$A$ charge $Q$ is placed at the midpoint of the line joining two identical point charges $q$. For what value of $q$ will the system be in equilibrium?

Two small spheres of masses $M_{1}$ and $M_{2}$ are suspended by weightless insulating threads of lengths $L_{1}$ and $L_{2}$. The spheres carry charges $Q_{1}$ and $Q_{2}$ respectively. The spheres are suspended such that they are in level with one another and the threads are inclined to the vertical at angles of $\theta_{1}$ and $\theta_{2}$ as shown. Which one of the following conditions is essential,if $\theta_{1}=\theta_{2}$?

Two point charges $+q_1$ and $+q_2$ repel each other with a force of $100 \ N$. $q_1$ is increased by $10 \%$ and $q_2$ is decreased by $10 \%$. If they are kept at their original positions, the change in the force of repulsion between them is:

Consider the following charged suspended ball system. If $\alpha < \beta$,then out of the following statements,which can be true at equilibrium? :-
$(a) Q_1 > Q_2, m_1 < m_2$
$(b) Q_1 > Q_2, m_1 > m_2$
$(c) Q_1 < Q_2, m_1 = m_2$
$(d) Q_1 < Q_2, m_1 > m_2$

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:

Two identical spheres each of radius $R$ are kept at a center-to-center spacing of $4R$ as shown in the figure. They are charged,and the electrostatic force of interaction between them is first calculated assuming them to be point-like charges at their centers $(F_c)$,and the force is also measured experimentally $(F_m)$. ($F_c$ and $F_m$ denote the magnitude of the force.)