Find out electric filed intensity at point $A(1,0,2)$ due to a point charge $-20\,\mu C$ situated at point $B(0, 2,1)$

$(a)$ 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.

Two equal negative charges $-\, q$ each are fixed at the points $(0, a)$ and $(0, -a)$ on the $Y$ -axis. A positive charge $Q$ is released from rest at the point $(2a, 0)$ on the $X$ -axis. The charge $Q$ will :-

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

Deutron and $\alpha – $ particle are put $1\,\mathop A\limits^o $ apart in air. Magnitude of intensity of electric field due to deutron at $\alpha – $ particle is