A cylindrical capacitor has two co-axial cylinders of length $15\; cm$ and radii $1.5 \;cm$ and $1.4\; cm .$ The outer cylinder is earthed and the inner cylinder is given a charge of $3.5\; \mu \,C .$ Determine the capacitance of the system and the potential of the inner cylinder. Neglect end effects (i.e., bending of field lines at the ends).

Two identical thin metal plates has charge $q _{1}$ and $q _{2}$ respectively such that $q _{1}> q _{2}$. The plates were brought close to each other to form a parallel plate capacitor of capacitance $C$. The potential difference between them is.

A spherical condenser has inner and outer spheres of radii $a$ and $b$ respectively. The space between the two is filled with air. The difference between the capacities of two condensers formed when outer sphere is earthed and when inner sphere is earthed will be

Eight drops of mercury of equal radii possessing equal charges combine to form a big drop. Then the capacitance of bigger drop compared to each individual small drop is……..$times$

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 $d(d > > r)$. Calculate the capacitance of the two ball system