between the plates and parallel to them with an initial speed of \(4.0 \times 10^{6} \mathrm{~m} / \mathrm{s}\). The electron hits the top plate a horizontal distance of \(20 \mathrm{~mm}\) from where the electron was projected.

(a) Which plate is negatively charged, top or bottom?

(b) What is the surface charge density on the plates if you know that the densities have the same magnitude?