Coulomb's Law — Prelims Questions

Two point charges, $q_1 = +4,mu\text{C}$ and $q_2 = -8,mu\text{C}$, are separated by a distance of $10,\text{cm}$ in vacuum. Calculate the magnitude of the electrostatic force between them. (Given: $k = 9 \times 10^9,\text{N m}^2/\text{C}^2$)

Two identical point charges $Q$ are placed at a distance $r$ from each other. A third point charge $q$ is placed on the line joining the first two charges such that all three charges are in equilibrium. What is the magnitude and sign of $q$?

Three charges, $q_1 = +Q$, $q_2 = +Q$, and $q_3 = -Q$, are placed at the vertices of an equilateral triangle of side length $a$. What is the magnitude of the net electrostatic force on charge $q_3$?

Two point charges, $q_1$ and $q_2$, exert a force $F$ on each other when placed in vacuum. If they are now placed in an insulating medium with a dielectric constant $epsilon_r = 4$, at the same distance, what will be the new force between them?

An electron and a proton are separated by a distance $r$. The electrostatic force between them is $F_e$, and the gravitational force between them is $F_g$. Which of the following statements is true?

A charge $Q$ is divided into two parts, $q$ and $(Q-q)$. These two parts are then separated by a certain distance. For the force between them to be maximum, what should be the value of $q$?

Which of the following statements about Coulomb's Law is INCORRECT?