Earth is assumed to be a charged conducting sphere having volume $V$ and surface area $A$. The capacitance of the earth in free space is ($\epsilon_0=$ permittivity of free space).

The radii of the inner and outer spheres of a spherical capacitor are $9\,cm$ and $10\,cm$ respectively. If the dielectric constant of the medium between the two spheres is $6$ and the charge on the inner sphere is $18 \times 10^{-9}\,C$,calculate the potential of the inner sphere,given that the outer sphere is earthed.

$A$ conductor is connected to a battery of $5\, V$. It acquires a charge of $50\ \mu C$. Calculate the capacitance of the conductor in $\mu F$.

$A$ spherical capacitor is made of two spherical shells of radii $a$ and $b$ $(b > a)$. The medium between the shells is air. What is the difference between the capacitances when the outer shell is grounded and when the inner shell is grounded?

Two concentric spherical shells $A$ and $B$ of radii $a$ and $b$ $(b > a)$ are placed in air. Shell $B$ is given a charge $+Q$ and shell $A$ is grounded. What is the capacitance of the system?

The capacity of a conductor does not depend upon: