Polystyrene has dielectric constant 2.6 and dielectric strength 2.0 ×× 10^7 V/m. A piece of polystyrene is used as a dielectric in a parallel-plate capacitor, filling the volume between the plates.

a. When the electric field between the plates is 80% of the dielectric strength, what is the energy density of the stored energy?
b. When the capacitor is connected to a battery with voltage 500.0 V, the electric field between the plates is 80% of the dielectric strength. What is the area of each plate if the capacitor stores 0.200 mJ of energy under these conditions?