A body of mass $M$ and charge $q$ is connected to a spring of spring constant $k$. It is oscillating along $x-$ direction about its equilibrium position, taken to be at $x = 0$, with an amplitude $A$. An electric field $E$ is applied along the $x-$ direction. Which of the following statements is correct?

For a uniformly charged ring of radius $R$, the electric field on its axis has the largest magnitude at a distance $h$ from its centre. Then value of $h$ is

Two point charges $Q$ and $-3Q$ are placed at some distance apart. If the electric field at the location of $Q$ is $E$ then at the locality of $ - 3Q$, it is

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 thin disc of radius $b = 2a$  has a concentric hole of radius $'a'$ in it (see figure). It carries uniform surface charge $'\sigma '$ on it. If the electric field on its axis at height $'h'$ $(h << a)$ from its centre is given as $'Ch'$ then value of $'C'$ is

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