Question

Polystyrene has dielectric constant 2.6 and dielectric strength 2.0 × 107 V/m. A piece of polystyrene is used as a dielectric in a parallel-plate capacitor, filling the volume between the plates. Part A When the electric field between the plates is 76 % of the dielectric strength, what is the energy density of the stored energy? Express your answer with the appropriate units. u = nothingnothing SubmitRequest Answer Part B When the capacitor is connected to a battery with voltage 500.0 V, the electric field between the plates is 76 % of the dielectric strength. What is the area of each plate if the capacitor stores 0.25 mJ of energy under these conditions? Express your answer with the appropriate units.

Answer 1

2.0 × 107 V/m = 214 V/m, which is a ridiculous number.

looking it up, 19.7 MV/m

take a 1 cm thickness, the breakdown voltage is
19.7 MV/m x 0.01 m = 0.197 MV or 197 kV
76 % of that is 150 kV

Take an area of 1 m²
C = ε₀εᵣ(A/d) in Farads
ε₀ is vacuum permittivity, 8.854e-12 F/m
εᵣ is dielectric constant or relative permittivity
of the material (vacuum = 1)
A and d are the area of the plate in m² and separation in m

C = 2.6(8.854e-12)(1)/(0.01) = 2.30e-9 F
E = ½CV²E= ½(2.30e-9)(150000)² = 25.9 J

energy density is energy/volume = 25.9 J / (1 m²)(0.01m) = 2590 J/m³