2. A parallel plate capacitor consists of plates at z = 1d/2. The surface charge density on each plate is o(2 = d/2) = 0o and o(z = -d/2) = -50. From the time t = 0, we start moving both plates in the r direction at a speed vr(t) that slowly increases with time. Assume that the plates are so large that they can be treated as infinite, but that they are massless. (a) What is the magnetic field at time t? Note that there are currents flowing when t > 0. (b) What is the rate of change of the electromagnetic energy density in the region between the capacitor plates? (c) What is the electromagnetic field momentum density in the region between the plates? (d) Calculate the Faraday electric field on the top and bottom plates. Show that the work done on the plates balances the rate of increase of electromagnetic energy. (e) Use the same Faraday electric field to calculate the force on the plates and show that it is equal to the rate of increase of electromagnetic momentum