Two charges, each equal to $q$, are kept at $x = -a$ and $x = a$ on the $x-$axis. A particle of mass $m$ and charge $q_0=\frac{q}{2}$ is placed at the origin. If charge $q_0$ is given a small displacement $(y < < a)$ along the $y-$axis, the net force acting on the particle is proportional to

A $10\,\mu C$ charge is divided into two parts and placed at $1\,cm$ distance so that the repulsive force between them is maximum. The charges of the two parts are :

Two identical charged spheres are suspended by strings of equal lengths. The strings make an angle of $30^o$ with each other. When suspended in a liquid of density $1\, g\, cm^{-3}$, the angle remains the same. If density of the material of the sphere is $4/3\, g\, cm^{-3}$, the dielectric constant of the liquid is

Consider a system of three charges $\frac{q}{3},\frac{q}{3}$ and $\frac{-2q}{3}$ placed at points $A,B$ and $C$, respectively, as shown in the figure. Take $O$ to be the centre of the circle of radius $R$ and angle $CAB = 60^o$

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

Two particle of equal mass $m$ and charge $q$ are placed at a distance of $16\, cm$. They do not experience any force. The value of $\frac{q}{m}$ is