Question

A capacitor is constructed using two concentric spheres and air as the dielectric medium (permittivity of air = \(8.854 \times 10^{-12} \, \text{F/m}\)). The radii of the inner and outer spheres are \(a = 10 \, \text{cm}\) and \(b = 15 \, \text{cm}\), respectively. The capacitance (in picofarads) is _________ (round off to 2 decimal places).

Answer 1

Correct Answer: 32.8

The capacitance of a spherical capacitor is given by the formula: \[ C = 4 \pi \epsilon_0 \frac{ab}{b - a} \] Substituting the given values: \[ C = 4 \pi \times 8.854 \times 10^{-12} \times \frac{0.1 \times 0.15}{0.15 - 0.1} \] \[ C = 4 \pi \times 8.854 \times 10^{-12} \times 0.3 = 3.34 \times 10^{-12} \, \text{F} = 33.4 \, \text{pF} \] Thus, the capacitance is \( \boxed{33.4} \, \text{pF} \).