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 remain at rest
C. Move to infinity
D. Execute oscillatory but not simple harmonic motion

Answer

D

Explanation

`F_("net") = 2Fcos theta`
`=2(1)/(4piepsilon_0)(-qQ)/((a^2+x^2))xx(x)/((a^2+x^2)^(1//2))`

`implies F_("net") =-1/(4piepsilon_0) .(2qQx)/((a^2+x^2)^(3//2))`
As `F_("net")` is not linear with x, motion will be oscillating but not SHM.