A parallel plate capacitor with an air gap has a capacitance of 70µF when the pl

Question

A parallel plate capacitor with an air gap has a capacitance of 70µF when the plates are 1.4mm apart. a)If it stores 0.1mC on each of the plates, what is the potential difference between the plates?b) What is the electric field between the plates? c)For the capacitor the air gap is replaced with water (k = 80), but the charge on the plates is kept the same. d) What is the electric potential difference now? e) What is the electric field now? f) The capacitor has its air gap replaced with water, but now the electric potential is held constant instead of the charge. g) What is the new amount of charge stored on the plates of the capacitor? i) What is the electric field between the plates?

Explanation / Answer

(a) Q = CV

V = Q / C = (.1 x 10^-3) / (70 x 10^-6) = 1.42 V

(b) E = V / d = 1.42 / (1.4 x 10^-3) = 1014.28571 V/m

(c) C' = kC = 80 x 70 = 5600 microF

(d) Q = CV

V = Q/C = (.1 x 10^-3) / (5600 x 10^-6) = .0178 V

(e) E = V/d = .0178 / (1.4 x 10^-3)

E = 12.71 v/m

(f) Q = CV

V = Q/C = (.1 x 10^-3) / (70 x 10^-6)

V = 1.42 V

(g) Q = CV = 5600 x 10^-6 x 1.42 = 0.007952 C

(i) E = V/d = 1.42 / (1.4 x 10^-3)

E = 1014.28 V/m

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