Question

Two equal negative charges $(-q$ each $)$ are fixed at the points $[0,a]$ 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 $Q$ will

• 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 1

Answer: (D)

$F_{\text{net }}=2F\cos \theta$
$=2\left[\frac{1}{4\pi {\epsilon }_0}\cdot \frac{q\cdot Q}{a^2+x^2}\right]\frac{x}{\sqrt{a^2+x^2}}$
$F_{\text{net }}=\frac{-2Qq\cdot x}{4\pi {\epsilon }_0{\left(a^2+x^2\right)}^{3/2}}$
As $F$ is not proportional to $x$, hence it is not $S.H.M.$ But the force is directed towards the origin always. Hence motion is oscillatory.