$A$ 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 $ABC$?

Five point charges each having magnitude $q$ are placed at the corners of a regular hexagon as shown in the figure. The net electric field at the centre $O$ is $\vec E$. To make the net electric field at $O$ equal to $6\vec E$,the charge placed on the remaining sixth corner should be: (in $,q$)

$A$ uniformly charged semicircular arc of radius $r$ has a linear charge density $\lambda$. What is the electric field at its centre? ($\varepsilon_0$ is the permittivity of free space)

Eleven equal point charges, each of magnitude $+Q$, are placed at all the hour positions of a circular clock of radius $r$, except at the $10$ o'clock position. What is the electric field strength at the centre of the clock?

Two point charges $Q_1$ and $Q_2$ are fixed at $x = 0$ and $x = a$. Assuming that the electric field strength is positive in the direction coinciding with the positive direction of $x$,which of the following options is correct?

$A$ unit negative charge with mass $M$ resides at the mid-point of the straight line of length $2a$ connecting two fixed charges of magnitude $+Q$ each. If it is given a very small displacement $x$ $(x \ll a)$ in a direction perpendicular to the straight line, it will: