Two charged particles, each with a charge of $+q$, are located along the $x$ -axis at $x = 2$ and $x = 4$, as shown below. Which of the following shows the graph of the magnitude of the electric field along the $x$ -axis from the origin to $x = 6$?

A wire of length $L\, (=20\, cm)$, is bent into a semicircular arc. If the two equal halves of the arc were each to be uniformly charged with charges $ \pm Q\,,\,\left[ {\left| Q \right| = {{10}^3}{\varepsilon _0}} \right]$ Coulomb where $\varepsilon _0$ is the permittivity (in $SI\, units$) of free space] the net electric field at the centre $O$ of the semicircular arc would be

Charge $q$ is uniformly distributed over a thin half ring of radius $R$. The electric field at the centre of the ring is

Find the electric field at point $P$ (as shown in figure) on the perpendicular bisector of a uniformly charged thin wire of length $L$ carrying a charge $Q.$ The distance of the point $P$ from the centre of the rod is $a=\frac{\sqrt{3}}{2} L$.

A positively charged pendulum is oscillating in a uniform electric field pointing upwards. Its time period as compared to that when it oscillates without electric field