Answer to Question #256557 in Electric Circuits for Taha

Question

Find the capacitance of a spherical capacitor filled with a dielectric of dielectric 

constant K.

Answer 1

$potential \\V_1=\frac{k(-q)}{Kr_2}$

Potential plate second

$V_2=\frac{k(+q)}{Kr_1}$

We know that

$∆V=V_1-V_2$

Put value

$∆V=\frac{q}{4\pi\epsilon_0K}[\frac{1}{r_1}-\frac{1}{r_2}]$

$∆V=\frac{q}{4\pi\epsilon_0K}[\frac{r_1-r_2}{r_1r_2}]$

$∆V=\frac{q}{4\pi\epsilon_0K}\frac{r_1-r_2}{r_1r_2}$

We know that capacitance

$C_0=\frac{q}{∆V}$

Put value

$C_0=4\pi\epsilon_0K\frac{r_1r_2}{r_1-r_2}$