The ratio of the forces between two small spheres with constant charge $(a)$ in air and $(b)$ in a medium of dielectric constant $K$ is:

Four charges equal to $-Q$ are placed at the four corners of a square and a charge $q$ is at its centre. If the system is in equilibrium, the value of $q$ is

Two identical spheres have charges $+q$ and $-q$ and are placed at a certain distance. The force between them is $F$. If a third identical sphere with charge $+q$ is placed exactly between the two spheres, what is the magnitude and direction of the force experienced by it?

For the regular pentagon system shown in the figure,find the net electrostatic force on the charge $q_0$ placed at the center.

The ratio of electrostatic and gravitational forces acting between an electron and a proton separated by a distance $5 \times 10^{-11} \, m$ will be (Charge on electron $= 1.6 \times 10^{-19} \, C$,mass of electron $= 9.1 \times 10^{-31} \, kg$,mass of proton $= 1.6 \times 10^{-27} \, kg$,$G = 6.7 \times 10^{-11} \, N m^2/kg^2$).

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