Question

What is the capacitance of the empty shelves if they have an area of 1.00×10² m² and are 0.200 m apart?

a. 8.85 × 10⁻¹¹ F
b. 4.44 × 10⁻¹² F
c. 1.77 × 10⁻¹⁰ F
d. 2.22 × 10⁻¹¹ F

Answer 1

The capacitance of the empty parallel-plate capacitor with plates having an area of 1.00 × 102 m2 and separated by 0.200 m is 4.44 × 10-10 F.

Step-by-step explanation:

The question is about calculating the capacitance of an empty parallel-plate capacitor which is a common topic in high school physics. The formula to find the capacitance (C) of a parallel-plate capacitor is given by:

C = ε0 (A/d), where ε0 is the permittivity of free space, A is the area of one plate, and d is the distance between the plates.

The permittivity of free space (ε0) has a value of 8.85 × 10-12 F/m (farads per meter). Using the provided area (A = 1.00 × 102 m2) and distance (d = 0.200 m), we can calculate the capacitance as follows:

C = (8.85 × 10-12 F/m) × (1.00 × 102 m2 / 0.200 m) = 4.425 × 10-10 F, which rounds to 4.44 × 10-10 F when expressed with three significant figures.

Therefore, the correct answer to the question is (c) 4.44 × 10-10 F (1.77 × 10-10 F).