Positive point charges are placed at the vertices of a star shape as shown in the figure. The direction of the electrostatic force on a negative point charge at the centre $O$ of the star is

Two pith balls carrying equal charges are suspended from a common point by strings of equal length. The equilibrium separation between them is $r$. Now,the strings are rigidly clamped at half the height. The equilibrium separation between the balls now becomes:

Two identical particles of mass $m$ and charge $q$ are shot at each other from a very great distance with an initial speed $v$. The distance of closest approach of these charges is

An infinite number of charges,each of charge $1 \,\mu C$,are placed on the $x$-axis at coordinates $x = 1, 2, 4, 8, ... \infty$. If a charge of $1 \, C$ is kept at the origin,what is the net force acting on the $1 \, C$ charge in Newtons?

Two identical pendulums $A$ and $B$ are suspended from the same point. The bobs are given positive charges,with $A$ having more charge than $B$. They diverge and reach equilibrium,with $A$ and $B$ making angles $\theta_1$ and $\theta_2$ with the vertical,respectively. Then:

Two charges are placed as shown in the figure. Where should a third charge be placed so that it remains at rest?