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

Explanation

`r_(1)=12 xx 10^(-2)m " "r_(2)=13 xx 10^(-2) m " "Q=2.5muC" k=32"`
`C=(4pi epsi_(0) r_(1)r_(2))/((r_(2)-r_(1))) xx k =(1 xx 12 xx 10^(-2) xx 13 xx 10^(-2) xx 32)/(9 xx 10^(9) xx 10^(-2))=(4 xx 13 xx 32 xx10^(-11))/(3)=5.5 xx 10^(9)F`
`V=1/(32) [(9 xx 10^(9) xx 2.5 xx 10^(-6))/(12 xx 10^(-2))-(9 xx 10^(9) xx 2.5 xx 10^(-6))/(13 xx 10^(-2))]`
`=(9 x 2.5 xx 10^(5))/(32) {1/(12)-(1)/(13)}=(9 xx 2.5 xx 10^(5))/(12 xx 13 xx 32)=450.7V`
`C=4pi epsi_(0) r=(12 xx 10^(-2))/(9 xx 10^(9))=1.33 xx 10^(-11)F`
Ratio `=(5.5 xx 10^(-9))/(4/3 xx 10^(-4))=(5.5 xx 300)/(4)=412.5`