Four equal positive charges are fixed at the vertices of a square of side $L$. The $Z$-axis is perpendicular to the plane of the square. The point $z = 0$ is the point where the diagonals of the square intersect. Find the plot of the electric field $E$ due to the four charges as one moves along the $Z$-axis.

$A$ glass rod rubbed with silk is used to charge a gold leaf electroscope and the leaves are observed to diverge. The electroscope thus charged is exposed to $X$-rays for a short period. Then

The dimension of $\frac{1}{2} \varepsilon_0 E^2$,where $\varepsilon_0$ is the permittivity of free space and $E$ is the electric field,is:

The force between two conducting spheres of same radius having charges $+8 \mu C$ and $-4 \mu C$ separated by some distance in air is $F$. If the spheres are connected by a conducting wire and after some time the wire is removed,then the magnitude of the force between the two conducting spheres is

Two identical balls having like charges and placed at a certain distance apart repel each other with a certain force. They are brought in contact and then moved apart to a distance equal to half their initial separation. The force of repulsion between them increases $4.5$ times in comparison with the initial value. The ratio of the initial charges of the balls is

Six charges,three positive and three negative of equal magnitude,are placed at the corners of a regular hexagon such that the electric field at the center $O$ is double the electric field obtained when only a charge of the same magnitude is placed at $R$. What are the charges at $P, Q, R, S, T,$ and $U$ respectively?