Infinite charges of magnitude $q$ each are placed at $x = 1, 2, 4, 8, ...$ meters on the $X$-axis. The value of the intensity of the electric field at the point $x = 0$ due to these charges will be:

$A$ thin metallic wire having a cross-sectional area of $10^{-4} \, m^2$ is used to make a ring of radius $30 \, cm$. $A$ positive charge of $2 \pi \, pC$ is uniformly distributed over the ring, while another positive charge of $30 \, pC$ is kept at the centre of the ring. The tension in the ring is . . . . . . $N$; provided that the ring does not get deformed (neglect the influence of gravity). (Given, $\frac{1}{4 \pi \epsilon_0} = 9 \times 10^9 \, SI$ units)

Two point charges $A$ and $B$ of magnitude $+8 \times 10^{-6}\,C$ and $-8 \times 10^{-6}\,C$ respectively are placed at a distance $d$ apart. The electric field at the middle point $O$ between the charges is $6.4 \times 10^{4}\,NC^{-1}$. The distance $d$ between the point charges $A$ and $B$ is ............ $m$. (in $.0$)

Four charges $q, 2q, -4q$ and $2q$ are placed in order at the four corners of a square of side $b$. The net field at the centre of the square is

Two point charges $+10 q$ and $-4 q$ are located at $x=0$ and $x=L$ respectively. What is the location of a point on the $x$-axis from the origin, where the net electric field due to these two point charges is zero? $(r = \text{required distance})$

Three equal charges $+q$ each are placed at the three vertices of an equilateral triangle. The electric field at the centroid of the triangle is . . . . . . . ('$r$' is the length of the side of the triangle).