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

The correct option is D Execute oscillatory periodic motion but not SHM

As per the question,

The net force on the charge Q is given as
$F=\frac{2Qqx}{4\pi {ϵ}_0(a^2+x^2{)}^{\frac{3}{2}}}$ towards origin. But this force is not proportional to x.
[due to a factor $(x^2+a^2{)}^{\frac{3}{2}}$ in the denominator]

Since F is not directly proportional to the x so,
$\therefore$ Motion is oscillatory but not SHM.