Two identical conducing spheres having unequal positive charges $q_1$ and $q_2$ separated by distance $r$. If they are made to touch each other and then separated again to the same distance. The electrostatic force between the spheres in this case will be (neglect induction of charges)

Four charges are placed at the circumference of the dial of a clock as shown in figure. If the clock has only hour hand, then the resultant force on a positive charge $q_0$ placed at the centre, points in the direction which shows the time as 

$ + 2\,C$ and $ + 6\,C$ two charges are repelling each other with a force of $12\,N$. If each charge is given $ – 2\,C$ of charge, then the value of the force will be

Two electrons each are fixed at a distance $'2d'$. A third charge proton placed at the midpoint is displaced slightly by a distance $x ( x << d )$ perpendicular to the line joining the two fixed charges. Proton will execute simple harmonic motion having angular frequency : $( m =$ mass of charged particle)

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].