Positive charge $Q$ is distributed uniformly over a circular ring of radius $R$. A point particle having a mass $(m)$ and a negative charge $-q$ is placed on its axis at a distance $x$ from the centre. Assuming $x < R,$ find the time period of oscillation of the particle, if it is released from there [neglect gravity].

As shown in the figure. a configuration of two equal point charges $\left( q _0=+2 \mu C \right)$ is placed on an inclined plane. Mass of each point charge is $20\,g$. Assume that there is no friction between charge and plane. For the system of two point charges to be in equilibrium (at rest) the height $h = x \times 10^{-3}\,m$ The value of $x$ is $..........$.(Take $\left.\frac{1}{4 \pi \varepsilon_0}=9 \times 10^9\,Nm ^2 C ^{-2}, g=10\,ms ^{-1}\right)$

In hydrogen like system the ratio of coulombian force and gravitational force between an electron and a proton is in the order of:

Two identical tennis balls each having mass $m$ and charge $q$ are suspended from a fixed point by threads of length $l$. What is the equilibrium separation when each thread makes a small angle $\theta$ with the vertical?

A particle of mass $1 \,{mg}$ and charge $q$ is lying at the mid-point of two stationary particles kept at a distance $'2 \,{m}^{\prime}$ when each is carrying same charge $'q'.$ If the free charged particle is displaced from its equilibrium position through distance $'x'$ $(x\,< \,1\, {m})$. The particle executes $SHM.$ Its angular frequency of oscillation will be $....\,\times 10^{8}\, {rad} / {s}$ if ${q}^{2}=10\, {C}^{2}$

Two identical conducting spheres, having charges of opposite sign, attract each other with a force of $0.108$ $N$ when separated by $0.5$ $m$. The spheres are connected by a conducting wire, which is then removed, and thereafter, they repel each other with a force of $ 0.036$ $N$. The initial charges on the spheres are