Question

The capacitance of an isolated metallic sphere of diameter $36\text{cm}$ will be

• A. $40\text{pF}$
  
• B. $20\text{pF}$
  
• C. $60\text{pF}$
  
• D. $30\text{pF}$
  

Answer 1

The correct option is B $20\text{pF}$


Given,

Radius of the sphere, $R=18\text{cm}$,

For an isolated metallic sphere, capacitance is given by the formula,$$C=4\pi {\epsilon }_{0}R$$Substituting the values, we get

$\Rightarrow C=\frac{1}{9\times {10}^9}\times 18\times {10}^{-2}$

$\Rightarrow C=2\times {10}^{-11}\text{F}$

$\Rightarrow C=20\times {10}^{-12}\text{F}$

As, $1\text{pF}={10}^{-12}\text{F}$

$\therefore C=20\text{pF}$

Hence, option $\left(B\right)$ is the correct answer.

Key Concept : Capacitance of an isolated spherical conductor.