Question

Two equal positive charges $Q$ are fixed at points $(a, 0)$ and $(-a, 0)$ on the $x$-axis. An opposite charge $-q$ at rest is released from point $(0, a)$ on the $y$-axis. The charge $-q$ will

• A. Move to infinity
• B. Move to origin and rest there
• C. Undergo SHM about the origin
• D. Execute oscillatory periodic motion but not SHM

Answer 1

Answer: (D)

In question
Net force on $q$ is not proportional to $( x )$
as $F \propto(-x)$ [For SHM] but Net force on $q$ is
$F=-\frac{K q \cdot Q x}{\left(x^{2}+a^{2}\right)^{\frac{1}{2}}}$
This is condition for periodic motion