Two point charges $(+Q)$ and $(-2Q)$ are fixed on the $X$-axis at positions $a$ and $2a$ from the origin,respectively. At what position on the axis is the resultant electric field zero?

Total charge $-Q$ is uniformly spread along the length of a ring of radius $R$. $A$ small test charge $+q$ of mass $m$ is kept at the centre of the ring and is given a gentle push along the axis of the ring.
$(a)$ Show that the particle executes a simple harmonic oscillation.
$(b)$ Obtain its time period.

The figures below show regular hexagons with charges at the vertices. In which of the following cases is the electric field at the center $NOT$ zero?

$A$ charged water drop of radius $0.1 \, \mu m$ is in equilibrium under an electric field. The charge on the drop is equivalent to the electronic charge. The intensity of the electric field is ........ $N/C$.

The electric field at the centre $O$ of a semicircle of radius $a$ having a linear charge density $\lambda$ is given by:

What is the magnitude of a point charge which produces an electric field of $2 \, N/C$ at a distance of $60 \, cm$? (Given: $1/(4\pi \varepsilon_0) = 9 \times 10^9 \, N \cdot m^2/C^2$)