Final answer:
To calculate the capacitance of a parallel-plate capacitor with given dimensions, use the capacitance formula with the area of the plates and the separation distance, converting all units appropriately to find the capacitance in pico-Farads (pF).
Step-by-step explanation:
To find the capacitance of a parallel-plate capacitor with circular plates, you can use the formula C = ε_0 * (A / d), where ε_0 is the vacuum permittivity (8.85 × 10⁻¹² F/m), A is the area of one of the plates, and d is the separation between the plates. Since you are provided with the radius of the circular plates, 32 cm, you must first convert it to meters and then calculate the area using the formula A = π * r². The separation distance is also given in millimeters, which needs to be converted to meters before using it in the formula.
Step 1: Convert the radius to meters: radius = 0.32 m.
Step 2: Calculate the area of the plates: A = π * (0.32 m)².
Step 3: Convert the separation to meters: d = 2.1 mm = 2.1 × 10⁻³ m.
Step 4: Calculate the capacitance using the formula and the given constants.
Step 5: Convert the result to picofarads by multiplying by 10¹².
By performing these calculations, and considering the units for capacitance in pF, you can find the capacitance value that is relevant to the student's schoolwork question.