Three charges are placed as shown in figure. The magnitude of $q_1$ is $2.00\, \mu C$, but its sign and the value of the charge $q_2$ are not known. Charge $q_3$ is $+4.00\, \mu C$, and the net force on $q_3$ is entirely in the negative $x-$ direction. As per the condition given the sign of $q_1$ and $q_2$ will be

A charge $q$ is placed at the centre of the line joining two equal charges $Q$. The system of the three charges will be in equilibrium, if $q$ is equal to

Two small conducting spheres of equal radius have charges $ + 10\,\mu C$ and $ - 20\,\mu C$ respectively and placed at a distance $R$ from each other experience force ${F_1}$. If they are brought in contact and separated to the same distance, they experience force ${F_2}$. The ratio of ${F_1}$ to ${F_2}$ is

When ${10^{14}}$ electrons are removed from a neutral metal sphere, the charge on the sphere becomes......$\mu C$

Two charges $ + 4e$ and $ + e$ are at a distance $x$ apart. At what distance, a charge $q$ must be placed from charge $ + e$ so that it is in equilibrium

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