What is the force acting on a charge placed in electric field $E$?

Two identical charges spheres are suspended by strings of equal length. The strings make an angle of ${30}^{°}$ with each other. When suspended in a liquid of density $0.8 \mathrm{g} {\mathrm{cm}}^{-3}$, the angle remains the same. What is the dielectric constant of liquid (density of material of sphere is $1.6 \mathrm{g} {\mathrm{cm}}^{-3}$.

Using Gauss’ theorem, derive an expression for the electric field intensity due to a charged thin spherical shell at Surface point.

Draw the graph showing the variation of electric field intensity obtained as above with distance from the centre.

Consider a sphere of radius $\mathrm{R}$with charge density distributed as

$\mathrm{\rho }\left(\mathrm{r}\right)=\mathrm{kr} \mathrm{for} \mathrm{r}\le \mathrm{R}$

$=0$ for $\mathrm{r}>\mathrm{R}$

Suppose the total charge on the sphere is $2\mathrm{e}$ where e is the electron charge. Where can two protons be embedded such that the force on each of them is zero. Assume that the introduction of the proton does not alter the negative charge distribution.