Two charges are placed as shown in the figure. Where should a third charge be placed so that it remains at rest?

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 $g = 10 \text{ m/s}^2$):

Two equal charges are separated by a distance $d$. $A$ third charge placed on a perpendicular bisector at $x$ distance will experience maximum Coulomb force when

Two charges $+q$ and $-3q$ are placed on the $x$-axis separated by a distance $d$. ($-3q$ is to the right of $q$). Where should a third charge $2q$ be placed such that it will not experience any net force?

$A$ and $B$ are two identical blocks made of a conducting material. These are placed on a horizontal frictionless table and connected by a light conducting spring of force constant $K$. The unstretched length of the spring is $L_0$. $A$ charge $Q/2$ is given to each block. Consequently,the spring stretches to an equilibrium length $L$. The value of $Q$ is

Two point charges $q_1$ and $q_2$ are placed at a distance of $50 \ cm$ from each other in air and interact with a certain force. Now,these charges are placed in an oil with a relative permittivity of $5$. If the force between them remains the same,the distance between them in the oil is ........ $cm$.