Six charges are placed at the corner of a regular hexagon as shown. If an electron is placed at its centre $O$, force on it will be:

$(a)$ Two insulated charged copper spheres $A$ and $B$ have their centres separated by a distance of $50 \;cm$. What is the mutual force of electrostatic repulsion if the charge on each is $6.5 \times 10^{-7}\; C?$ The radii of $A$ and $B$ are negligible compared to the distance of separation.

$(b)$ What is the force of repulsion if each sphere is charged double the above amount, and the distance between them is halved?

Two charges $ + 4e$ and $ + e$ are at a distance $x$ apart. At what distance, a charge $q$ must be placed from charge $ + e$ so that it is in equilibrium

A given charge is situated at a certain distance from an electric dipole in the end-on position experiences a force $F$. If the distance of the charge is doubled, the force acting on the charge will be

Two point charges $+8q$ and $ - 2q$ are located at $x = 0$ and $x = L$ respectively. The location of a point on the $x$-axis at which the net electric field due to these two point charges is zero is

$ABC$ is a right angled triangle in which $AB = 3\,cm$ and $BC = 4\,cm$. And  $\angle ABC = \pi /2$. The three charges $ + 15,\; + 12$ and $ - 20\,e.s.u.$ are placed respectively on $A$, $B$ and $C$. The force acting on $B$ is.......$dynes$