Write the limitations of Coulomb's law.

Two point charges $+Q$ and $+q$ repel each other with a force of $100 \,N$. Keeping the distance between them unchanged, if $Q$ is increased by $10 \%$ and $q$ is decreased by $10 \%$, the force of repulsion between them will:

Two small conducting balls of identical mass $20 \text{ g}$ and identical charge $10^{-10} \text{ C}$ hang from non-conducting threads of length $L = 300 \text{ cm}$. If the equilibrium separation of the balls is $x$ and $x \ll L$,then the magnitude of $x$ is (Assume $4 \pi \varepsilon_0 = \frac{1}{9 \times 10^9} \text{ F/m}$ and $g = 10 \text{ m/s}^2$):

Five charges, each $+Q$, are placed at five vertices of a regular hexagon of side length $L$. What is the magnitude of the force on a charge $-Q$ placed at the center of the hexagon?

$A$ particle of mass $M$ and charge $q$ is placed at the midpoint between two fixed charges each of magnitude $Q$,separated by a distance $2d$. The system is collinear as shown in the figure. If the particle is displaced by a small distance $x$ $(x \ll d)$ along the line joining the two charges and released,it will oscillate about the mean position with a time period $T$. ($\varepsilon_{0}$ is the permittivity of free space)

Two free positive charges $4q$ and $q$ are at a distance $l$ apart. What charge $Q$ is needed to achieve equilibrium for the entire system and where should it be placed from charge $q$?