Two small spheres each of mass $10 \, mg$ are suspended from a point by threads $0.5 \, m$ long. They are equally charged and repel each other to a distance of $0.20 \, m$. The charge on each of the sphere is $\frac{a}{21} \times 10^{-8} \, C$. The value of $a$ will be ...... . [Given $g = 10 \, ms^{-2}$]

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

If $\varepsilon_0$ and $\varepsilon$ represent the permittivity of free space and absolute permittivity of a medium,then the relative permittivity of the medium is:

Three charges each of magnitude $q$ are placed at the corners of an equilateral triangle. The electrostatic force on the charge $Q$ placed at the center is (each side of the triangle is $L$):

Two charges $Q$ are placed at opposite corners of a square. Two charges $q$ are placed at the other two corners. If the net electric force on $Q$ is zero,then $Q/q$ is equal to:

Two charged spheres are suspended by strings of equal length. 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. The dielectric constant of the liquid is ........ (The density of the material of the sphere is $1.6 \ g/cm^3$.)