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

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.

$A$ ring of charge with radius $R = 0.5\, m$ having a gap of length $l = 0.02\, m$,carries a total charge of $Q = +1\, C$. The electric field at the centre is

If the net electric field at point $P$ along the $Y$-axis is zero,then the ratio of $\left|\frac{q_2}{q_3}\right|$ is $\frac{8}{5 \sqrt{x}}$,where $x = . . . . . .$

Two uniform spherical charge regions $S_1$ and $S_2$ having positive and negative charges overlap each other as shown in the figure. Points $O_1$ and $O_2$ are their centres and points $A, B, C, D$ and $E$ are on the line joining centres $O_1$ and $O_2$. What happens to the electric field from $C$ to $D$?

Two equal negative charges $-q$ are fixed at points $(0, -a)$ and $(0, a)$ in the $x-y$ plane. $A$ positive charge $Q$ is released from rest at a point $(2a, 0)$. The charge $Q$ will