Two identical charged spheres are suspended by strings of equal lengths. The strings make an angle of $30^{\circ}$ with each other. When suspended in a liquid of density $0.8 \;g\, cm ^{-3}$, the angle remains the same. If density of the material of the sphere is $1.6\; g \,cm ^{-3}$, the dielectric constant of the liquid is
$2$
$1$
$4$
$3$
Four charges are arranged at the corners of a square $ABCD$, as shown in the adjoining figure. The force on the charge kept at the centre $O$ is
A charge $q$ is placed in the middle of a line joining the two equal and like point charge $Q$. This charge $q$ will remain in equilibrium for which value of $q$ is
Two positive ions, each carrying a charge $q,$ are separated by a distance $d.$ If $F$ is the force of repulsion between the ions, the number of electrons missing from each ion will be ($e$ being the charge on an electron)
Two small metal balls of different masses $m_1$ and $m_2$ are connected by strings of equal length to a fixed point. When the balls are given equal charges, the angles that the two strings make with the vertical are $30^{\circ}$ and $60^{\circ}$, respectively. The ratio $m_1 / m_2$ is close to
A point charge $q_1$ exerts force $F$ upon another point charge $q_2$. If a third charge $q_3$ be placed near the charge $q_2$, then the force that charge $q_1$ exerts on the charge $q_2$ will be