Acertain dielectric with a dielectric constant = 24 can withstand an electric field of 4 107 v/m. suppose we want to use this dielectric to construct a 0.89 µf capacitor that can withstand a potential difference of 1930 v. (a) what is the minimum plate separation? (b) what must the area of the plates be?

Explanation:

Electric field E = 4 x 10⁷ V / m

Dielectric constant k = 24

capacitance of capacitor

C = kε₀ A / d

d = plate separation

A =  plate area

C = .89 x 10⁻⁶

V / d = electric field

for minimum d , electric field will be maximum

V / d  = 4 x 10⁷

1930 / d = 4 x 10⁷

d = 1930 / 4 x 10⁷

d = 482.5 x 10⁻⁷ m

= 48.25 x 10⁻⁶ m

C = kε₀ A / d

.89 x 10⁻⁶ = 24 ε₀ A / d

A = .89 x 10⁻⁶  X d /  24 ε₀

A = .89 x 10⁻⁶  X 48.25 x 10⁻⁶  /  24  x 8.85 x 10⁻¹²

= 42.9 / 212.4

= .2019 m²

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