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

In a hydrogen atom, the electron and proton are bound at a distance of about $0.53\; \mathring A:$

$(a)$ Estimate the potential energy of the system in $eV$, taking the zero of the potential energy at infinite separation of the electron from proton.

$(b)$ What is the minimum work required to free the electron, given that its kinetic energy in the orbit is half the magnitude of potential energy obtained in $(a)?$

$(c)$ What are the answers to $(a)$ and $(b)$ above if the zero of potential energy is taken at $1.06\;\mathring A$ separation?

If $50$ joule of work must be done to move an electric charge of $2 \,C$ from a point, where potential is $-10$ volt to another point, where potential is $V$ volt, the value of $V$ is ......... $V$

Obtain equation of electric energy of a single charge.

An $\alpha$ particle and a proton are accelerated from rest through the same potential difference. The ratio of linear momenta acquired by above two particals will be.

When one electron is taken towards the other electron, then the electric potential energy of the system