$A$ sphere of $4\, cm$ radius is suspended within a hollow sphere of $6\, cm$ radius. The inner sphere is charged to a potential of $3\, e.s.u.$ and the outer sphere is earthed. The charge on the inner sphere is.....$e.s.u.$

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	$iv$. $\frac{4\pi \epsilon_0 r_1 r_2}{r_2 - r_1}$

$1000$ small water drops,each of capacitance $C$,join together to form one large spherical drop. The capacitance of the bigger sphere is ......... $C$.

Two identical charged spherical drops, each of capacitance $C$, merge to form a single drop. The resultant capacitance is

Two similar conducting balls having charges $+q$ and $-q$ are placed at a separation $d$ from each other in air. The radius of each ball is $r$ and the separation between their centres is $d$ $(d \gg r)$. Calculate the capacitance of the two-ball system.

Eight drops of mercury of equal radii combine to form a big drop. The capacitance of a bigger drop as compared to each smaller drop is (in $\times$)