In the figure shown,the distance from point $A$ to the point where the electric field intensity is zero is .......... $cm$.

$A$ cube of a metal is given a positive charge $Q$. For the above system,which of the following statements is true?

An infinite number of electric charges, each equal to $5 \text{ nC}$ (magnitude), are placed along the $X$-axis at $x = 1 \text{ cm}, x = 2 \text{ cm}, x = 4 \text{ cm}, x = 8 \text{ cm}, \dots$ and so on. In this setup, if the consecutive charges have opposite signs, then the electric field in $\text{N/C}$ at $x = 0$ is: $\left(\frac{1}{4 \pi \varepsilon_0} = 9 \times 10^9 \text{ N} \cdot \text{m}^2/\text{C}^2\right)$

Four charges,each of magnitude $q$ coulomb,are placed at points $(-1,0,0), (1,0,0), (0,-1,0)$ and $(0,1,0)$ in the $xy$-plane. The distances along the axes are measured in metres. The magnitude of the electric field at the point $(0,0,1)$ on the $Z$-axis is

$A$ sphere $A$ of radius $R$ has a charge $Q$ on it. The electric field at point $B$ at a distance $r$ from the center of sphere $A$ is $E$. Now,another sphere of radius $2R$ having a charge $-2Q$ is placed at $B$. What is the magnitude of the total electric field at the point midway between $A$ and $B$ due to both spheres?

Four point positive charges of same magnitude $Q$ are placed at four corners of a rigid square frame in $xy$ plane as shown in the figure. The plane of the frame is perpendicular to the $z$-axis. If a negative point charge is placed at a distance $z$ away from the above frame $(z << L)$,then: