Three charges $4q,\,Q$ and $q$ are in a straight line in the position of $0$, $l/2$ and $l$ respectively. The resultant force on $q$ will be zero, if $Q = $

If on the concentric hollow spheres of radii $r$ and $R( > r)$ the charge $Q$ is distributed such that their surface densities are same then the potential at their common centre is

A $2\,\mu F$ capacitor is charged as shown in the figure. The percentage of its stored energy dissipated after the switch $S$ is turned to position $2$, is.....$\%$

$A$ and $C$ are concentric conducting spherical shells of radius $a$ and $c$ respectively. $A$ is surrounded by a concentric dielectric radius $a$ , outer radius $b$ and dielectric constant $k$ . If sphere $A$ be given a charges $Q$ , the potential at the outer surface of the dielectric is 

The plates of a parallel plate capacitor are charged up to $100\, volt$. A $2\, mm$ thick plate is inserted between the plates, then to maintain the same potential difference, the distance between the capacitor plates is increased by $1.6\, mm$. The dielectric constant of the plate is

The equivalent capacitance of the combinatio shown in Figure is