Given:
Capacitance (C) = 2 nF = 2 x 10^-9 F
Plate separation (d) = 1 cm = 0.01 m
Permittivity of free space (ε₀) = 8.85 x 10^-12 C^2/N m^2
The formula for the capacitance of a parallel plate capacitor is:
C = (ε₀ * A) / d
Rearranging the formula to solve for the area of the plates (A):
A = (C * d) / ε₀
Plugging in the values:
A = (2 x 10^-9 F * 0.01 m) / (8.85 x 10^-12 C^2/N m^2)
A = (2 x 10^-11) / (8.85 x 10^-12)
A = 2.26 x 10^-11 / 8.85 x 10^-12
A = 2.55 m^2
Therefore, the area of the plates of the capacitor is 2.55 square meters.
