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 $800 kg m ^{-3}$ and dielectric constant $21$ . 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

A charged ball $B$ hangs from a silk thread $S$, which makes an angle $\theta $ with a large charged conducting sheet $P$, as shown in the figure. The surface charge density $\sigma $ of the sheet is proportional to

For given arrangement, where four charge fixed at ends of as quare as given, find value of additional charge $Q$ to be put on one of the vertices so that component of net electric field along the vertical symmetric axis is zero at every point on the vertical

The surface charge density of a thin charged disc of radius $R$ is $\sigma $. The value of the electric field at the centre of the disc is $\frac{\sigma }{{2\,{ \in _0}}}$. With respect to the field at the centre, the electric field along the axis at a distance $R$ from the centre of the disc

Two charges $q$ and $3 q$ are separated by a distance ' $r$ ' in air. At a distance $x$ from charge $q$, the resultant electric field is zero. The value of $x$ is :