The capacitance of a parallel plate capacitor formed by the circular plates of diameter 4.0 cm is equal to the capacitance or a sphere of diameter 200 cm. Find the distance between two plates.

Options

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

Answer

A, D

Explanation

Suppose the capacitance of a sphere is `C_(1)`
`:. C_(1)= 4pi epsilon_(0)` R
The capacitance of a parallel plate capacitor
`C_(2)=(epsilon_(0)A)/(d)`
but `C_(1)=C_(2)`
`:. 4 pi in_(0)R = (epsilon_(0)pir^(2))/(d)`
`:. D=(r^(2))/(4R)`
but `r= 2.0 cm =2xx10^(-2)` m
R = `(200)/(2) = 100 cm = 1 m`
`:. d = (4xx10^(-4))/(4xx1)`
`:. d = 1 xx10^(-4)` m