Six point charges are placed at the vertices of a regular hexagon of side $a$ as shown. If $E$ represents the electric field and $V$ represents the electric potential at the center $O$,then:

$A$ Van de Graaff generator produces:

Consider a uniformly charged hemispherical shell of radius $R$ and charge $Q$. If the electric field at point $A (0, 0, -z_0)$ is $\vec E$,then find the electric field at point $B (0, 0, z_0)$,where $z_0 < R$.

Two small conducting spheres of equal radius have charges of $10\ \mu C$ and $-20\ \mu C$ respectively and are placed at a distance $R$ from each other,experiencing a force $F_1$. If they are brought in contact and then separated to the same distance,the new force between them is $F_2$. Find the ratio $F_1 : F_2$.

An empty thick conducting shell of inner radius $a$ and outer radius $b$ is shown in the figure. It is observed that the inner face of the shell carries a uniform charge density $-\sigma$ and the outer surface carries a uniform charge density $+\sigma$. If a point charge $q_A$ is placed at the center and another point charge $q_B$ is placed at a distance $c (> b)$ from the center of the shell,then choose the correct statement.

For a thin spherical shell of radius $R$ with a uniform surface charge density, which of the following graphs best represents the variation of the electric field magnitude $|\vec{E}(r)|$ and the electric potential $V(r)$ with the distance $r$ from the center?