A battery used for charging an air capacitor is removed after the capacitor is fully charged. Some mica sheets (dielectric constant $K$ ) are inserted between the two plates. If $E$ is the energy of the air capacitor, then the energy stored in the mica capacitor will be

Four charges are fixed along the $y$-axis as shown. A positive charge approaches the system along the $x$-axis with initial speed just enough to cross the origin. Then its total energy at the origin is

The diagram shows the arrangement of three small uniformly charged spheres $A$, $B$ and $C$. The arrows indicate the direction of the electrostatic forces acting between the spheres (for example, the left arrow on sphere $A$ indicates the electrostatic force on sphere $A$ due to sphere $B$). At least two of the spheres are positively charged. Which sphere, if any, could be negatively charged?

Figures below show regular hexagons, with charges at the vertices. In which of the following cases the electric field at the centre is not zero?