A spherical capacitor has an inner sphere of radius 12 cm and an outer sphere of radius 13 cm. The outer sphere is earthed and the inner sphere is given a charge of `2.5 muC`. The space between the concentric spheres is filled with a liquid of dielectric constant 32.
(a) Determine the capacitance of the capacitor. (b) What is the potential of the inner sphere ?
(c) Compare the capacitance of this capacitor with that of an isolated sphere of radius 12 cm.Explain why the later is much smaller ?

Options

A. `5.5 xx 10^(-9)F`
B. `6.5 xx 10^(-9)F`
C. `7.5 xx 10^(-9)F`
D. `8.5 xx 10^(-9)F`

Answer

A

Explanation

Here, `r_(a) = 12 cm = 12 xx 10^(-2)m`,
`r_(b) = 13 cm = 13 xx 10^(-2) m`
`q = 2.5 mu C = 2.5 xx 10^(-6) C, K = 32`
As `C = 4pi epsilon_(0)(Kr_(0)r_(b))/(r_(b) - r_(a))`
`= (1)/(9 xx 10^(9))(32 xx 12 xx 10^(-2) xx 13 xx 10^(-2))/((13-12) xx 10^(-2)) = 5.5 xx 10^(-9) F`