$n$ the rectangle, shown below, the two corners have charges ${q_1} = - 5\,\mu C$ and ${q_2} = + 2.0\,\mu C$. The work done in moving a charge $ + 3.0\,\mu C$ from $B$ to $A$ is.........$J$ $(1/4\pi {\varepsilon _0} = {10^{10}}\,N{\rm{ - }}{m^2}/{C^2})$

An elementary particle of mass $m$ and charge $ + e$ is projected with velocity $v$ at a much more massive particle of charge $Ze,$ where $Z > 0.$What is the closest possible approach of the incident particle

When three electric dipoles are near each other, they each experience the electric field of the other two, and the three dipole system has a certain potential energy. Figure below shows three arrangements $(1)$ , $(2)$ and $(3)$ in which three electric dipoles are side by side. All three dipoles have the same magnitude of electric dipole moment, and the spacings between adjacent dipoles are identical. If $U_1$ , $U_2$ and $U_3$ are potential energies of the arrangements $(1)$ , $(2)$ and $(3)$ respectively then

A particle $A$ has charge $+q$ and particle $B$ has charge $+4 q$ 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 speeds $\frac{V_A}{V_B}$ will become

Two charged particles of masses $m$ and $2m$ have charges $+2q$ and $+q$ respectively. They are kept in uniform electric field and allowed to move for some time. The ratio of their kinetic energies will be

Three charges, each $+q,$ are placed at the comers of an isosceles triangle $ABC$ of  sides $BC$ and $AC, 2a.$ $D$ and $E$ are the mid-points of $BC$ and $CA.$ The work done in taking a charge $Q$ from $D$ to $E$ is