Final answer:
To determine the proper value of L for the metal squares in order to construct a 400 pF capacitor, use the capacitance formula for a parallel-plate capacitor and solve for L.
Step-by-step explanation:
The question pertains to constructing a parallel-plate capacitor with a specified capacitance of 400 pF using metal plates with spacers in between them. To determine the proper value of L for the metal squares, we can use the formula for the capacitance of a parallel-plate capacitor:
C = ε₀(εr)(A/d)
Where ε₀ is the permittivity of free space, εr is the relative permittivity or dielectric constant (for air, εr is close to 1), A is the area of the plates in square meters, and d is the separation between the plates in meters. Given the capacitance (C = 400 pF), the thickness of the spacers (d = 0.20 mm), and that we're using air as the dielectric as the spacers are thin:
C = (8.85 × 10⁻¹² F/m)(1)(L²/0.20 × 10⁻³ m)
Solving for L and converting it to centimeters gives:
L = √((400 × 10⁻±² F)(0.20 × 10⁻³ m)/(8.85 × 10⁻¹² F/m)) × 100 cm/m
This calculation will yield the proper value of L in centimeters.