Answer :
a) The capacitance of the spherical capacitor is 3.07 × 10^(-12) F
b) Number 3.07 × 10^(-12) Units F
The step-by-step calculations:
1. Given radii: r₁ = 36.9 mm and r₂ = 41.3 mm.
Convert radii to meters:
r₁ = 0.0369 m
r₂ = 0.0413 m
2. Use the formula for the capacitance of a spherical capacitor:
C = (4πε₀r₁r₂) / (r₂ - r₁)
3. Substitute the values into the formula:
C = (4π × 8.85 × 10^(-12) × 0.0369 × 0.0413) / (0.0413 - 0.0369) F
4. Perform the calculations:
C = (4π × 8.85 × 10^(-12) × 0.001523) / 0.0044 F
C = (1.35 × 10^(-14)) / 0.0044 F
C = 3.07 × 10^(-12) F
5. Convert the result to scientific notation:
C = 3.07 × 10^(-12) F
So, the capacitance of the spherical capacitor is 3.07 × 10^(-12) F.