A parallel plate air capacitor consists of two circular plates of diameter `8 cm` . At what distance should the plates be held so as to have the same capacitance as that of a sphere of a diameter `20 cm` ?

Options

A. `4xx10^(-3)m`
B. `1xx10^(-3)cm`
C. `1xx10^(-2)cm`
D. `1xx10^(-3)m`

Answer

D

Explanation

`r_(1)=(4)/(2)=2xx10^(-2)cm`
`r_(2)=(20)/(2)=10xx20^(-2)cm`
Capacity of parallel plate capacitor = Capacitor of spherical capacitor
`(epsilon_(0)A)/(d)=4piepsilon_(0)r_(2)`
`"or "(epsilon_(0)pi r_(1)^(2))/(d)=4pi epsilon_(0)r_(2)`
`d=(r_(1)^(2))/(4_(2))`
`=((2xx10^(-2))^(2))/(4xx10xx10^(-2))=(4xx10^(-4))/(4xx10^(-1))`
Distance between plates, `d=1xx10^(-3)m`