Final answer:
The capacitance of the spherical capacitor is approximately 1.06 x 10^-10 F. The plate area of a parallel-plate capacitor with the same plate separation and capacitance is approximately 3.79 x 10^-9 m².
Step-by-step explanation:
(a) To calculate the capacitance of a spherical capacitor, we can use the formula:
C = 4πε₀ab / (b - a)
Where C is the capacitance, ε₀ is the permittivity of free space (8.85 x 10-12 F/m), a is the radius of the inner sphere, and b is the radius of the outer sphere.
In this case, the inner sphere has a radius of 33.0 mm (0.033 m) and the outer sphere has a radius of 42.0 mm (0.042 m).
Plugging in the values:
C = (4π * 8.85e-12 * 0.033 * 0.042) / (0.042 - 0.033)
C ≈ 1.06 x 10-10 F
(b) To find the plate area of a parallel-plate capacitor with the same plate separation and capacitance, we can use the formula:
A = C * d / ε₀
Where A is the plate area, C is the capacitance, d is the plate separation, and ε₀ is the permittivity of free space.
Using the previously calculated capacitance:
A = (1.06 x 10-10 F * 0.033 m) / 8.85e-12 F/m
A ≈ 3.79 x 10-9 m²