Question

The capacity of a spherical conductor is \(1.0\) pF. Its radius will be:

• A. \(1\, \text{m}\)
• B. \(9\, \text{km}\)
• C. \(10\, \text{m}\)
• D. \(11\, \text{cm}\)

Hint:

Capacitance of spherical conductor depends linearly on its radius: \[ C = 4\pi \varepsilon_0 r. \]

Answer 1

The Correct Option is D

The capacitance \( C \) of a spherical conductor is given by: \[ C = 4\pi \varepsilon_0 r, \] where \( r \) is the radius. Given: \[ C = 1.0 \, \text{pF} = 1.0 \times 10^{-12} \, \text{F}, \quad \varepsilon_0 = 8.854 \times 10^{-12} \, \text{F/m}. \] Solving for \( r \): \[ r = \frac{C}{4\pi \varepsilon_0} = \frac{1.0 \times 10^{-12}}{4\pi \times 8.854 \times 10^{-12}} \approx 0.009 \, \text{m} = 0.9 \, \text{cm}. \] Since 0.9 cm is close to 1 cm, the closest given option is (D) 11 cm (probably a typo in options; correct value is about 0.9 cm). Please verify options.