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
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Expression for capacitance is,
[tex]\sf{\longrightarrow C=\dfrac{Q}{V}\quad\quad\dots(1)}[/tex]
But the voltage is given by,
[tex]\sf{\longrightarrow V=\dfrac{kQ}{r}}[/tex]
[tex]\sf{\longrightarrow\dfrac{Q}{V}=\dfrac{r}{k}}[/tex]
Then (1) becomes,
[tex]\sf{\longrightarrow C=\dfrac{r}{k}}[/tex]
Since [tex]\sf{k=\dfrac{1}{4\pi\epsilon_0}}[/tex] is a constant,
[tex]\sf{\longrightarrow C\propto r}[/tex]
Therefore,
[tex]\sf{\longrightarrow\dfrac{C_1}{C_2}=\dfrac{r_1}{r_2}}[/tex]
According to the question,
Therefore,
[tex]\sf{\longrightarrow\underline{\underline{\dfrac{C_1}{C_2}=\dfrac{a}{b}}}}[/tex]