The 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

If the circumference of a sphere is $2 \ m$,find the capacitance of the sphere in water in $pF$. (Take dielectric constant of water $K = 80$)

Two spherical conductors $A$ and $B$ of radii $a$ and $b$ $(b > a)$ are placed in air concentrically. $B$ is given a charge $+Q$ and $A$ is grounded. The equivalent capacitance of this system is:

Match the following types of capacitors with their respective capacitance formulas:

Capacitor Type	Capacitance Formula
$A$. Cylindrical capacitor	$i$. $4\pi \epsilon_0 R$
$B$. Spherical capacitor	$ii$. $\frac{K A \epsilon_0}{d}$
$C$. Parallel plate capacitor with dielectric	$iii$. $\frac{2\pi \epsilon_0 \ell}{\ln(r_2/r_1)}$
$D$. Isolated spherical conductor	$iv$. $\frac{4\pi \epsilon_0 r_1 r_2}{r_2 - r_1}$

$A$ 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.

The electric field between the two spheres of a charged spherical capacitor: