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 $[2 a, 0]$ 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 }}=2 F \cos \theta$
$=2\left[\frac{1}{4 \pi \varepsilon_{0}} \cdot \frac{q \cdot Q}{a^{2}+x^{2}}\right] \frac{x}{\sqrt{a^{2}+x^{2}}}$
$F_{\text {net }}=\frac{-2 Q q \cdot x}{4 \pi \varepsilon_{0}\left(a^{2}+x^{2}\right)^{3 / 2}}$
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.