If one intends to build a 1.0 farad capacitor using circular discs separated by a distance of 1.0 mm , what must be the radius of the discs?

Step-by-step solution

The capacitance of a parallel plate capacitor is given by C = ₀ A d . For circular discs of radius r , the area is A = r^2 . Substituting the area into the capacitance formula gives C = ₀ r^2 d . Rearranging for r^2 , we get r^2 = C d ₀ . We know that 1 4 ₀ = 9 10^9 1 ₀ = 36 10^9 . Substituting the given values C = 1.0 F and d = 1.0 mm = 10⁻³ m : r^2 = 1.0 10⁻³ 36 10^9 = 36 10^6 m ^2 r = 36 10^6 = 6000 m = 6 km