Question

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?

Answer 1

Answer:

(a) 1133J/m

(b) 5.714m²

Explanation:

(a) u = 1/2×εE²

εo = 8.85×10-¹² F/m

E = 0.8 × 2.0×10⁷V/m = 1.6×10⁷V/m

u = 1/2×8.85×10-¹² × (1.6×10⁷)²= 1132.8J/m

(b)

U = 1/2CV² = 1/2(Aεo/d)×V²

U = 1/2(Aεo/d)×V²

U = 200mJ = 200×10-³

d = V/E = 500/ (1.6×10⁷) =3.13×10-⁵m

200×10-³ = 0.5×A×8.85×10-¹²×500²/3.13×10-⁵

200×10-³ = 0.035A

A = 200×10-³/ 0.035 = 5.714m².