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).

Eight drops of mercury of equal radii and possessing equal charge combine to form a big drop. If the capacity of each drop is $C$,then the capacity of the big drop is: (in $C$)

The capacity of an isolated sphere is increased $n$ times when it is enclosed by an earthed concentric sphere. The ratio of their radii is

$A$ 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?

The unit of electric permittivity is

$A$ spherical capacitor consists of two concentric spherical conductors,held in position by suitable insulating supports. Show that the capacitance of a spherical capacitor is given by $C = \frac{4 \pi \varepsilon_{0} r_{1} r_{2}}{r_{1} - r_{2}}$,where $r_{1}$ and $r_{2}$ are the radii of outer and inner spheres,respectively.