Question

The capacity of a spherical capacitor is C when inner sphere is charged and ourter shell is is earthed. C2 is capacity when outer
shell is is charged and innersphere is earthed. If a and b are radii of inner sphere and outer shell, the value of
C1/C2
will be​

Answer 1

Expression for capacitance is,

$\sf{\longrightarrow C=\dfrac{Q}{V}\quad\quad\dots(1)}$

But the voltage is given by,

$\sf{\longrightarrow V=\dfrac{kQ}{r}}$

$\sf{\longrightarrow\dfrac{Q}{V}=\dfrac{r}{k}}$

Then (1) becomes,

$\sf{\longrightarrow C=\dfrac{r}{k}}$

Since $\sf{k=\dfrac{1}{4\pi\epsilon_0}}$ is a constant,

$\sf{\longrightarrow C\propto r}$

Therefore,

$\sf{\longrightarrow\dfrac{C_1}{C_2}=\dfrac{r_1}{r_2}}$

According to the question,

• $\sf{r_1=a}$

• $\sf{r_2=b}$

Therefore,

$\sf{\longrightarrow\underline{\underline{\dfrac{C_1}{C_2}=\dfrac{a}{b}}}}$