Q.
Two equal negative charges −q are fixed at points (0,a) and (0,−a) on the y -axis. A positive charge Q is released from rest at the point (2a,0) on the x -axis. The charge Q will
By symmetry of problem, the components of force on Q due to charges at A and B along y -axis will cancel each other while along x -axis will add up and will be along CO. Under the action of this force, charge Q will move towards O. If at any time charge Q is at a distance x from O F=24πε01(a2+x2)−qQ×(a2+x2)1/2x
i.e., F=−4πε01⋅(a2+x2)3/22qQx
As the restoring force F is not linear, motion will be oscillatory (with amplitude 2a ) but not simple harmonic.