Question

The distance between the plate of a circular parallel plate condenser of diameter $40mm$, in order to make its capacitance equal to that of a metallic sphere of radius $1m$, will be :

• A. $0.01mm$
• B. $0.1mm$
• C. $1mm$
• D. $10mm$

Answer 1

Answer: (B)

$0.1mm$

The capacitance of circular parallel plate is $C=\frac{A{ϵ}_0}{d}=\frac{\pi r^2{ϵ}_0}{d}$
The capacitance of single metallic sphere is $C^{\prime }=4\pi {ϵ}_{0}a$
here, $C=C^{\prime }\Rightarrow \frac{\pi r^2{ϵ}_0}{d}=4\pi {ϵ}_{0}a$
or $d=\frac{r^2}{4a}=\frac{{20}^2}{4\left(1000\right)}=0.1mm$