Question

The capacity of a sperical conductor in $MKS$ system is :

• A. $\frac{R}{4\pi {ϵ}_0}$
• B. $\frac{4\pi {ϵ}_0}{R}$
• C. $4\pi {ϵ}_{0}R$
• D. $4\pi {ϵ}_0{R}^2$

Answer 1

The correct option is C $4\pi {ϵ}_{0}R$

The potential is given as,

$V=\frac{q}{4\pi {\epsilon }_{0}R}$

The capacitance is given as,

$C=\frac{q}{V}$

$=\frac{q}{\frac{q}{4\pi {\epsilon }_{0}R}}$

$=4\pi {\epsilon }_{0}R$

Thus, the capacity of a spherical conductor is $4\pi {\epsilon }_{0}R$.