Question

An isolated sphere has a capacitance of 60 pF, what is the radius of the sphere?

• A. 540 cm
• B. 54 cm
• C. 0.054 cm
• D. 0.54 cm

Hint:

For an isolated sphere, capacitance is directly proportional to its radius: \(C = 4\pi\varepsilon_0 R\). Convert units properly when solving.

Answer 1

The Correct Option is B

The capacitance of an isolated sphere is given by: \[ C = 4\pi \varepsilon_0 R \] Given: \( C = 60 \, \text{pF} = 60 \times 10^{-12} \, \text{F} \), \(\varepsilon_0 = 8.85 \times 10^{-12} \, \text{F/m}\)
\[ R = \frac{C}{4\pi \varepsilon_0} = \frac{60 \times 10^{-12}}{4\pi \times 8.85 \times 10^{-12}} \approx \frac{60}{111.3} \approx 0.539 \, \text{m} = 54 \, \text{cm} \]