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

In the figure,the force on the charge at $A$ in the direction perpendicular to $BC$ is ...... .

Electric charges of $1 \mu C, -1 \mu C$ and $2 \mu C$ are placed in air at the corners $A, B$ and $C$ respectively of an equilateral triangle $ABC$ having a side length of $10 \ cm$. The resultant force on the charge at $C$ is: (in $N$)

Four identical pendulums are made by attaching a small ball of mass $100 \,g$ on a $20 \,cm$ long thread and suspended from the same point. Now,each ball is given charge $Q$,so that balls move away from each other with each thread making an angle of $45^{\circ}$ from the vertical. The value of $Q$ is close to ..............$\mu C$ $\left(\frac{1}{4 \pi \varepsilon_0}=9 \times 10^9\right.$ in $SI$ units $)$

$A$ 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 positively charged spheres of masses $m_1$ and $m_2$ are suspended from a common point at the ceiling by identical insulating massless strings of length $l$. Charges on the two spheres are $q_1$ and $q_2$,respectively. At equilibrium,both strings make the same angle $\theta$ with the vertical. Then