Question

Two equal negative charges q are fixed at the point (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 will:

• A. Execute SHM about the origin
• B. Move to the origin and remain at rest
• C. Move to infinity
• D. Execute oscillatory but not SHM

Answer 1

Answer: (D)

Execute oscillatory but not SHM

The net force acting on Q when at a distance $d$ from the origin

$=2\times \frac{1}{4\pi {ϵ}_0}\frac{Qq}{\sqrt{d^2+a^2}}\frac{d}{\sqrt{d^2+a^2}}$

$=\frac{1}{4\pi {ϵ}_0}\frac{2Qqd}{d^2+a^2}$

Since the force acting is not directly proportional to the distance from the equilibrium position($d$), the oscillation is not SHM.