$A$ metallic ring is uniformly charged as shown in the figure. $AC$ and $BD$ are two mutually perpendicular diameters. The magnitude of the electric field at $O$ due to arc $AB$ is $E$. What would be the magnitude of the electric field at $O$ due to arc $ABC$?

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

Two point charges $-10 \mu C$ and $+5 \mu C$ are situated on the $X$-axis at $x=0$ and $x=\sqrt{2} \ m$. The point along the $X$-axis where the electric field becomes zero is:

At a certain distance from a point charge,the electric field is $500\,V/m$ and the potential is $3000\,V$. What is this distance in meters?

$A$ point charge $q$ is placed at the origin. Let $E_A, E_B,$ and $E_C$ be the electric fields at three points $A(1, 2, 3)$,$B(1, 1, -1)$,and $C(2, 2, 2)$ respectively due to the charge $q$. Then,the correct relations among them are:
$1. E_A \perp E_B$
$2. E_A \parallel E_C$
$3. |E_B| = 4|E_C|$
$4. |E_B| = 8|E_C|$

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: