Three charges $+3q$,$Q$,and $+q$ are placed in a straight line of length $\ell$ at points at distances $0$,$\frac{\ell}{2}$,and $\ell$ respectively. The value of $Q$ in order to have the net force on $+q$ to be zero is $Q = xq$. The value of $x$ is:

Two identical charged spheres are suspended by strings of equal length. The strings make an angle of $30^{\circ}$ with each other. When they are immersed in a liquid of density $0.8 \, g \cdot cm^{-3}$,the angle remains the same. If the density of the material of the spheres is $1.6 \, g \cdot cm^{-3}$,find the dielectric constant of the liquid.

Two identical non-conducting solid spheres of same mass and charge are suspended in air from a common point by two non-conducting,massless strings of same length. At equilibrium,the angle between the strings is $\alpha$. The spheres are now immersed in a dielectric liquid of density $\rho_l = 800 \ kg \ m^{-3}$ and dielectric constant $K = 21$. If the angle between the strings remains the same after the immersion,then
$(A)$ electric force between the spheres remains unchanged
$(B)$ electric force between the spheres reduces
$(C)$ mass density of the spheres is $840 \ kg \ m^{-3}$
$(D)$ the tension in the strings holding the spheres remains unchanged

Two point charges $+3\,\mu C$ and $+8\,\mu C$ repel each other with a force of $40\,N$. If a charge of $-5\,\mu C$ is added to each of them,then the force between them will become....$N$

Three charges, each of $+1 \mu C$, are placed at the corners of an equilateral triangle. If the repulsive force between any two charges is $F$, then the net force on any one charge will be:

Three charges $q, Q$ and $+4q$ are placed in a straight line of length $d$ at positions $0, d/3$ and $2d/3$ respectively. In order to make the net force on $q$ be zero, the value of $Q$ should be