Which of the following statement$(s)$ is/are correct?

$(A)$ If the electric field due to a point charge varies as $r^{-25}$ instead of $r^{-2}$, then the Gauss law will still be valid.

$(B)$ The Gauss law can be used to calculate the field distribution around an electric dipole.

$(C)$ If the electric field between two point charges is zero somewhere, then the sign of the two charges is the same.

$(D)$ The work done by the external force in moving a unit positive charge from point $A$ at potential $V_A$ to point $B$ at potential $V_B$ is $\left(V_B-V_A\right)$.

Distinguish difference between electric potential and electric potential energy

There exists an electric field of magnitude $E$ in $x$-direction. If the work done in moving a charge of $0.2 \,C$ through a distance of $2 \,m$ along a line making an angle $60^{\circ}$ with $x$-axis is $4 \,J$, then the value of $E$ is …….. $N / C$

In Millikan's experiment, an oil drop having charge $q$ gets stationary on applying a potential difference $V$ in between two plates separated by a distance $d$. The weight of the drop is

Two particles each of mass $m$ and charge $q$ are separated by distance $r_1$ and the system is left free to move at $t = 0$. At time $t$ both the particles are found to be separated by distance $r_2$. The speed of each particle is