Two equal negative charges `-q` are fixed at points `(0, -a)` and `(0,a)` on y-axis. A poistive charge Q is released from rest at point `(2a, 0)` on the x-axis. The charge Q will

Options

A. Execute simple harmonic motion about the origin
B. Move to the origin and remains at rest
C. Move to infinity
D. Execute oscillatory but not simple harmonic motion.

Answer

d

Explanation

By symmetry of problem the components of force on `Q` due to charges at `A` and `B` along y-axis will cancel each other 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=2(1)/(4piepsilon_(0))(-qQ)/((a^(2)+x^(2)))xx(x)/((a^(2)+x^(2))^(1//2))`
i.e., `F=1/(4piepsilon_(0))*(2qQx)/((a^(2)+x^(2))^(3//2))`
As the rrestoring force `F` is not linear, motion will be oscillatory (with amplitude `2a`) but not simple harmonic.