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22 October, 16:33

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?

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  1. 22 October, 18:09
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    (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.
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