Question

A negatively charged particle is placed exactly midway between two fixed particles having equal positive charge. What will happen to the charge
(a) if it is displaced at right angle to the line joining the positive charges?
(b) if it is displaced along the line joining the positive charges?

Answer 1

in both the case if particle is displaced slightly then it will perfom SHM otherwise oscilatory if displaced by large displacement in field...

Answer 2

(a) The negative particle placed at equidistance point of two equal opposite positive charge, the negative charge is in electromagnetic field created by the charge. So, when the positive charge are kept perpendicular to the negative charge, it will start to oscillate between the two perpendicular placed charges as the negative charge is initially at midpoint and will perform simple harmonic motion.      

(b) Secondly, when the positive charge is displaced along the line of two positive charges, the negative charge will either move towards the displacement position accordingly, if they are displaced inwards then the charge will move equidistantly towards each of the positive charge or if they are displaced outwards then too negative will maintain the equi-position or if they are displaced disproportionately then the negative charge will again try to attain equi-focal point of charge.