Consider a colloidal suspension of the latex particles confined among two plates. The plates are charged, so there is an electric potential difference V between them (as shown below). The number of particles is N and the temperature is T. The system is isolated from the environment and gravitational effects are negligible.

Let each particle carries a positive charge +q so that they are more likely to be close to the plate at the top in the figure, which is negatively charged, than the bottom one, which is positively charged. The system is much dilute, so particles are independent of each other and the electrostatic interaction among particles can be neglected. For simplicity, suppose that in the z direction each particle might only be at one of the given two locations: either attached to the top plate or attached to the bottom one.

i) Compute the fraction of particles attached to the top plate. Sketch this as a function of:

(a) T,
(b) V.

Discuss the physical meaning of your outcomes.