Three charges are placed as shown in the figure. The magnitude of $q_1$ is $2.00\, \mu C$,but its sign and the value of the charge $q_2$ are not known. Charge $q_3$ is $+4.00\, \mu C$,and the net force on $q_3$ is entirely in the negative $x-$ direction. The magnitude of $q_2$ is

The force between two identical spheres charged with the same charge $q$ is $F$. If $50\%$ of the charge from one sphere is transferred to the second sphere,then the new force will be:

Two point charges placed in air separated by distance $R$ exert a force $F$ on each other. Now the space between those charges is filled with a medium of dielectric constant $K$. At distance $R_1$ between the charges, the same force is exerted as $F$. Then:

Coulomb's law for electrostatic force between two point charges and Newton's law for gravitational force between two stationary point masses,both have inverse-square dependence on the distance between the charges and masses respectively.
$(a)$ Compare the strength of these forces by determining the ratio of their magnitudes $(i)$ for an electron and a proton and $(ii)$ for two protons.
$(b)$ Estimate the accelerations of electron and proton due to the electrical force of their mutual attraction when they are $1 \mathring A \left( = 10^{-10} \, m \right)$ apart? $\left( m_{p} = 1.67 \times 10^{-27} \, kg, m_{e} = 9.11 \times 10^{-31} \, kg \right)$

$A$ charge $q$ is placed at the centre of the line joining two equal charges $Q$. The system of the three charges will be in equilibrium if $q$ is equal to:

Two small balls,each having a negative charge $Q$,are suspended from a fixed point by two identical insulating strings of length $L$. This entire arrangement is placed inside a satellite in a region where there is no gravity (weightless condition). The angle between the strings is ......... and the tension in each string is ......... Newtons.