2. Consider a mix of sand (effectively silicon dioxide) with & = 3.9 and oil with cy = 2.2. For some reason (and I have no idea why, but this is one of those weird things that happens in physics problems, so bear with me on this) oil has been poured into a large horizontal tray of sand that is 10cm in height. The density of the sand is constant, but the density of the oil increases linearly with depth - it accounts for 0% of the volume at the upper surface of the sand and 20% of the volume at the bottom (since it can fit between sandgrains). (a) Assume the permittivity is the linear combination of the two distinct mate- rials; what is the permittivity of this mixture as a function of height? (b) Now (and for who knows what reason) the tray of sand is placed between two plates with a potential difference of 100 Volts. What is the resulting charge distribution? (At the top, bottom and interior of the mixture; you can assume the mixture is homogeneous and use the results for surface and volume charges directly.)