A parallel-plate capacitor is constructed from circular discs, each with a radius of 5.0 cm . Determine the capacitance if the separation between the plates is 1.0 mm .

Step-by-step solution

Given: Radius of circular disc, r = 5.0 cm = 5 10⁻² m Separation between plates, d = 1.0 mm = 10⁻³ m Permittivity of free space, ₀ = 8.85 10⁻¹² F/m Area of the plate, A = r^2 = (5 10⁻²)^2 = 25 10⁻⁴ m ^2 Capacitance of a parallel-plate capacitor is given by: C = ₀ A d Substituting the values: C = 8.85 10⁻¹² 25 10⁻⁴ 10⁻³ C = 8.85 25 3.14 10⁻¹³ C = 694.7 10⁻¹³ F C 6.95 10⁻¹¹ F