Polystyrene has dielectric constant 2.6 and dielectric strength 2.0 times 10^7 V

Question

Polystyrene has dielectric constant 2.6 and dielectric strength 2.0 times 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?

Explanation / Answer

a.) The energy density of a capacitor is given by = 0.5E2

where = Ko  and where K is the dielectric constant and E is the electric field.

= 2.6 x 8.854187817 × 1012 = 2.302088832 x 10-11

E = 80 % of dielectric strength = 0.8 x 2 x 107 = 1.6 x 107

So, the energy density = 0.5 x  2.302088832 x 10-11 x (1.6 x 107 )2 = 2946.673705 J /m3

b.) if d is the distance between the capacitor plates, then E = V/d

So, 1.6 x 107 = 500 / d

d = 3.125 x 10-5 m

Now, energy stored in a capacitor is given by 0.5CV2

So, 0.2 x 10-3 = 0.5 x C x 5002

C = 1.6 x 10-9 F

Capacitance of a capacitor is given by C = A /d where A is the area of the parallel plate capacitor.

1.6 x 10-9 =  2.302088832 x 10-11 x A / 3.125 x 10-5

A = 2.171940514 x 10-3 m2

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