A particle $A$ has charge $ + q$ and a particle $B$ has charge $ + \,4q$ with each of them having the same mass $m$. When allowed to fall from rest through the same electric potential difference, the ratio of their speed $\frac{{{v_A}}}{{{v_B}}}$ will become

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 the electric field of a point charge $q$, a certain charge is carried from point $A$ to $B$, $C$, $D$ and $E$. Then the work done

As shown in figure, on bringing a charge $Q$ from point $A$ to $B$ and from $B$ to $C$, the work done are $2\, joule$ and $-3\, joule$ respectively. The work done to bring the charge from $C$ to $A$ is

When a proton is accelerated through $1\,V$, then its kinetic energy will be.....$eV$

In the figure, the inner (shaded) region $A$ represents a sphere of radius $r_A=1$, within which the electrostatic charge density varies with the radial distance $r$ from the center as $\rho_A=k r$, where $k$ is positive. In the spherical shell $B$ of outer radius $r_B$, the electrostatic charge density varies as $\rho_{\bar{B}}=\frac{2 k}{r}$. Assume that dimensions are taken care of. All physical quantities are in their $SI$ units.

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