Force between two identical spheres charged with same charge is $F$. If $50\%$ charge of one sphere is transferred to second sphere then new force will be

The ratio of coulomb's electrostatic force to the gravitational force between an electron and a proton separated by some distance is $2.4 \times 10^{39}$. The ratio of the proportionality constant, $K=\frac{1}{4 \pi \varepsilon_0}$ to the Gravitational constant $G$ is nearly (Given that the charge of the proton and electron each $=1.6 \times 10^{-19}\; C$, the mass of the electron $=9.11 \times 10^{-31}\; kg$, the mass of the proton $=1.67 \times 10^{-27}\,kg$ ):

Two charges $ + 4e$ and $ + e$ are at a distance $x$ apart. At what distance, a charge $q$ must be placed from charge $ + e$ so that it is in equilibrium

Two charges each of magnitude $Q$ are fixed at $2a$ distance apart. A third charge ($-q$ of mass $'m'$) is placed at the mid point of the two charges; now $-q$ charge is slightly displaced perpendicular to the line joining the charges then find its time period

Charges $4Q$, $q$ and $Q$ and placed along $x$-axis at positions $x = 0,x = l/2$ and $x = l$, respectively. Find the value of $q$ so that force on charge $Q$ is zero

A point charge $q_1$ exerts an electric force on a second point charge $q_2$. If third charge $q_3$ is brought near, the electric force of $q_1$ exerted on $q_2$