$A$ uniformly charged sphere has a total charge $Q$ and radius $R$. The electric field $E$ is a function of the distance $r$ from the center. Which of the following graphs represents this relationship?

Two charges $Q$ are placed at two vertices of an equilateral triangle of side $a$. What is the electric field at the third vertex?

The figure shows a rod $AB$,which is bent in a $120^{\circ}$ circular arc of radius $R$. $A$ charge $(-Q)$ is uniformly distributed over the rod $AB$. What is the electric field $\overrightarrow{E}$ at the centre of curvature $O$?

$A$ thin,positively charged metal ring of radius $R$ is fixed in the $X-Y$ plane with its center at the origin $O$. $A$ negatively charged particle $P$ is released from rest at the point $(0, 0, Z_0)$,where $Z_0 > 0$. Describe the motion of the particle.

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?

$A$ wire of length $L = 20 \, cm$ is bent into a semicircular arc. If the two equal halves of the arc are uniformly charged with charges $+Q$ and $-Q$ respectively,where $|Q| = 10^3 \varepsilon_0$ Coulomb and $\varepsilon_0$ is the permittivity of free space,find the net electric field at the centre $O$ of the semicircular arc.