$(a)$ Consider an arbitrary electrostatic field configuration. A small test charge is placed at a null point (i.e., where $E =0$ ) of the configuration. Show that the equilibrium of the test charge is necessarily unstable.

$(b)$ Verify this result for the simple configuration of two charges of the same magnitude and sign placed a certain distance apart.

Mention characteristics of electric field.

What is the magnitude of a point charge due to which the electric field $30\,cm$ away has the magnitude $2\,newton/coulomb$ $[1/4\pi {\varepsilon _0} = 9 \times {10^9}\,N{m^2}/{C^2}]$

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 $a=\frac{\sqrt{3}}{2} L$.

Diagram shows symmetrically placed rectangular insulators with uniformly charged distributions of equal magnitude. At the origin, the net field net ${\vec E_{net}}$ is :-