Simplified model. We will first look at a simplified model of the system where we disregard the edge effects. We assume that the plates are very long compared to the other lengths in the system, i.e. iota > `h and` iota >d. The upper and lower metal plate are connected to the plus pole and the middle plate is connected to the minus pole of a battery with emf V0. The wire from the minus pole to the battery has a resistance R. You can assume that the other wires have zero resistance. 

The capacitor consisting of the three plates has a capacitance C which we will calculate below.

Task 1: 

Use Gauss's law to find the electric field along the y-axis expressed by the charge Q on the capacitor and relevant quantities (eg varepsilon 0, d, h, L, and `).

Task 2: 

Use the Laplace equation to find the electric potential and the electric field along the same line expressed by the potential difference V0. Explain what assumptions you make about the boundary conditions.