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 $\left(V_B-V_A\right)$.

If an $\alpha$-particle and a proton are accelerated from rest by a potential difference of 1 megavolt then the ratio of their kinetic energy will be

Charge $q_{2}$ is at the centre of a circular path with radius $r$. Work done in carrying charge $q_{1}$, once around this equipotential path, would be

Derive the formula for the electric potential energy of system of three charges.

The work done to take an electron from rest where potential is $-60\, V$ to another point where potential is $-20\, V$ is given by.....$eV$

A charge of $8\; mC$ is located at the origin. Calculate the work done in $J$ in taking a small charge of $-2 \times 10^{-9} \;C$ from a point $P (0,0,3\; cm )$ to a point $Q (0,4\; cm , 0),$ via a point $R (0,6\; cm , g \;cm )$