The capacitance of the air-filled capacitor is 0.118 πr² meter.
The ideal air-filled parallel-plate capacitor is a simple case of the capacitor. The capacitance of the air-filled capacitor can be determined as
C = ε₀ . A / d
where C is the capacitance of the capacitor, ε₀ is the vacuum permeability (8,85 x 10‾¹² F/m), A is the area of plate (m²) and d is a distance of the plate (m).
From the question above, we know that:
A = 4 x π x r²
C = 300 pF
By substituting the parameter, we get
C = ε₀ . A / d
300 x 10‾¹² = 8,85 x 10‾¹² . 4 x π x r² / d
d = 35.4 x 10‾¹² x π x r² / 300 x 10‾¹²
d = 0.118 πr² meter
where r is radius of plate.
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