Three point charges $q,-2 q$ and $2 q$ are placed on $x$-axis at a distance $x=0, x=\frac{3}{4} R$ and $x=R$ respectively from origin as shown. If $q =2 \times 10^{-6}\,C$ and $R =2\,cm$, the magnitude of net force experienced by the charge $-2 q$ is .......... $N$

Two identical charged spheres suspended from a common point by two massless strings of lengths $l,$ are initially at a distance $d\;(d < < l)$ apart because of their mutual repulsion. The charges begin to leak from both the spheres at a constant rate. As a result, the spheres approach each other with a velocity $v.$ Then $v$ varies as a function of the distance $x$ between the spheres, as 

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].

Two particles $X $ and $Y$, of equal mass and with unequal positive charges, are free to move and are initially far away from each other. With $Y$ at rest, $X$ begins to move towards it with initial velocity $u$. After a long time, finally

Suppose the charge of a proton and an electron differ slightly. One of them is $-e,$ the other is $(e + \Delta e).$ If the net of electrostatic force and gravitational force between two hydrogen atoms placed at a distanced (much greater than atomic size) apart is zero, then $\Delta e$ is of the order of $[$ Given: mass of hydrogen $m_h = 1.67 \times 10^{- 27}\,\, kg]$

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....$N$