1. Concept: The physical dimensions of a parallel plate capacitor completely dictate its capacitance in a vacuum/air.
2. Formula: $$ C = \frac{A \epsilon_0}{d} $$
3. Solution: - Given area: \( A = 2.0 \text{ m}^2 \).
- Given distance: \( d = 2.0 \text{ mm} = 2.0 \times 10^{-3} \text{ m} \).
- Permittivity constant: \( \epsilon_0 = 8.85 \times 10^{-12} \text{ F/m} \).
- Substitute values: \( C = \frac{(2.0) (8.85 \times 10^{-12})}{2.0 \times 10^{-3}} \)
- The 2.0 cancels out, leaving: \( C = 8.85 \times 10^{-12} \times 10^3 = 8.85 \times 10^{-9} \text{ F} \).
4. Why other options are incorrect: The applied voltage is a distractor and does not change the physical capacitance. Other options result from incorrectly utilizing the voltage or making arithmetic errors with the powers of 10.
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