A capacitor consists of two square plates, 6.2 cm on a side, separated by a 2.0 mm air gap. How much energy would be stored in the capacitor if a mica dielectric is placed between the plates? Assume the mica is 2.0 mm thick (and therefore fills the space between the plates). The charges on the plates are equal and opposite and of magnitude 440 μC.

Question

Collin Noble

Chemistry

14 October, 12:20

A capacitor consists of two square plates, 6.2 cm on a side, separated by a 2.0 mm air gap. How much energy would be stored in the capacitor if a mica dielectric is placed between the plates? Assume the mica is 2.0 mm thick (and therefore fills the space between the plates). The charges on the plates are equal and opposite and of magnitude 440 μC.

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Answers (1)

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Day · Answer 1

E = 1053.365 J

Explanation:

E = Q²/2C

∴ Q = 440μC * (1 E-6 C / μC) = 4.4 E-4 C

∴ C = k*εo*A / d

∴ k mica = 5.4

∴ εo = 8.8542 E-12 C² / N. m²

∴ A = 6.2cm * 6.2 cm = 38.44 cm² * (m/100cm) ² = 3.844 E-3 m²

∴ d = 2mm * (m / 1000mm) = 2 E-3 m

⇒ C = ((5.4) * (8.8542 E-12) * (3.844 E-3)) / 2 E-3

⇒ C = 9.1896 E-11 C²/N. m

⇒ E = (4.4 E-4) ² / (2*9.1896 E-11)

⇒ E = 1053.365 N. m = 1053.365 J