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:

The figure shows a nonconducting ring which has positive and negative charge non-uniformly distributed on it such that the total charge is zero. Which of the following statements is true?

$A$ clock dial has point charges $-q, -2q, -3q, \ldots, -12q$ at the positions of the corresponding numbers on the dial respectively. The time at which the hour hand points in the direction of the net electric field at the centre of the dial is (Assume clock hands do not influence the net electric field). (in $:30$)

$A$ thin spherical insulating shell of radius $R$ carries a uniformly distributed charge such that the potential at its surface is $V_0$. $A$ hole with a small area $\alpha 4 \pi R^2$ (where $\alpha \ll 1$) is made on the shell without affecting the rest of the shell. Which one of the following statements is correct?

Electric charges $Q$ are placed on the $x$-axis at $x = 1, 2, 4, 8, \dots \text{meters}$ respectively. What are the electric field and electric potential at $x = 0$?

$A$ charge $Q$ of mass $m$ revolves around a charge $q$ due to the electrostatic attraction between them. The time period of its motion can be given by the formula: